There is as great diversity among authors in the modes which they have adopted of defining logic as in their treatment of the details of it This is what might naturally be expected on any subject on which writers have availed themselves of the same language as a means of delivering different ideas Ethics and jurisprudence are liable to the remark in common with logic Almost every writer having taken a different view of some of the particulars which these branches of knowledge are usually understood to include each has so framed his definition as to indicate beforehand his own peculiar tenets and sometimes to beg the question in their favour This diversity is not so much an evil to be complained of as an inevitable and in some degree a proper result of the imperfect state of those sciences It is not to be expected that there should be agreement about the definition of any thing until there is agreement about the thing itself To define is to select from among all the properties of a thing those which shall be understood to be designated and declared by its name and the properties must be well known to us before we can be competent to determine which of them are fittest to be chosen for this purpose Accordingly in the case of so complex an aggregation of particulars as are comprehended in any thing which can be called a science the definition we set out with is seldom that which a more extensive knowledge of the subject shows to be the most appropriate Until we know the particulars themselves we can not fix upon the most correct and compact mode of circumscribing them by a general description It was not until after an extensive and accurate acquaintance with the details of chemical phenomena that it was found possible to frame a rational definition of chemistry and the definition of the science of life and organization is still a matter of dispute So long as the sciences are imperfect the definitions must partake of their imperfection and if the former are progressive the latter ought to be so too As much therefore as is to be expected from a definition placed at the commencement of a subject is that it should define the scope of our inquiries and the definition which I am about to offer of the science of logic pretends to nothing more than to be a statement of the question which I have put to myself and which this book is an attempt to resolve The reader is at liberty to object to it as a definition of logic but it is at all events a correct definition of the subject of this volume Logic has often been called the Art of Reasoning A writer who has done more than any other person to restore this study to the rank from which it had fallen in the estimation of the cultivated class in our own country has adopted the above definition with an amendment he has defined Logic to be the Science as well as the Art of reasoning meaning by the former term the analysis of the mental process which takes place whenever we reason and by the latter the rules grounded on that analysis for conducting the process correctly There can be no doubt as to the propriety of the emendation A right understanding of the mental process itself of the conditions it depends on and the steps of which it consists is the only basis on which a system of rules fitted for the direction of the process can possibly be founded Art necessarily presupposes knowledge art in any but its infant state presupposes scientific knowledge and if every art does not bear the name of a science it is only because several sciences are often necessary to form the groundwork of a single art So complicated are the conditions which govern our practical agency that to enable one thing to be done it is often requisite to know the nature and properties of many things Logic then comprises the science of reasoning as well as an art founded on that science But the word Reasoning again like most other scientific terms in popular use abounds in ambiguities In one of its acceptations it means syllogizing or the mode of inference which may be called with sufficient accuracy for the present purpose concluding from generals to particulars In another of its senses to reason is simply to infer any assertion from assertions already admitted and in this sense induction is as much entitled to be called reasoning as the demonstrations of geometry Writers on logic have generally preferred the former acceptation of the term the latter and more extensive signification is that in which I mean to use it I do this by virtue of the right I claim for every author to give whatever provisional definition he pleases of his own subject But sufficient reasons will I believe unfold themselves as we advance why this should be not only the provisional but the final definition It involves at all events no arbitrary change in the meaning of the word for with the general usage of the English language the wider signification I believe accords better than the more restricted one But reasoning even in the widest sense of which the word is susceptible does not seem to comprehend all that is included either in the best or even in the most current conception of the scope and province of our science The employment of the word Logic to denote the theory of Argumentation is derived from the Aristotelian or as they are commonly termed the scholastic logicians Yet even with them in their systematic treatises Argumentation was the subject only of the third part the two former treated of Terms and of Propositions under one or other of which heads were also included Definition and Division By some indeed these previous topics were professedly introduced only on account of their connection with reasoning and as a preparation for the doctrine and rules of the syllogism Yet they were treated with greater minuteness and dwelt on at greater length than was required for that purpose alone More recent writers on logic have generally understood the term as it was employed by the able author of the Port Royal Logic viz as equivalent to the Art of Thinking Nor is this acceptation confined to books and scientific inquiries Even in ordinary conversation the ideas connected with the word Logic include at least precision of language and accuracy of classification and we perhaps oftener hear persons speak of a logical arrangement or of expressions logically defined than of conclusions logically deduced from premises Again a man is often called a great logician or a man of powerful logic not for the accuracy of his deductions but for the extent of his command over premises because the general propositions required for explaining a difficulty or refuting a sophism copiously and promptly occur to him because in short his knowledge besides being ample is well under his command for argumentative use Whether therefore we conform to the practice of those who have made the subject their particular study or to that of popular writers and common discourse the province of logic will include several operations of the intellect not usually considered to fall within the meaning of the terms Reasoning and Argumentation These various operations might be brought within the compass of the science and the additional advantage be obtained of a very simple definition if by an extension of the term sanctioned by high authorities we were to define logic as the science which treats of the operations of the human understanding in the pursuit of truth For to this ultimate end naming classification definition and all other operations over which logic has ever claimed jurisdiction are essentially subsidiary They may all be regarded as contrivances for enabling a person to know the truths which are needful to him and to know them at the precise moment at which they are needful Other purposes indeed are also served by these operations for instance that of imparting our knowledge to others But viewed with regard to this purpose they have never been considered as within the province of the logician The sole object of Logic is the guidance of one’s own thoughts the communication of those thoughts to others falls under the consideration of Rhetoric in the large sense in which that art was conceived by the ancients or of the still more extensive art of Education Logic takes cognizance of our intellectual operations only as they conduce to our own knowledge and to our command over that knowledge for our own uses If there were but one rational being in the universe that being might be a perfect logician and the science and art of logic would be the same for that one person as for the whole human race But if the definition which we formerly examined included too little that which is now suggested has the opposite fault of including too much Truths are known to us in two ways some are known directly and of themselves some through the medium of other truths The former are the subject of Intuition or Consciousness the latter of Inference The truths known by intuition are the original premises from which all others are inferred Our assent to the conclusion being grounded on the truth of the premises we never could arrive at any knowledge by reasoning unless something could be known antecedently to all reasoning Examples of truths known to us by immediate consciousness are our own bodily sensations and mental feelings I know directly and of my own knowledge that I was vexed yesterday or that I am hungry today Examples of truths which we know only by way of inference are occurrences which took place while we were absent the events recorded in history or the theorems of mathematics The two former we infer from the testimony adduced or from the traces of those past occurrences which still exist the latter from the premises laid down in books of geometry under the title of definitions and axioms Whatever we are capable of knowing must belong to the one class or to the other must be in the number of the primitive data or of the conclusions which can be drawn from these With the original data or ultimate premises of our knowledge with their number or nature the mode in which they are obtained or the tests by which they may be distinguished logic in a direct way at least has in the sense in which I conceive the science nothing to do These questions are partly not a subject of science at all partly that of a very different science Whatever is known to us by consciousness is known beyond possibility of question What one sees or feels whether bodily or mentally one can not but be sure that one sees or feels No science is required for the purpose of establishing such truths no rules of art can render our knowledge of them more certain than it is in itself There is no logic for this portion of our knowledge But we may fancy that we see or feel what we in reality infer A truth or supposed truth which is really the result of a very rapid inference may seem to be apprehended intuitively It has long been agreed by thinkers of the most opposite schools that this mistake is actually made in so familiar an instance as that of the eyesight There is nothing of which we appear to ourselves to be more directly conscious than the distance of an object from us Yet it has long been ascertained that what is perceived by the eye is at most nothing more than a variously coloured surface that when we fancy we see distance all we really see is certain variations of apparent size and degrees of faintness of colour that our estimate of the object’s distance from us is the result partly of a rapid inference from the muscular sensations accompanying the adjustment of the focal distance of the eye to objects unequally remote from us and partly of a comparison made with so much rapidity that we are unconscious of making it between the size and colour of the object as they appear at the time and the size and colour of the same or of similar objects as they appeared when close at hand or when their degree of remoteness was known by other evidence The perception of distance by the eye which seems so like intuition is thus in reality an inference grounded on experience an inference too which we learn to make and which we make with more and more correctness as our experience increases though in familiar cases it takes place so rapidly as to appear exactly on a par with those perceptions of sight which are really intuitive our perceptions of colour Of the science therefore which expounds the operations of the human understanding in the pursuit of truth one essential part is the inquiry What are the facts which are the objects of intuition or consciousness and what are those which we merely infer But this inquiry has never been considered a portion of logic Its place is in another and a perfectly distinct department of science to which the name metaphysics more particularly belongs that portion of mental philosophy which attempts to determine what part of the furniture of the mind belongs to it originally and what part is constructed out of materials furnished to it from without To this science appertain the great and much debated questions of the existence of matter the existence of spirit and of a distinction between it and matter the reality of time and space as things without the mind and distinguishable from the objects which are said to exist in them For in the present state of the discussion on these topics it is almost universally allowed that the existence of matter or of spirit of space or of time is in its nature unsusceptible of being proved and that if any thing is known of them it must be by immediate intuition To the same science belong the inquiries into the nature of Conception Perception Memory and Belief all of which are operations of the understanding in the pursuit of truth but with which as phenomena of the mind or with the possibility which may or may not exist of analysing any of them into simpler phenomena the logician as such has no concern To this science must also be referred the following and all analogous questions To what extent our intellectual faculties and our emotions are innate to what extent the result of association Whether God and duty are realities the existence of which is manifest to us a priori by the constitution of our rational faculty or whether our ideas of them are acquired notions the origin of which we are able to trace and explain and the reality of the objects themselves a question not of consciousness or intuition but of evidence and reasoning The province of logic must be restricted to that portion of our knowledge which consists of inferences from truths previously known whether those antecedent data be general propositions or particular observations and perceptions Logic is not the science of Belief but the science of Proof or Evidence In so far as belief professes to be founded on proof the office of logic is to supply a test for ascertaining whether or not the belief is well grounded With the claims which any proposition has to belief on the evidence of consciousness that is without evidence in the proper sense of the word logic has nothing to do By far the greatest portion of our knowledge whether of general truths or of particular facts being avowedly matter of inference nearly the whole not only of science but of human conduct is amenable to the authority of logic To draw inferences has been said to be the great business of life Every one has daily hourly and momentary need of ascertaining facts which he has not directly observed not from any general purpose of adding to his stock of knowledge but because the facts themselves are of importance to his interests or to his occupations The business of the magistrate of the military commander of the navigator of the physician of the agriculturist is merely to judge of evidence and to act accordingly They all have to ascertain certain facts in order that they may afterward apply certain rules either devised by themselves or prescribed for their guidance by others and as they do this well or ill so they discharge well or ill the duties of their several callings It is the only occupation in which the mind never ceases to be engaged and is the subject not of logic but of knowledge in general Logic however is not the same thing with knowledge though the field of logic is coextensive with the field of knowledge Logic is the common judge and arbiter of all particular investigations It does not undertake to find evidence but to determine whether it has been found Logic neither observes nor invents nor discovers but judges It is no part of the business of logic to inform the surgeon what appearances are found to accompany a violent death This he must learn from his own experience and observation or from that of others his predecessors in his peculiar pursuit But logic sits in judgment on the sufficiency of that observation and experience to justify his rules and on the sufficiency of his rules to justify his conduct It does not give him proofs but teaches him what makes them proofs and how he is to judge of them It does not teach that any particular fact proves any other but points out to what conditions all facts must conform in order that they may prove other facts To decide whether any given fact fulfils these conditions or whether facts can be found which fulfil them in a given case belongs exclusively to the particular art or science or to our knowledge of the particular subject It is in this sense that logic is what it was so expressively called by the schoolmen and by Bacon ars artium the science of science itself All science consists of data and conclusions from those data of proofs and what they prove now logic points out what relations must subsist between data and whatever can be concluded from them between proof and every thing which it can prove If there be any such indispensable relations and if these can be precisely determined every particular branch of science as well as every individual in the guidance of his conduct is bound to conform to those relations under the penalty of making false inferences of drawing conclusions which are not grounded in the realities of things Whatever has at any time been concluded justly whatever knowledge has been acquired otherwise than by immediate intuition depended on the observance of the laws which it is the province of logic to investigate If the conclusions are just and the knowledge real those laws whether known or not have been observed We need not therefore seek any further for a solution of the question so often agitated respecting the utility of logic If a science of logic exists or is capable of existing it must be useful If there be rules to which every mind consciously or unconsciously conforms in every instance in which it infers rightly there seems little necessity for discussing whether a person is more likely to observe those rules when he knows the rules than when he is unacquainted with them A science may undoubtedly be brought to a certain not inconsiderable stage of advancement without the application of any other logic to it than what all persons who are said to have a sound understanding acquire empirically in the course of their studies Mankind judged of evidence and often correctly before logic was a science or they never could have made it one And they executed great mechanical works before they understood the laws of mechanics But there are limits both to what mechanicians can do without principles of mechanics and to what thinkers can do without principles of logic A few individuals by extraordinary genius or by the accidental acquisition of a good set of intellectual habits may work without principles in the same way or nearly the same way in which they would have worked if they had been in possession of principles But the bulk of mankind require either to understand the theory of what they are doing or to have rules laid down for them by those who have understood the theory In the progress of science from its easiest to its more difficult problems each great step in advance has usually had either as its precursor or as its accompaniment and necessary condition a corresponding improvement in the notions and principles of logic received among the most advanced thinkers And if several of the more difficult sciences are still in so defective a state if not only so little is proved but disputation has not terminated even about the little which seemed to be so the reason perhaps is that men’s logical notions have not yet acquired the degree of extension or of accuracy requisite for the estimation of the evidence proper to those particular departments of knowledge Logic then is the science of the operations of the understanding which are subservient to the estimation of evidence both the process itself of advancing from known truths to unknown and all other intellectual operations in so far as auxiliary to this It includes therefore the operation of Naming for language is an instrument of thought as well as a means of communicating our thoughts It includes also Definition and Classification For the use of these operations putting all other minds than one’s own out of consideration is to serve not only for keeping our evidences and the conclusions from them permanent and readily accessible in the memory but for so marshalling the facts which we may at any time be engaged in investigating as to enable us to perceive more clearly what evidence there is and to judge with fewer chances of error whether it be sufficient These therefore are operations specially instrumental to the estimation of evidence and as such are within the province of Logic There are other more elementary processes concerned in all thinking such as Conception Memory and the like but of these it is not necessary that Logic should take any peculiar cognizance since they have no special connection with the problem of Evidence further than that like all other problems addressed to the understanding it presupposes them Our object then will be to attempt a correct analysis of the intellectual process called Reasoning or Inference and of such other mental operations as are intended to facilitate this as well as on the foundation of this analysis and pari passu with it to bring together or frame a set of rules or canons for testing the sufficiency of any given evidence to prove any given proposition With respect to the first part of this undertaking I do not attempt to decompose the mental operations in question into their ultimate elements It is enough if the analysis as far as it goes is correct and if it goes far enough for the practical purposes of logic considered as an art The separation of a complicated phenomenon into its component parts is not like a connected and interdependent chain of proof If one link of an argument breaks the whole drops to the ground but one step toward an analysis holds good and has an independent value though we should never be able to make a second The results which have been obtained by analytical chemistry are not the less valuable though it should be discovered that all which we now call simple substances are really compounds All other things are at any rate compounded of those elements whether the elements themselves admit of decomposition is an important inquiry but does not affect the certainty of the science up to that point I shall accordingly attempt to analyse the process of inference and the processes subordinate to inference so far only as may be requisite for ascertaining the difference between a correct and an incorrect performance of those processes The reason for thus limiting our design is evident It has been said by objectors to logic that we do not learn to use our muscles by studying their anatomy The fact is not quite fairly stated for if the action of any of our muscles were vitiated by local weakness or other physical defect a knowledge of their anatomy might be very necessary for effecting a cure But we should be justly liable to the criticism involved in this objection were we in a treatise on logic to carry the analysis of the reasoning process beyond the point at which any inaccuracy which may have crept into it must become visible In learning bodily exercises to carry on the same illustration we do and must analyse the bodily motions so far as is necessary for distinguishing those which ought to be performed from those which ought not To a similar extent and no further it is necessary that the logician should analyse the mental processes with which Logic is concerned Logic has no interest in carrying the analysis beyond the point at which it becomes apparent whether the operations have in any individual case been rightly or wrongly performed in the same manner as the science of music teaches us to discriminate between musical notes and to know the combinations of which they are susceptible but not what number of vibrations in a second correspond to each which though useful to be known is useful for totally different purposes The extension of Logic as a Science is determined by its necessities as an Art whatever it does not need for its practical ends it leaves to the larger science which may be said to correspond not to any particular art but to art in general the science which deals with the constitution of the human faculties and to which in the part of our mental nature which concerns Logic as well as in all other parts it belongs to decide what are ultimate facts and what are resolvable into other facts And I believe it will be found that most of the conclusions arrived at in this work have no necessary connection with any particular views respecting the ulterior analysis Logic is common ground on which the partisans of Hartley and of Reid of Locke and of Kant may meet and join hands Particular and detached opinions of all these thinkers will no doubt occasionally be controverted since all of them were logicians as well as metaphysicians but the field on which their principal battles have been fought lies beyond the boundaries of our science It can not indeed be pretended that logical principles can be altogether irrelevant to those more abstruse discussions nor is it possible but that the view we are led to take of the problem which logic proposes must have a tendency favourable to the adoption of some one opinion on these controverted subjects rather than another For metaphysics in endeavouring to solve its own peculiar problem must employ means the validity of which falls under the cognizance of logic It proceeds no doubt as far as possible merely by a closer and more attentive interrogation of our consciousness or more properly speaking of our memory and so far is not amenable to logic But wherever this method is insufficient to attain the end of its inquiries it must proceed like other sciences by means of evidence Now the moment this science begins to draw inferences from evidence logic becomes the sovereign judge whether its inferences are well grounded or what other inferences would be so This however constitutes no nearer or other relation between logic and metaphysics than that which exists between logic and every other science And I can conscientiously affirm that no one proposition laid down in this work has been adopted for the sake of establishing or with any reference to its fitness for being employed in establishing preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided La scolastique qui produisit dans la logique comme dans la morale et dans une partie de la mtaphysique une subtilit une prcision d’ides dont l’habitude inconnue aux anciens a contribu plus qu’on ne croit au progrs de la bonne philosophie CONDORCET Vie de Turgot To the schoolmen the vulgar languages are principally indebted for what precision and analytic subtlety they possess SIR W HAMILTON Discussions in Philosophy It is so much the established practice of writers on logic to commence their treatises by a few general observations in most cases it is true rather meagre on Terms and their varieties that it will perhaps scarcely be required from me in merely following the common usage to be as particular in assigning my reasons as it is usually expected that those should be who deviate from it The practice indeed is recommended by considerations far too obvious to require a formal justification Logic is a portion of the Art of Thinking Language is evidently and by the admission of all philosophers one of the principal instruments or helps of thought and any imperfection in the instrument or in the mode of employing it is confessedly liable still more than in almost any other art to confuse and impede the process and destroy all ground of confidence in the result For a mind not previously versed in the meaning and right use of the various kinds of words to attempt the study of methods of philosophizing would be as if some one should attempt to become an astronomical observer having never learned to adjust the focal distance of his optical instruments so as to see distinctly Since Reasoning or Inference the principal subject of logic is an operation which usually takes place by means of words and in complicated cases can take place in no other way those who have not a thorough insight into the signification and purposes of words will be under chances amounting almost to certainty of reasoning or inferring incorrectly And logicians have generally felt that unless in the very first stage they removed this source of error unless they taught their pupil to put away the glasses which distort the object and to use those which are adapted to his purpose in such a manner as to assist not perplex his vision he would not be in a condition to practice the remaining part of their discipline with any prospect of advantage Therefore it is that an inquiry into language so far as is needful to guard against the errors to which it gives rise has at all times been deemed a necessary preliminary to the study of logic But there is another reason of a still more fundamental nature why the import of words should be the earliest subject of the logician’s consideration because without it he can not examine into the import of Propositions Now this is a subject which stands on the very threshold of the science of logic The object of logic as defined in the Introductory Chapter is to ascertain how we come by that portion of our knowledge much the greatest portion which is not intuitive and by what criterion we can in matters not selfevident distinguish between things proved and things not proved between what is worthy and what is unworthy of belief Of the various questions which present themselves to our inquiring faculties some receive an answer from direct consciousness others if resolved at all can only be resolved by means of evidence Logic is concerned with these last But before inquiring into the mode of resolving questions it is necessary to inquire what are those which offer themselves what questions are conceivable what inquiries are there to which mankind have either obtained or been able to imagine it possible that they should obtain an answer This point is best ascertained by a survey and analysis of Propositions The answer to every question which it is possible to frame must be contained in a Proposition or Assertion Whatever can be an object of belief or even of disbelief must when put into words assume the form of a proposition All truth and all error lie in propositions What by a convenient misapplication of an abstract term we call a Truth means simply a True Proposition and errors are false propositions To know the import of all possible propositions would be to know all questions which can be raised all matters which are susceptible of being either believed or disbelieved How many kinds of inquiries can be propounded how many kinds of judgments can be made and how many kinds of propositions it is possible to frame with a meaning are but different forms of one and the same question Since then the objects of all Belief and of all Inquiry express themselves in propositions a sufficient scrutiny of Propositions and of their varieties will apprise us what questions mankind have actually asked of themselves and what in the nature of answers to those questions they have actually thought they had grounds to believe Now the first glance at a proposition shows that it is formed by putting together two names A proposition according to the common simple definition which is sufficient for our purpose is discourse in which something is affirmed or denied of something Thus in the proposition Gold is yellow the quality yellow is affirmed of the substance gold In the proposition Franklin was not born in England the fact expressed by the words born in England is denied of the man Franklin Every proposition consists of three parts the Subject the Predicate and the Copula The predicate is the name denoting that which is affirmed or denied The subject is the name denoting the person or thing which something is affirmed or denied of The copula is the sign denoting that there is an affirmation or denial and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse Thus in the proposition The earth is round the Predicate is the word round which denotes the quality affirmed or as the phrase is predicated the earth words denoting the object which that quality is affirmed of compose the Subject the word is which serves as the connecting mark between the subject and predicate to show that one of them is affirmed of the other is called the Copula Dismissing for the present the copula of which more will be said hereafter every proposition then consists of at least two names brings together two names in a particular manner This is already a first step toward what we are in quest of It appears from this that for an act of belief one object is not sufficient the simplest act of belief supposes and has something to do with two objects two names to say the least and since the names must be names of something two nameable things A large class of thinkers would cut the matter short by saying two ideas They would say that the subject and predicate are both of them names of ideas the idea of gold for instance and the idea of yellow and that what takes place or part of what takes place in the act of belief consists in bringing as it is often expressed one of these ideas under the other But this we are not yet in a condition to say whether such be the correct mode of describing the phenomenon is an after consideration The result with which for the present we must be contented is that in every act of belief two objects are in some manner taken cognizance of that there can be no belief claimed or question propounded which does not embrace two distinct either material or intellectual subjects of thought each of them capable or not of being conceived by itself but incapable of being believed by itself I may say for instance the sun The word has a meaning and suggests that meaning to the mind of any one who is listening to me But suppose I ask him Whether it is true whether he believes it He can give no answer There is as yet nothing to believe or to disbelieve Now however let me make of all possible assertions respecting the sun the one which involves the least of reference to any object besides itself let me say the sun exists Here at once is something which a person can say he believes But here instead of only one we find two distinct objects of conception the sun is one object existence is another Let it not be said that this second conception existence is involved in the first for the sun may be conceived as no longer existing The sun does not convey all the meaning that is conveyed by the sun exists my father does not include all the meaning of my father exists for he may be dead a round square does not include the meaning of a round square exists for it does not and can not exist When I say the sun my father or a round square I do not call upon the hearer for any belief or disbelief nor can either the one or the other be afforded me but if I say the sun exists my father exists or a round square exists I call for belief and should in the first of the three instances meet with it in the second with belief or disbelief as the case might be in the third with disbelief This first step in the analysis of the object of belief which though so obvious will be found to be not unimportant is the only one which we shall find it practicable to make without a preliminary survey of language If we attempt to proceed further in the same path that is to analyse any further the import of Propositions we find forced upon us as a subject of previous consideration the import of Names For every proposition consists of two names and every proposition affirms or denies one of these names of the other Now what we do what passes in our mind when we affirm or deny two names of one another must depend on what they are names of since it is with reference to that and not to the mere names themselves that we make the affirmation or denial Here therefore we find a new reason why the signification of names and the relation generally between names and the things signified by them must occupy the preliminary stage of the inquiry we are engaged in It may be objected that the meaning of names can guide us at most only to the opinions possibly the foolish and groundless opinions which mankind have formed concerning things and that as the object of philosophy is truth not opinion the philosopher should dismiss words and look into things themselves to ascertain what questions can be asked and answered in regard to them This advice which no one has it in his power to follow is in reality an exhortation to discard the whole fruits of the labours of his predecessors and conduct himself as if he were the first person who had ever turned an inquiring eye upon nature What does any one’s personal knowledge of Things amount to after subtracting all which he has acquired by means of the words of other people Even after he has learned as much as people usually do learn from others will the notions of things contained in his individual mind afford as sufficient a basis for a catalogue raisonn as the notions which are in the minds of all mankind In any enumeration and classification of Things which does not set out from their names no varieties of things will of course be comprehended but those recognized by the particular inquirer and it will still remain to be established by a subsequent examination of names that the enumeration has omitted nothing which ought to have been included But if we begin with names and use them as our clue to the things we bring at once before us all the distinctions which have been recognized not by a single inquirer but by all inquirers taken together It doubtless may and I believe it will be found that mankind have multiplied the varieties unnecessarily and have imagined distinctions among things where there were only distinctions in the manner of naming them But we are not entitled to assume this in the commencement We must begin by recognizing the distinctions made by ordinary language If some of these appear on a close examination not to be fundamental the enumeration of the different kinds of realities may be abridged accordingly But to impose upon the facts in the first instance the yoke of a theory while the grounds of the theory are reserved for discussion in a subsequent stage is not a course which a logician can reasonably adopt A name says Hobbes is a word taken at pleasure to serve for a mark which may raise in our mind a thought like to some thought we had before and which being pronounced to others may be to them a sign of what thought the speaker had before in his mind This simple definition of a name as a word or set of words serving the double purpose of a mark to recall to ourselves the likeness of a former thought and a sign to make it known to others appears unexceptionable Names indeed do much more than this but whatever else they do grows out of and is the result of this as will appear in its proper place Are names more properly said to be the names of things or of our ideas of things The first is the expression in common use the last is that of some metaphysicians who conceived that in adopting it they were introducing a highly important distinction The eminent thinker just quoted seems to countenance the latter opinion But seeing he continues names ordered in speech as is defined are signs of our conceptions it is manifest they are not signs of the things themselves for that the sound of this word stone should be the sign of a stone can not be understood in any sense but this that he that hears it collects that he that pronounces it thinks of a stone If it be merely meant that the conception alone and not the thing itself is recalled by the name or imparted to the hearer this of course can not be denied Nevertheless there seems good reason for adhering to the common usage and calling as indeed Hobbes himself does in other places the word sun the name of the sun and not the name of our idea of the sun For names are not intended only to make the hearer conceive what we conceive but also to inform him what we believe Now when I use a name for the purpose of expressing a belief it is a belief concerning the thing itself not concerning my idea of it When I say the sun is the cause of day I do not mean that my idea of the sun causes or excites in me the idea of day or in other words, that thinking of the sun makes me think of day I mean that a certain physical fact which is called the sun’s presence and which in the ultimate analysis resolves itself into sensations not ideas causes another physical fact which is called day It seems proper to consider a word as the name of that which we intend to be understood by it when we use it of that which any fact that we assert of it is to be understood of that in short concerning which when we employ the word we intend to give information Names therefore shall always be spoken of in this work as the names of things themselves and not merely of our ideas of things But the question now arises of what things and to answer this it is necessary to take into consideration the different kinds of names It is usual before examining the various classes into which names are commonly divided to begin by distinguishing from names of every description those words which are not names but only parts of names Among such are reckoned particles as of to truly often the inflected cases of nouns substantive as me him John’s and even adjectives as large heavy These words do not express things of which any thing can be affirmed or denied We can not say Heavy fell or A heavy fell Truly or A truly was asserted Of or An of was in the room Unless indeed we are speaking of the mere words themselves as when we say Truly is an English word or Heavy is an adjective In that case they are complete names viz names of those particular sounds or of those particular collections of written characters This employment of a word to denote the mere letters and syllables of which it is composed was termed by the schoolmen the suppositio materialis of the word In any other sense we can not introduce one of these words into the subject of a proposition unless in combination with other words as A heavy body fell A truly important fact was asserted A member of parliament was in the room An adjective however is capable of standing by itself as the predicate of a proposition as when we say Snow is white and occasionally even as the subject for we may say White is an agreeable colour The adjective is often said to be so used by a grammatical ellipsis Snow is white instead of Snow is a white object White is an agreeable colour instead of A white colour or The colour white is agreeable The Greeks and Romans were allowed by the rules of their language to employ this ellipsis universally in the subject as well as in the predicate of a proposition In English this can not generally speaking be done We may say The earth is round but we can not say Round is easily moved we must say A round object This distinction however is rather grammatical than logical Since there is no difference of meaning between round and a round object it is only custom which prescribes that on any given occasion one shall be used and not the other We shall therefore without scruple speak of adjectives as names whether in their own right or as representative of the more circuitous forms of expression above exemplified The other classes of subsidiary words have no title whatever to be considered as names An adverb or an accusative case can not under any circumstances except when their mere letters and syllables are spoken of figure as one of the terms of a proposition Words which are not capable of being used as names but only as parts of names were called by some of the schoolmen Syncategorematic terms from with and to predicate because it was only with some other word that they could be predicated A word which could be used either as the subject or predicate of a proposition without being accompanied by any other word was termed by the same authorities a Categorematic term A combination of one or more Categorematic and one or more Syncategorematic words as A heavy body or A court of justice they sometimes called a mixed term but this seems a needless multiplication of technical expressions A mixed term is in the only useful sense of the word Categorematic It belongs to the class of what have been called manyworded names For as one word is frequently not a name but only part of a name so a number of words often compose one single name and no more These words The place which the wisdom or policy of antiquity had destined for the residence of the Abyssinian princes form in the estimation of the logician only one name one Categorematic term A mode of determining whether any set of words makes only one name or more than one is by predicating something of it and observing whether by this predication we make only one assertion or several Thus when we say John Nokes who was the mayor of the town died yesterday by this predication we make but one assertion whence it appears that John Nokes who was the mayor of the town is no more than one name It is true that in this proposition besides the assertion that John Nokes died yesterday there is included another assertion namely that John Nokes was mayor of the town But this last assertion was already made we did not make it by adding the predicate died yesterday Suppose however that the words had been John Nokes and the mayor of the town they would have formed two names instead of one For when we say John Nokes and the mayor of the town died yesterday we make two assertions one that John Nokes died yesterday the other that the mayor of the town died yesterday It being needless to illustrate at any greater length the subject of manyworded names we proceed to the distinctions which have been established among names not according to the words they are composed of but according to their signification All names are names of something real or imaginary but all things have not names appropriated to them individually For some individual objects we require and consequently have separate distinguishing names there is a name for every person and for every remarkable place Other objects of which we have not occasion to speak so frequently we do not designate by a name of their own but when the necessity arises for naming them we do so by putting together several words each of which by itself might be and is used for an indefinite number of other objects as when I say this stone this and stone being each of them names that may be used of many other objects besides the particular one meant though the only object of which they can both be used at the given moment consistently with their signification may be the one of which I wish to speak Were this the sole purpose for which names that are common to more things than one could be employed if they only served by mutually limiting each other to afford a designation for such individual objects as have no names of their own they could only be ranked among contrivances for economizing the use of language But it is evident that this is not their sole function It is by their means that we are enabled to assert general propositions to affirm or deny any predicate of an indefinite number of things at once The distinction therefore between general names and individual or singular names is fundamental and may be considered as the first grand division of names A general name is familiarly defined a name which is capable of being truly affirmed in the same sense of each of an indefinite number of things An individual or singular name is a name which is only capable of being truly affirmed in the same sense of one thing Thus man is capable of being truly affirmed of John George Mary and other persons without assignable limit and it is affirmed of all of them in the same sense for the word man expresses certain qualities and when we predicate it of those persons we assert that they all possess those qualities But John is only capable of being truly affirmed of one single person at least in the same sense For though there are many persons who bear that name it is not conferred upon them to indicate any qualities or any thing which belongs to them in common and can not be said to be affirmed of them in any sense at all consequently not in the same sense The king who succeeded William the Conqueror is also an individual name For that there can not be more than one person of whom it can be truly affirmed is implied in the meaning of the words Even the king when the occasion or the context defines the individual of whom it is to be understood may justly be regarded as an individual name It is not unusual by way of explaining what is meant by a general name to say that it is the name of a class But this though a convenient mode of expression for some purposes is objectionable as a definition since it explains the clearer of two things by the more obscure It would be more logical to reverse the proposition and turn it into a definition of the word class A class is the indefinite multitude of individuals denoted by a general name It is necessary to distinguish general from collective names A general name is one which can be predicated of each individual of a multitude a collective name can not be predicated of each separately but only of all taken together The 76th regiment of foot in the British army which is a collective name is not a general but an individual name for though it can be predicated of a multitude of individual soldiers taken jointly it can not be predicated of them severally We may say Jones is a soldier and Thompson is a soldier and Smith is a soldier but we can not say Jones is the 76th regiment and Thompson is the 76th regiment and Smith is the 76th regiment We can only say Jones and Thompson and Smith and Brown and so forth enumerating all the soldiers are the 76th regiment The 76th regiment is a collective name but not a general one a regiment is both a collective and a general name General with respect to all individual regiments of each of which separately it can be affirmed collective with respect to the individual soldiers of whom any regiment is composed The second general division of names is into concrete and abstract A concrete name is a name which stands for a thing an abstract name is a name which stands for an attribute of a thing Thus John the sea this table are names of things White also is a name of a thing or rather of things Whiteness again is the name of a quality or attribute of those things Man is a name of many things humanity is a name of an attribute of those things Old is a name of things old age is a name of one of their attributes I have used the words concrete and abstract in the sense annexed to them by the schoolmen who notwithstanding the imperfections of their philosophy were unrivaled in the construction of technical language and whose definitions in logic at least though they never went more than a little way into the subject have seldom I think been altered but to be spoiled A practice however has grown up in more modern times which if not introduced by Locke has gained currency chiefly from his example of applying the expression abstract name to all names which are the result of abstraction or generalization and consequently to all general names instead of confining it to the names of attributes The metaphysicians of the Condillac school whose admiration of Locke passing over the profoundest speculations of that truly original genius usually fastens with peculiar eagerness upon his weakest points have gone on imitating him in this abuse of language until there is now some difficulty in restoring the word to its original signification A more wanton alteration in the meaning of a word is rarely to be met with for the expression general name the exact equivalent of which exists in all languages I am acquainted with was already available for the purpose to which abstract has been misappropriated while the misappropriation leaves that important class of words the names of attributes without any compact distinctive appellation The old acceptation however has not gone so completely out of use as to deprive those who still adhere to it of all chance of being understood By abstract then I shall always in Logic proper mean the opposite of concrete by an abstract name the name of an attribute by a concrete name the name of an object Do abstract names belong to the class of general or to that of singular names Some of them are certainly general I mean those which are names not of one single and definite attribute but of a class of attributes Such is the word colour which is a name common to whiteness redness etc Such is even the word whiteness in respect of the different shades of whiteness to which it is applied in common the word magnitude in respect of the various degrees of magnitude and the various dimensions of space the word weight in respect of the various degrees of weight Such also is the word attribute itself the common name of all particular attributes But when only one attribute neither variable in degree nor in kind is designated by the name as visibleness tangibleness equality squareness milkwhiteness then the name can hardly be considered general for though it denotes an attribute of many different objects the attribute itself is always conceived as one not many To avoid needless logomachies the best course would probably be to consider these names as neither general nor individual and to place them in a class apart It may be objected to our definition of an abstract name that not only the names which we have called abstract but adjectives which we have placed in the concrete class are names of attributes that white for example is as much the name of the colour as whiteness is But as before remarked a word ought to be considered as the name of that which we intend to be understood by it when we put it to its principal use that is when we employ it in predication When we say snow is white milk is white linen is white we do not mean it to be understood that snow or linen or milk is a colour We mean that they are things having the colour The reverse is the case with the word whiteness what we affirm to be whiteness is not snow but the colour of snow Whiteness therefore is the name of the colour exclusively white is a name of all things whatever having the colour a name not of the quality whiteness but of every white object It is true this name was given to all those various objects on account of the quality and we may therefore say without impropriety that the quality forms part of its signification but a name can only be said to stand for or to be a name of the things of which it can be predicated We shall presently see that all names which can be said to have any signification all names by applying which to an individual we give any information respecting that individual may be said to imply an attribute of some sort but they are not names of the attribute it has its own proper abstract name This leads to the consideration of a third great division of names into connotative and nonconnotative the latter sometimes but improperly called absolute This is one of the most important distinctions which we shall have occasion to point out and one of those which go deepest into the nature of language A nonconnotative term is one which signifies a subject only or an attribute only A connotative term is one which denotes a subject and implies an attribute By a subject is here meant any thing which possesses attributes Thus John or London or England are names which signify a subject only Whiteness length virtue signify an attribute only None of these names therefore are connotative But white long virtuous are connotative The word white denotes all white things as snow paper the foam of the sea etc and implies or in the language of the schoolmen connotes the attribute whiteness The word white is not predicated of the attribute but of the subjects snow etc but when we predicate it of them we convey the meaning that the attribute whiteness belongs to them The same may be said of the other words above cited Virtuous for example is the name of a class which includes Socrates Howard the Man of Ross and an undefinable number of other individuals past present and to come These individuals collectively and severally can alone be said with propriety to be denoted by the word of them alone can it properly be said to be a name But it is a name applied to all of them in consequence of an attribute which they are supposed to possess in common the attribute which has received the name of virtue It is applied to all beings that are considered to possess this attribute and to none which are not so considered All concrete general names are connotative The word man for example denotes Peter Jane John and an indefinite number of other individuals of whom taken as a class it is the name But it is applied to them because they possess and to signify that they possess certain attributes These seem to be corporeity animal life rationality and a certain external form which for distinction we call the human Every existing thing which possessed all these attributes would be called a man and any thing which possessed none of them or only one or two or even three of them without the fourth would not be so called For example if in the interior of Africa there were to be discovered a race of animals possessing reason equal to that of human beings but with the form of an elephant they would not be called men Swift’s Houyhnhnms would not be so called Or if such newlydiscovered beings possessed the form of man without any vestige of reason it is probable that some other name than that of man would be found for them How it happens that there can be any doubt about the matter will appear hereafter The word man therefore signifies all these attributes and all subjects which possess these attributes But it can be predicated only of the subjects What we call men are the subjects the individual Stiles and Nokes not the qualities by which their humanity is constituted The name therefore is said to signify the subjects directly the attributes indirectly it denotes the subjects and implies or involves or indicates or as we shall say henceforth connotes the attributes It is a connotative name Connotative names have hence been also called denominative because the subject which they denote is denominated by or receives a name from the attribute which they connote Snow and other objects receive the name white because they possess the attribute which is called whiteness Peter James and others receive the name man because they possess the attributes which are considered to constitute humanity The attribute or attributes may therefore be said to denominate those objects or to give them a common name It has been seen that all concrete general names are connotative Even abstract names though the names only of attributes may in some instances be justly considered as connotative for attributes themselves may have attributes ascribed to them and a word which denotes attributes may connote an attribute of those attributes Of this description for example is such a word as fault equivalent to bad or hurtful quality This word is a name common to many attributes and connotes hurtfulness an attribute of those various attributes When for example we say that slowness in a horse is a fault we do not mean that the slow movement the actual change of pace of the slow horse is a bad thing but that the property or peculiarity of the horse from which it derives that name the quality of being a slow mover is an undesirable peculiarity In regard to those concrete names which are not general but individual a distinction must be made Proper names are not connotative they denote the individuals who are called by them but they do not indicate or imply any attributes as belonging to those individuals When we name a child by the name Paul or a dog by the name Caesar these names are simply marks used to enable those individuals to be made subjects of discourse It may be said indeed that we must have had some reason for giving them those names rather than any others and this is true but the name once given is independent of the reason A man may have been named John because that was the name of his father a town may have been named Dartmouth because it is situated at the mouth of the Dart But it is no part of the signification of the word John that the father of the person so called bore the same name nor even of the word Dartmouth to be situated at the mouth of the Dart If sand should choke up the mouth of the river or an earthquake change its course and remove it to a distance from the town the name of the town would not necessarily be changed That fact therefore can form no part of the signification of the word for otherwise when the fact confessedly ceased to be true no one would any longer think of applying the name Proper names are attached to the objects themselves and are not dependent on the continuance of any attribute of the object But there is another kind of names which although they are individual names that is predicable only of one object are really connotative For though we may give to an individual a name utterly unmeaning which we call a proper name a word which answers the purpose of showing what thing it is we are talking about but not of telling any thing about it yet a name peculiar to an individual is not necessarily of this description It may be significant of some attribute or some union of attributes which being possessed by no object but one determines the name exclusively to that individual The sun is a name of this description God when used by a monotheist is another These however are scarcely examples of what we are now attempting to illustrate being in strictness of language general not individual names for however they may be in fact predicable only of one object there is nothing in the meaning of the words themselves which implies this and accordingly when we are imagining and not affirming we may speak of many suns and the majority of mankind have believed and still believe that there are many gods But it is easy to produce words which are real instances of connotative individual names It may be part of the meaning of the connotative name itself that there can exist but one individual possessing the attribute which it connotes as for instance the only son of John Stiles the first emperor of Rome Or the attribute connoted may be a connection with some determinate event and the connection may be of such a kind as only one individual could have or may at least be such as only one individual actually had and this may be implied in the form of the expression The father of Socrates is an example of the one kind since Socrates could not have had two fathers the author of the Iliad the murderer of Henri Quatre of the second For though it is conceivable that more persons than one might have participated in the authorship of the Iliad or in the murder of Henri Quatre the employment of the article the implies that in fact this was not the case What is here done by the word the is done in other cases by the context thus Caesar’s army is an individual name if it appears from the context that the army meant is that which Caesar commanded in a particular battle The still more general expressions the Roman army or the Christian army may be individualized in a similar manner Another case of frequent occurrence has already been noticed it is the following The name being a manyworded one may consist in the first place of a general name capable therefore in itself of being affirmed of more things than one but which is in the second place so limited by other words joined with it that the entire expression can only be predicated of one object consistently with the meaning of the general term This is exemplified in such an instance as the following the present prime minister of England Prime Minister of England is a general name the attributes which it connotes may be possessed by an indefinite number of persons in succession however not simultaneously since the meaning of the name itself imports among other things that there can be only one such person at a time This being the case and the application of the name being afterward limited by the article and the word present to such individuals as possess the attributes at one indivisible point of time it becomes applicable only to one individual And as this appears from the meaning of the name without any extrinsic proof it is strictly an individual name From the preceding observations it will easily be collected that whenever the names given to objects convey any information that is whenever they have properly any meaning the meaning resides not in what they denote but in what they connote The only names of objects which connote nothing are proper names and these have strictly speaking no signification If like the robber in the Arabian Nights we make a mark with chalk on a house to enable us to know it again the mark has a purpose but it has not properly any meaning The chalk does not declare any thing about the house it does not mean This is such a person’s house or This is a house which contains booty The object of making the mark is merely distinction I say to myself All these houses are so nearly alike that if I lose sight of them I shall not again be able to distinguish that which I am now looking at from any of the others I must therefore contrive to make the appearance of this one house unlike that of the others that I may hereafter know when I see the mark not indeed any attribute of the house but simply that it is the same house which I am now looking at Morgiana chalked all the other houses in a similar manner and defeated the scheme how simply by obliterating the difference of appearance between that house and the others The chalk was still there but it no longer served the purpose of a distinctive mark When we impose a proper name we perform an operation in some degree analogous to what the robber intended in chalking the house We put a mark not indeed upon the object itself but so to speak upon the idea of the object A proper name is but an unmeaning mark which we connect in our minds with the idea of the object in order that whenever the mark meets our eyes or occurs to our thoughts we may think of that individual object Not being attached to the thing itself it does not like the chalk enable us to distinguish the object when we see it but it enables us to distinguish it when it is spoken of either in the records of our own experience or in the discourse of others to know that what we find asserted in any proposition of which it is the subject is asserted of the individual thing with which we were previously acquainted When we predicate of any thing its proper name when we say pointing to a man this is Brown or Smith or pointing to a city that it is York we do not merely by so doing convey to the reader any information about them except that those are their names By enabling him to identify the individuals we may connect them with information previously possessed by him by saying This is York we may tell him that it contains the Minster But this is in virtue of what he has previously heard concerning York not by any thing implied in the name It is otherwise when objects are spoken of by connotative names When we say The town is built of marble we give the hearer what may be entirely new information and this merely by the signification of the manyworded connotative name built of marble Such names are not signs of the mere objects invented because we have occasion to think and speak of those objects individually but signs which accompany an attribute a kind of livery in which the attribute clothes all objects which are recognized as possessing it They are not mere marks but more that is to say significant marks and the connotation is what constitutes their significance As a proper name is said to be the name of the one individual which it is predicated of so as well from the importance of adhering to analogy as for the other reasons formerly assigned a connotative name ought to be considered a name of all the various individuals which it is predicable of or in other words denotes and not of what it connotes But by learning what things it is a name of we do not learn the meaning of the name for to the same thing we may with equal propriety apply many names not equivalent in meaning Thus I call a certain man by the name Sophroniscus I call him by another name The father of Socrates Both these are names of the same individual but their meaning is altogether different they are applied to that individual for two different purposes the one merely to distinguish him from other persons who are spoken of the other to indicate a fact relating to him the fact that Socrates was his son I further apply to him these other expressions a man a Greek an Athenian a sculptor an old man an honest man a brave man All these are or may be names of Sophroniscus not indeed of him alone but of him and each of an indefinite number of other human beings Each of these names is applied to Sophroniscus for a different reason and by each whoever understands its meaning is apprised of a distinct fact or number of facts concerning him but those who knew nothing about the names except that they were applicable to Sophroniscus would be altogether ignorant of their meaning It is even possible that I might know every single individual of whom a given name could be with truth affirmed and yet could not be said to know the meaning of the name A child knows who are its brothers and sisters long before it has any definite conception of the nature of the facts which are involved in the signification of those words In some cases it is not easy to decide precisely how much a particular word does or does not connote that is we do not exactly know the case not having arisen what degree of difference in the object would occasion a difference in the name Thus it is clear that the word man besides animal life and rationality connotes also a certain external form but it would be impossible to say precisely what form that is to decide how great a deviation from the form ordinarily found in the beings whom we are accustomed to call men would suffice in a newlydiscovered race to make us refuse them the name of man Rationality also being a quality which admits of degrees it has never been settled what is the lowest degree of that quality which would entitle any creature to be considered a human being In all such cases the meaning of the general name is so far unsettled and vague mankind have not come to any positive agreement about the matter When we come to treat of Classification we shall have occasion to show under what conditions this vagueness may exist without practical inconvenience and cases will appear in which the ends of language are better promoted by it than by complete precision in order that in natural history for instance individuals or species of no very marked character may be ranged with those more strongly characterized individuals or species to which in all their properties taken together they bear the nearest resemblance But this partial uncertainty in the connotation of names can only be free from mischief when guarded by strict precautions One of the chief sources indeed of lax habits of thought is the custom of using connotative terms without a distinctly ascertained connotation and with no more precise notion of their meaning than can be loosely collected from observing what objects they are used to denote It is in this manner that we all acquire and inevitably so our first knowledge of our vernacular language A child learns the meaning of the words man or white by hearing them applied to a variety of individual objects and finding out by a process of generalization and analysis which he could not himself describe what those different objects have in common In the case of these two words the process is so easy as to require no assistance from culture the objects called human beings and the objects called white differing from all others by qualities of a peculiarly definite and obvious character But in many other cases objects bear a general resemblance to one another which leads to their being familiarly classed together under a common name while without more analytic habits than the generality of mankind possess it is not immediately apparent what are the particular attributes upon the possession of which in common by them all their general resemblance depends When this is the case people use the name without any recognized connotation that is without any precise meaning they talk and consequently think vaguely and remain contented to attach only the same degree of significance to their own words which a child three years old attaches to the words brother and sister The child at least is seldom puzzled by the starting up of new individuals on whom he is ignorant whether or not to confer the title because there is usually an authority close at hand competent to solve all doubts But a similar resource does not exist in the generality of cases and new objects are continually presenting themselves to men women and children which they are called upon to class proprio motu They accordingly do this on no other principle than that of superficial similarity giving to each new object the name of that familiar object the idea of which it most readily recalls or which on a cursory inspection it seems to them most to resemble as an unknown substance found in the ground will be called according to its texture earth sand or a stone In this manner names creep on from subject to subject until all traces of a common meaning sometimes disappear and the word comes to denote a number of things not only independently of any common attribute but which have actually no attribute in common or none but what is shared by other things to which the name is capriciously refused Even scientific writers have aided in this perversion of general language from its purpose sometimes because like the vulgar they knew no better and sometimes in deference to that aversion to admit new words which induces mankind on all subjects not considered technical to attempt to make the original stock of names serve with but little augmentation to express a constantly increasing number of objects and distinctions and consequently to express them in a manner progressively more and more imperfect To what a degree this loose mode of classing and denominating objects has rendered the vocabulary of mental and moral philosophy unfit for the purposes of accurate thinking is best known to whoever has most meditated on the present condition of those branches of knowledge Since however the introduction of a new technical language as the vehicle of speculations on subjects belonging to the domain of daily discussion is extremely difficult to effect and would not be free from inconvenience even if effected the problem for the philosopher and one of the most difficult which he has to resolve is in retaining the existing phraseology how best to alleviate its imperfections This can only be accomplished by giving to every general concrete name which there is frequent occasion to predicate a definite and fixed connotation in order that it may be known what attributes when we call an object by that name we really mean to predicate of the object And the question of most nicety is how to give this fixed connotation to a name with the least possible change in the objects which the name is habitually employed to denote with the least possible disarrangement either by adding or subtraction of the group of objects which in however imperfect a manner it serves to circumscribe and hold together and with the least vitiation of the truth of any propositions which are commonly received as true This desirable purpose of giving a fixed connotation where it is wanting is the end aimed at whenever any one attempts to give a definition of a general name already in use every definition of a connotative name being an attempt either merely to declare or to declare and analyse the connotation of the name And the fact that no questions which have arisen in the moral sciences have been subjects of keener controversy than the definitions of almost all the leading expressions is a proof how great an extent the evil to which we have adverted has attained Names with indeterminate connotation are not to be confounded with names which have more than one connotation that is to say ambiguous words A word may have several meanings but all of them fixed and recognized ones as the word post for example or the word box the various senses of which it would be endless to enumerate And the paucity of existing names in comparison with the demand for them may often render it advisable and even necessary to retain a name in this multiplicity of acceptations distinguishing these so clearly as to prevent their being confounded with one another Such a word may be considered as two or more names accidentally written and spoken alike The fourth principal division of names is into positive and negative Positive as man tree good negative as notman nottree notgood To every positive concrete name a corresponding negative one might be framed After giving a name to any one thing or to any plurality of things we might create a second name which should be a name of all things whatever except that particular thing or things These negative names are employed whenever we have occasion to speak collectively of all things other than some thing or class of things When the positive name is connotative the corresponding negative name is connotative likewise but in a peculiar way connoting not the presence but the absence of an attribute Thus notwhite denotes all things whatever except white things and connotes the attribute of not possessing whiteness For the nonpossession of any given attribute is also an attribute and may receive a name as such and thus negative concrete names may obtain negative abstract names to correspond to them Names which are positive in form are often negative in reality and others are really positive though their form is negative The word inconvenient for example does not express the mere absence of convenience it expresses a positive attribute that of being the cause of discomfort or annoyance So the word unpleasant notwithstanding its negative form does not connote the mere absence of pleasantness but a less degree of what is signified by the word painful which it is hardly necessary to say is positive Idle on the other hand is a word which though positive in form expresses nothing but what would be signified either by the phrase not working or by the phrase not disposed to work and sober either by not drunk or by not drunken There is a class of names called privative A privative name is equivalent in its signification to a positive and a negative name taken together being the name of something which has once had a particular attribute or for some other reason might have been expected to have it but which has it not Such is the word blind which is not equivalent to not seeing or to not capable of seeing for it would not except by a poetical or rhetorical figure be applied to stocks and stones A thing is not usually said to be blind unless the class to which it is most familiarly referred or to which it is referred on the particular occasion be chiefly composed of things which can see as in the case of a blind man or a blind horse or unless it is supposed for any reason that it ought to see as in saying of a man that he rushed blindly into an abyss or of philosophers or the clergy that the greater part of them are blind guides The names called privative therefore connote two things the absence of certain attributes and the presence of others from which the presence also of the former might naturally have been expected The fifth leading division of names is into relative and absolute or let us rather say relative and nonrelative for the word absolute is put upon much too hard duty in metaphysics not to be willingly spared when its services can be dispensed with It resembles the word civil in the language of jurisprudence which stands for the opposite of criminal the opposite of ecclesiastical the opposite of military the opposite of political in short the opposite of any positive word which wants a negative Relative names are such as father son ruler subject like equal unlike unequal longer shorter cause effect Their characteristic property is that they are always given in pairs Every relative name which is predicated of an object supposes another object or objects of which we may predicate either that same name or another relative name which is said to be the correlative of the former Thus when we call any person a son we suppose other persons who must be called parents When we call any event a cause we suppose another event which is an effect When we say of any distance that it is longer we suppose another distance which is shorter When we say of any object that it is like we mean that it is like some other object which is also said to be like the first In this last case both objects receive the same name the relative term is its own correlative It is evident that these words when concrete are like other concrete general names connotative they denote a subject and connote an attribute and each of them has or might have a corresponding abstract name to denote the attribute connoted by the concrete Thus the concrete like has its abstract likeness the concretes father and son have or might have the abstracts paternity and filiety or sonship The concrete name connotes an attribute and the abstract name which answers to it denotes that attribute But of what nature is the attribute Wherein consists the peculiarity in the connotation of a relative name The attribute signified by a relative name say some is a relation and this they give if not as a sufficient explanation at least as the only one attainable If they are asked What then is a relation they do not profess to be able to tell It is generally regarded as something peculiarly recondite and mysterious I can not however perceive in what respect it is more so than any other attribute indeed it appears to me to be so in a somewhat less degree I conceive rather that it is by examining into the signification of relative names or, in other words, into the nature of the attribute which they connote that a clear insight may best be obtained into the nature of all attributes of all that is meant by an attribute It is obvious in fact that if we take any two correlative names father and son for instance though the objects denoted by the names are different they both in a certain sense connote the same thing They can not indeed be said to connote the same attribute to be a father is not the same thing as to be a son But when we call one man a father another a son what we mean to affirm is a set of facts which are exactly the same in both cases To predicate of A that he is the father of B and of B that he is the son of A is to assert one and the same fact in different words The two propositions are exactly equivalent neither of them asserts more or asserts less than the other The paternity of A and the filiety of B are not two facts but two modes of expressing the same fact That fact when analysed consists of a series of physical events or phenomena in which both A and B are parties concerned and from which they both derive names What those names really connote is this series of events that is the meaning and the whole meaning which either of them is intended to convey The series of events may be said to constitute the relation the schoolmen called it the foundation of the relation fundamentum relationis In this manner any fact or series of facts in which two different objects are implicated and which is therefore predicable of both of them may be either considered as constituting an attribute of the one or an attribute of the other According as we consider it in the former or in the latter aspect it is connoted by the one or the other of the two correlative names Father connotes the fact regarded as constituting an attribute of A son connotes the same fact as constituting an attribute of B It may evidently be regarded with equal propriety in either light And all that appears necessary to account for the existence of relative names is that whenever there is a fact in which two individuals are concerned an attribute grounded on that fact may be ascribed to either of these individuals A name therefore is said to be relative when over and above the object which it denotes it implies in its signification the existence of another object also deriving a denomination from the same fact which is the ground of the first name Or to express the same meaning in other words a name is relative when being the name of one thing its signification can not be explained but by mentioning another Or we may state it thus when the name can not be employed in discourse so as to have a meaning unless the name of some other thing than what it is itself the name of be either expressed or understood These definitions are all at bottom equivalent being modes of variously expressing this one distinctive circumstance that every other attribute of an object might without any contradiction be conceived still to exist if no object besides that one had ever existed but those of its attributes which are expressed by relative names would on that supposition be swept away Names have been further distinguished into univocal and aequivocal these however are not two kinds of names but two different modes of employing names A name is univocal or applied univocally with respect to all things of which it can be predicated in the same sense it is aequivocal or applied aequivocally as respects those things of which it is predicated in different senses It is scarcely necessary to give instances of a fact so familiar as the double meaning of a word In reality as has been already observed an aequivocal or ambiguous word is not one name but two names accidentally coinciding in sound File meaning a steel instrument and file meaning a line of soldiers have no more title to be considered one word because written alike than grease and Greece have because they are pronounced alike They are one sound appropriated to form two different words An intermediate case is that of a name used analogically or metaphorically that is a name which is predicated of two things not univocally or exactly in the same signification but in significations somewhat similar and which being derived one from the other one of them may be considered the primary and the other a secondary signification As when we speak of a brilliant light and a brilliant achievement The word is not applied in the same sense to the light and to the achievement but having been applied to the light in its original sense that of brightness to the eye it is transferred to the achievement in a derivative signification supposed to be somewhat like the primitive one The word however is just as properly two names instead of one in this case as in that of the most perfect ambiguity And one of the commonest forms of fallacious reasoning arising from ambiguity is that of arguing from a metaphorical expression as if it were literal that is as if a word when applied metaphorically were the same name as when taken in its original sense which will be seen more particularly in its place Looking back now to the commencement of our inquiry let us attempt to measure how far it has advanced Logic we found is the Theory of Proof But proof supposes something provable which must be a Proposition or Assertion since nothing but a Proposition can be an object of belief or therefore of proof A Proposition is discourse which affirms or denies something of some other thing This is one step there must it seems be two things concerned in every act of belief But what are these Things They can be no other than those signified by the two names which being joined together by a copula constitute the Proposition If therefore we knew what all names signify we should know every thing which in the existing state of human knowledge is capable either of being made a subject of affirmation or denial or of being itself affirmed or denied of a subject We have accordingly in the preceding chapter reviewed the various kinds of Names in order to ascertain what is signified by each of them And we have now carried this survey far enough to be able to take an account of its results and to exhibit an enumeration of all kinds of Things which are capable of being made predicates or of having any thing predicated of them after which to determine the import of Predication that is of Propositions can be no arduous task The necessity of an enumeration of Existences as the basis of Logic did not escape the attention of the schoolmen and of their master Aristotle the most comprehensive if not also the most sagacious of the ancient philosophers The Categories or Predicaments the former a Greek word the latter its literal translation in the Latin language were believed to be an enumeration of all things capable of being named an enumeration by the summa genera ie the most extensive classes into which things could be distributed which therefore were so many highest Predicates one or other of which was supposed capable of being affirmed with truth of every nameable thing whatsoever The following are the classes into which according to this school of philosophy Things in general might be reduced Substantia Quantitas Qualitas Relatio Actio Passio Ubi Quando Situs Habitus The imperfections of this classification are too obvious to require and its merits are not sufficient to reward a minute examination It is a mere catalogue of the distinctions rudely marked out by the language of familiar life with little or no attempt to penetrate by philosophic analysis to the rationale even of those common distinctions Such an analysis however superficially conducted would have shown the enumeration to be both redundant and defective Some objects are omitted and others repeated several times under different heads It is like a division of animals into men quadrupeds horses asses and ponies That for instance could not be a very comprehensive view of the nature of Relation which could exclude action passivity and local situation from that category The same observation applies to the categories Quando or position in time and Ubi or position in space while the distinction between the latter and Situs is merely verbal The incongruity of erecting into a summum genus the class which forms the tenth category is manifest On the other hand the enumeration takes no notice of any thing besides substances and attributes In what category are we to place sensations or any other feelings and states of mind as hope joy fear sound smell taste pain pleasure thought judgment conception and the like Probably all these would have been placed by the Aristotelian school in the categories of actio and passio and the relation of such of them as are active to their objects and of such of them as are passive to their causes would rightly be so placed but the things themselves the feelings or states of mind wrongly Feelings or states of consciousness are assuredly to be accounted among realities but they can not be reckoned either among substances or attributes Before recommencing under better auspices the attempt made with such imperfect success by the early logicians we must take notice of an unfortunate ambiguity in all the concrete names which correspond to the most general of all abstract terms the word Existence When we have occasion for a name which shall be capable of denoting whatever exists as contradistinguished from nonentity or Nothing there is hardly a word applicable to the purpose which is not also and even more familiarly taken in a sense in which it denotes only substances But substances are not all that exists attributes if such things are to be spoken of must be said to exist feelings certainly exist Yet when we speak of an object or of a thing we are almost always supposed to mean a substance There seems a kind of contradiction in using such an expression as that one thing is merely an attribute of another thing And the announcement of a Classification of Things would I believe prepare most readers for an enumeration like those in natural history beginning with the great divisions of animal vegetable and mineral and subdividing them into classes and orders If rejecting the word Thing we endeavour to find another of a more general import or at least more exclusively confined to that general import a word denoting all that exists and connoting only simple existence no word might be presumed fitter for such a purpose than being originally the present participle of a verb which in one of its meanings is exactly equivalent to the verb exists and therefore suitable even by its grammatical formation to be the concrete of the abstract existence But this word strange as the fact may appear is still more completely spoiled for the purpose which it seemed expressly made for than the word Thing Being is by custom exactly synonymous with substance except that it is free from a slight taint of a second ambiguity being implied impartially to matter and to mind while substance though originally and in strictness applicable to both is apt to suggest in preference the idea of matter Attributes are never called Beings nor are feelings A Being is that which excites feelings and which possesses attributes The soul is called a Being God and angels are called Beings but if we were to say extension colour wisdom virtue are beings we should perhaps be suspected of thinking with some of the ancients that the cardinal virtues are animals or at the least of holding with the Platonic school the doctrine of selfexistent Ideas or with the followers of Epicurus that of Sensible Forms which detach themselves in every direction from bodies and by coming in contact with our organs cause our perceptions We should be supposed in short to believe that Attributes are Substances In consequence of this perversion of the word Being philosophers looking about for something to supply its place laid their hands upon the word Entity a piece of barbarous Latin invented by the schoolmen to be used as an abstract name in which class its grammatical form would seem to place it but being seized by logicians in distress to stop a leak in their terminology it has ever since been used as a concrete name The kindred word essence born at the same time and of the same parents scarcely underwent a more complete transformation when from being the abstract of the verb to be it came to denote something sufficiently concrete to be enclosed in a glass bottle The word Entity since it settled down into a concrete name has retained its universality of signification somewhat less impaired than any of the names before mentioned Yet the same gradual decay to which after a certain age all the language of psychology seems liable has been at work even here If you call virtue an entity you are indeed somewhat less strongly suspected of believing it to be a substance than if you called it a being but you are by no means free from the suspicion Every word which was originally intended to connote mere existence seems after a time to enlarge its connotation to separate existence or existence freed from the condition of belonging to a substance which condition being precisely what constitutes an attribute attributes are gradually shut out and along with them feelings which in ninetynine cases out of a hundred have no other name than that of the attribute which is grounded on them Strange that when the greatest embarrassment felt by all who have any considerable number of thoughts to express is to find a sufficient variety of precise words fitted to express them there should be no practice to which even scientific thinkers are more addicted than that of taking valuable words to express ideas which are sufficiently expressed by other words already appropriated to them When it is impossible to obtain good tools the next best thing is to understand thoroughly the defects of those we have I have therefore warned the reader of the ambiguity of the names which for want of better I am necessitated to employ It must now be the writer’s endeavour so to employ them as in no case to leave the meaning doubtful or obscure No one of the above terms being altogether unambiguous I shall not confine myself to any one but shall employ on each occasion the word which seems least likely in the particular case to lead to misunderstanding nor do I pretend to use either these or any other words with a rigorous adherence to one single sense To do so would often leave us without a word to express what is signified by a known word in some one or other of its senses unless authors had an unlimited license to coin new words together with what it would be more difficult to assume unlimited power of making readers understand them Nor would it be wise in a writer on a subject involving so much of abstraction to deny himself the advantage derived from even an improper use of a term when by means of it some familiar association is called up which brings the meaning home to the mind as it were by a flash The difficulty both to the writer and reader of the attempt which must be made to use vague words so as to convey a precise meaning is not wholly a matter of regret It is not unfitting that logical treatises should afford an example of that to facilitate which is among the most important uses of logic Philosophical language will for a long time and popular language still longer retain so much of vagueness and ambiguity that logic would be of little value if it did not among its other advantages exercise the understanding in doing its work neatly and correctly with these imperfect tools After this preamble it is time to proceed to our enumeration We shall commence with Feelings the simplest class of nameable things the term Feeling being of course understood in its most enlarged sense
A Feeling and a State of consciousness are in the language of philosophy equivalent expressions every thing is a feeling of which the mind is conscious every thing which it feels or, in other words, which forms a part of its own sentient existence In popular language Feeling is not always synonymous with State of Consciousness being often taken more peculiarly for those states which are conceived as belonging to the sensitive or to the emotional phasis of our nature and sometimes with a still narrower restriction to the emotional alone as distinguished from what are conceived as belonging to the percipient or to the intellectual phasis But this is an admitted departure from correctness of language just as by a popular perversion the exact converse of this the word Mind is withdrawn from its rightful generality of signification and restricted to the intellect The still greater perversion by which Feeling is sometimes confined not only to bodily sensations but to the sensations of a single sense that of touch needs not be more particularly adverted to Feeling in the proper sense of the term is a genus of which Sensation Emotion and Thought are subordinate species Under the word Thought is here to be included whatever we are internally conscious of when we are said to think from the consciousness we have when we think of a red colour without having it before our eyes to the most recondite thoughts of a philosopher or poet Be it remembered however that by a thought is to be understood what passes in the mind itself and not any object external to the mind which the person is commonly said to be thinking of He may be thinking of the sun or of God but the sun and God are not thoughts his mental image however of the sun and his idea of God are thoughts states of his mind not of the objects themselves and so also is his belief of the existence of the sun or of God or his disbelief if the case be so Even imaginary objects which are said to exist only in our ideas are to be distinguished from our ideas of them I may think of a hobgoblin as I may think of the loaf which was eaten yesterday or of the flower which will bloom tomorrow But the hobgoblin which never existed is not the same thing with my idea of a hobgoblin any more than the loaf which once existed is the same thing with my idea of a loaf or the flower which does not yet exist but which will exist is the same with my idea of a flower They are all not thoughts but objects of thought though at the present time all the objects are alike nonexistent In like manner a Sensation is to be carefully distinguished from the object which causes the sensation our sensation of white from a white object nor is it less to be distinguished from the attribute whiteness which we ascribe to the object in consequence of its exciting the sensation Unfortunately for clearness and due discrimination in considering these subjects our sensations seldom receive separate names We have a name for the objects which produce in us a certain sensation the word white We have a name for the quality in those objects to which we ascribe the sensation the name whiteness But when we speak of the sensation itself as we have not occasion to do this often except in our scientific speculations language which adapts itself for the most part only to the common uses of life has provided us with no singleworded or immediate designation we must employ a circumlocution and say The sensation of white or The sensation of whiteness we must denominate the sensation either from the object or from the attribute by which it is excited Yet the sensation though it never does might very well be conceived to exist without any thing whatever to excite it We can conceive it as arising spontaneously in the mind But if it so arose we should have no name to denote it which would not be a misnomer In the case of our sensations of hearing we are better provided we have the word Sound and a whole vocabulary of words to denote the various kinds of sounds For as we are often conscious of these sensations in the absence of any perceptible object we can more easily conceive having them in the absence of any object whatever We need only shut our eyes and listen to music to have a conception of a universe with nothing in it except sounds and ourselves hearing them and what is easily conceived separately easily obtains a separate name But in general our names of sensations denote indiscriminately the sensation and the attribute Thus colour stands for the sensations of white red etc but also for the quality in the coloured object We talk of the colours of things as among their properties In the case of sensations another distinction has also to be kept in view which is often confounded and never without mischievous consequences This is the distinction between the sensation itself and the state of the bodily organs which precedes the sensation and which constitutes the physical agency by which it is produced One of the sources of confusion on this subject is the division commonly made of feelings into Bodily and Mental Philosophically speaking there is no foundation at all for this distinction even sensations are states of the sentient mind not states of the body as distinguished from it What I am conscious of when I see the colour blue is a feeling of blue colour which is one thing the picture on my retina or the phenomenon of hitherto mysterious nature which takes place in my optic nerve or in my brain is another thing of which I am not at all conscious and which scientific investigation alone could have apprised me of These are states of my body but the sensation of blue which is the consequence of these states of body is not a state of body that which perceives and is conscious is called Mind When sensations are called bodily feelings it is only as being the class of feelings which are immediately occasioned by bodily states whereas the other kinds of feelings thoughts for instance or emotions are immediately excited not by any thing acting upon the bodily organs but by sensations or by previous thoughts This however is a distinction not in our feelings but in the agency which produces our feelings all of them when actually produced are states of mind Besides the affection of our bodily organs from without and the sensation thereby produced in our minds many writers admit a third link in the chain of phenomena which they call a Perception and which consists in the recognition of an external object as the exciting cause of the sensation This perception they say is an act of the mind proceeding from its own spontaneous activity while in a sensation the mind is passive being merely acted upon by the outward object And according to some metaphysicians it is by an act of the mind similar to perception except in not being preceded by any sensation that the existence of God the soul and other hyperphysical objects is recognized These acts of what is termed perception whatever be the conclusion ultimately come to respecting their nature must I conceive take their place among the varieties of feelings or states of mind In so classing them I have not the smallest intention of declaring or insinuating any theory as to the law of mind in which these mental processes may be supposed to originate or the conditions under which they may be legitimate or the reverse Far less do I mean as Dr Whewell seems to suppose must be meant in an analogous case to indicate that as they are merely states of mind it is superfluous to inquire into their distinguishing peculiarities I abstain from the inquiry as irrelevant to the science of logic In these socalled perceptions or direct recognitions by the mind of objects whether physical or spiritual which are external to itself I can see only cases of belief but of belief which claims to be intuitive or independent of external evidence When a stone lies before me I am conscious of certain sensations which I receive from it but if I say that these sensations come to me from an external object which I perceive the meaning of these words is that receiving the sensations I intuitively believe that an external cause of those sensations exists The laws of intuitive belief and the conditions under which it is legitimate are a subject which as we have already so often remarked belongs not to logic but to the science of the ultimate laws of the human mind To the same region of speculation belongs all that can be said respecting the distinction which the German metaphysicians and their French and English followers so elaborately draw between the acts of the mind and its merely passive states between what it receives from and what it gives to the crude materials of its experience I am aware that with reference to the view which those writers take of the primary elements of thought and knowledge this distinction is fundamental But for the present purpose which is to examine not the original groundwork of our knowledge but how we come by that portion of it which is not original the difference between active and passive states of mind is of secondary importance For us they all are states of mind they all are feelings by which let it be said once more I mean to imply nothing of passivity but simply that they are psychological facts facts which take place in the mind and are to be carefully distinguished from the external or physical facts with which they may be connected either as effects or as causes Among active states of mind there is however one species which merits particular attention because it forms a principal part of the connotation of some important classes of names I mean volitions or acts of the will When we speak of sentient beings by relative names a large portion of the connotation of the name usually consists of the actions of those beings actions past present and possible or probable future Take for instance the words Sovereign and Subject What meaning do these words convey but that of innumerable actions done or to be done by the sovereign and the subjects to or in regard to one another reciprocally So with the words physician and patient leader and follower tutor and pupil In many cases the words also connote actions which would be done under certain contingencies by persons other than those denoted as the words mortgagor and mortgagee obligor and obligee and many other words expressive of legal relation which connote what a court of justice would do to enforce the legal obligation if not fulfilled There are also words which connote actions previously done by persons other than those denoted either by the name itself or by its correlative as the word brother From these instances it may be seen how large a portion of the connotation of names consists of actions Now what is an action Not one thing but a series of two things the state of mind called a volition followed by an effect The volition or intention to produce the effect is one thing the effect produced in consequence of the intention is another thing the two together constitute the action I form the purpose of instantly moving my arm that is a state of my mind my arm not being tied or paralytic moves in obedience to my purpose that is a physical fact consequent on a state of mind The intention followed by the fact or if we prefer the expression the fact when preceded and caused by the intention is called the action of moving my arm Of the first leading division of nameable things viz Feelings or States of Consciousness we began by recognizing three subdivisions Sensations Thoughts and Emotions The first two of these we have illustrated at considerable length the third Emotions not being perplexed by similar ambiguities does not require similar exemplification And finally we have found it necessary to add to these three a fourth species commonly known by the name Volitions We shall now proceed to the two remaining classes of nameable things all things which are regarded as external to the mind being considered as belonging either to the class of Substances or to that of Attributes Logicians have endeavoured to define Substance and Attribute but their definitions are not so much attempts to draw a distinction between the things themselves as instructions what difference it is customary to make in the grammatical structure of the sentence according as we are speaking of substances or of attributes Such definitions are rather lessons of English or of Greek Latin or German than of mental philosophy An attribute say the school logicians must be the attribute of something colour for example must be the colour of something goodness must be the goodness of something and if this something should cease to exist or should cease to be connected with the attribute the existence of the attribute would be at an end A substance on the contrary is selfexistent in speaking about it we need not put of after its name A stone is not the stone of any thing the moon is not the moon of any thing but simply the moon Unless indeed the name which we choose to give to the substance be a relative name if so it must be followed either by of or by some other particle implying as that preposition does a reference to something else but then the other characteristic peculiarity of an attribute would fail the something might be destroyed and the substance might still subsist Thus a father must be the father of something and so far resembles an attribute in being referred to something besides himself if there were no child there would be no father but this when we look into the matter only means that we should not call him father The man called father might still exist though there were no child as he existed before there was a child and there would be no contradiction in supposing him to exist though the whole universe except himself were destroyed But destroy all white substances and where would be the attribute whiteness Whiteness without any white thing is a contradiction in terms This is the nearest approach to a solution of the difficulty that will be found in the common treatises on logic It will scarcely be thought to be a satisfactory one If an attribute is distinguished from a substance by being the attribute of something it seems highly necessary to understand what is meant by of a particle which needs explanation too much itself to be placed in front of the explanation of any thing else And as for the selfexistence of substance it is very true that a substance may be conceived to exist without any other substance but so also may an attribute without any other attribute and we can no more imagine a substance without attributes than we can imagine attributes without a substance Metaphysicians however have probed the question deeper and given an account of Substance considerably more satisfactory than this Substances are usually distinguished as Bodies or Minds Of each of these philosophers have at length provided us with a definition which seems unexceptionable A body according to the received doctrine of modern metaphysicians may be defined the external cause to which we ascribe our sensations When I see and touch a piece of gold I am conscious of a sensation of yellow colour and sensations of hardness and weight and by varying the mode of handling I may add to these sensations many others completely distinct from them The sensations are all of which I am directly conscious but I consider them as produced by something not only existing independently of my will but external to my bodily organs and to my mind This external something I call a body It may be asked how come we to ascribe our sensations to any external cause And is there sufficient ground for so ascribing them It is known that there are metaphysicians who have raised a controversy on the point maintaining that we are not warranted in referring our sensations to a cause such as we understand by the word Body or to any external cause whatever Though we have no concern here with this controversy nor with the metaphysical niceties on which it turns one of the best ways of showing what is meant by Substance is to consider what position it is necessary to take up in order to maintain its existence against opponents It is certain then that a part of our notion of a body consists of the notion of a number of sensations of our own or of other sentient beings habitually occurring simultaneously My conception of the table at which I am writing is compounded of its visible form and size which are complex sensations of sight its tangible form and size which are complex sensations of our organs of touch and of our muscles its weight which is also a sensation of touch and of the muscles its colour which is a sensation of sight its hardness which is a sensation of the muscles its composition which is another word for all the varieties of sensation which we receive under various circumstances from the wood of which it is made and so forth All or most of these various sensations frequently are and as we learn by experience always might be experienced simultaneously or in many different orders of succession at our own choice and hence the thought of any one of them makes us think of the others and the whole becomes mentally amalgamated into one mixed state of consciousness which in the language of the school of Locke and Hartley is termed a Complex Idea Now there are philosophers who have argued as follows If we conceive an orange to be divested of its natural colour without acquiring any new one to lose its softness without becoming hard its roundness without becoming square or pentagonal or of any other regular or irregular figure whatever to be deprived of size of weight of taste of smell to lose all its mechanical and all its chemical properties and acquire no new ones to become in short invisible intangible imperceptible not only by all our senses but by the senses of all other sentient beings real or possible nothing say these thinkers would remain For of what nature they ask could be the residuum and by what token could it manifest its presence To the unreflecting its existence seems to rest on the evidence of the senses But to the senses nothing is apparent except the sensations We know indeed that these sensations are bound together by some law they do not come together at random but according to a systematic order which is part of the order established in the universe When we experience one of these sensations we usually experience the others also or know that we have it in our power to experience them But a fixed law of connection making the sensations occur together does not say these philosophers necessarily require what is called a substratum to support them The conception of a substratum is but one of many possible forms in which that connection presents itself to our imagination a mode of as it were realizing the idea If there be such a substratum suppose it at this instant miraculously annihilated and let the sensations continue to occur in the same order and how would the substratum be missed By what signs should we be able to discover that its existence had terminated Should we not have as much reason to believe that it still existed as we now have And if we should not then be warranted in believing it how can we be so now A body therefore according to these metaphysicians is not any thing intrinsically different from the sensations which the body is said to produce in us it is in short a set of sensations or rather of possibilities of sensation joined together according to a fixed law The controversies to which these speculations have given rise and the doctrines which have been developed in the attempt to find a conclusive answer to them have been fruitful of important consequences to the Science of Mind The sensations it was answered which we are conscious of and which we receive not at random but joined together in a certain uniform manner imply not only a law or laws of connection but a cause external to our mind which cause by its own laws determines the laws according to which the sensations are connected and experienced The schoolmen used to call this external cause by the name we have already employed a substratum and its attributes as they expressed themselves inhered literally stuck in it To this substratum the name Matter is usually given in philosophical discussions It was soon however acknowledged by all who reflected on the subject that the existence of matter can not be proved by extrinsic evidence The answer therefore now usually made to Berkeley and his followers is that the belief is intuitive that mankind in all ages have felt themselves compelled by a necessity of their nature to refer their sensations to an external cause that even those who deny it in theory yield to the necessity in practice and both in speech thought and feeling do equally with the vulgar acknowledge their sensations to be the effects of something external to them this knowledge therefore it is affirmed is as evidently intuitive as our knowledge of our sensations themselves is intuitive And here the question merges in the fundamental problem of metaphysics properly so called to which science we leave it But although the extreme doctrine of the Idealist metaphysicians that objects are nothing but our sensations and the laws which connect them has not been generally adopted by subsequent thinkers the point of most real importance is one on which those metaphysicians are now very generally considered to have made out their case viz that all we know of objects is the sensations which they give us and the order of the occurrence of those sensations Kant himself on this point is as explicit as Berkeley or Locke However firmly convinced that there exists a universe of Things in themselves totally distinct from the universe of phenomena or of things as they appear to our senses and even when bringing into use a technical expression Noumenon to denote what the thing is in itself as contrasted with the representation of it in our minds he allows that this representation the matter of which he says consists of our sensations though the form is given by the laws of the mind itself is all we know of the object and that the real nature of the Thing is and by the constitution of our faculties ever must remain at least in the present state of existence an impenetrable mystery to us Of things absolutely or in themselves says Sir William Hamilton be they external be they internal we know nothing or know them only as incognizable and become aware of their incomprehensible existence only as this is indirectly and accidentally revealed to us through certain qualities related to our faculties of knowledge and which qualities again we can not think as unconditional irrelative existent in and of ourselves All that we know is therefore phenomenal phenomenal of the unknown The same doctrine is laid down in the clearest and strongest terms by M Cousin whose observations on the subject are the more worthy of attention as in consequence of the ultraGerman and ontological character of his philosophy in other respects they may be regarded as the admissions of an opponent There is not the slightest reason for believing that what we call the sensible qualities of the object are a type of any thing inherent in itself or bear any affinity to its own nature A cause does not as such resemble its effects an east wind is not like the feeling of cold nor heat like the steam of boiling water Why then should matter resemble our sensations Why should the inmost nature of fire or water resemble the impressions made by those objects upon our senses Or on what principle are we authorized to deduce from the effects any thing concerning the cause except that it is a cause adequate to produce those effects It may therefore safely be laid down as a truth both obvious in itself and admitted by all whom it is at present necessary to take into consideration that of the outward world we know and can know absolutely nothing except the sensations which we experience from it Body having now been defined the external cause and according to the more reasonable opinion the unknown external cause to which we refer our sensations it remains to frame a definition of Mind Nor after the preceding observations will this be difficult For as our conception of a body is that of an unknown exciting cause of sensations so our conception of a mind is that of an unknown recipient or percipient of them and not of them alone but of all our other feelings As body is understood to be the mysterious something which excites the mind to feel so mind is the mysterious something which feels and thinks It is unnecessary to give in the case of mind as we gave in the case of matter a particular statement of the sceptical system by which its existence as a Thing in itself, distinct from the series of what are denominated its states is called in question But it is necessary to remark that on the inmost nature whatever be meant by inmost nature of the thinking principle as well as on the inmost nature of matter we are and with our faculties must always remain entirely in the dark All which we are aware of even in our own minds is in the words of James Mill a certain thread of consciousness a series of feelings that is of sensations thoughts emotions and volitions more or less numerous and complicated There is a something I call Myself or by another form of expression my mind which I consider as distinct from these sensations thoughts etc a something which I conceive to be not the thoughts but the being that has the thoughts and which I can conceive as existing forever in a state of quiescence without any thoughts at all But what this being is though it is myself I have no knowledge other than the series of its states of consciousness As bodies manifest themselves to me only through the sensations of which I regard them as the causes so the thinking principle or mind in my own nature makes itself known to me only by the feelings of which it is conscious I know nothing about myself save my capacities of feeling or being conscious including of course thinking and willing and were I to learn any thing new concerning my own nature I can not with my present faculties conceive this new information to be any thing else than that I have some additional capacities as yet unknown to me of feeling thinking or willing Thus then as body is the insentient cause to which we are naturally prompted to refer a certain portion of our feelings so mind may be described as the sentient subject in the scholastic sense of the term of all feelings that which has or feels them But of the nature of either body or mind further than the feelings which the former excites and which the latter experiences we do not according to the best existing doctrine know any thing and if any thing logic has nothing to do with it or with the manner in which the knowledge is acquired With this result we may conclude this portion of our subject and pass to the third and only remaining class or division of Nameable Things From what has already been said of Substance what is to be said of Attribute is easily deducible For if we know not and can not know any thing of bodies but the sensations which they excite in us or in others those sensations must be all that we can at bottom mean by their attributes and the distinction which we verbally make between the properties of things and the sensations we receive from them must originate in the convenience of discourse rather than in the nature of what is signified by the terms Attributes are usually distributed under the three heads of Quality Quantity and Relation We shall come to the two latter presently in the first place we shall confine ourselves to the former Let us take then as our example one of what are termed the sensible qualities of objects and let that example be whiteness When we ascribe whiteness to any substance as for instance snow when we say that snow has the quality whiteness what do we really assert Simply that when snow is present to our organs we have a particular sensation which we are accustomed to call the sensation of white But how do I know that snow is present Obviously by the sensations which I derive from it and not otherwise I infer that the object is present because it gives me a certain assemblage or series of sensations And when I ascribe to it the attribute whiteness my meaning is only that of the sensations composing this group or series that which I call the sensation of white colour is one This is one view which may be taken of the subject But there is also another and a different view It may be said that it is true we know nothing of sensible objects except the sensations they excite in us that the fact of our receiving from snow the particular sensation which is called a sensation of white is the ground on which we ascribe to that substance the quality whiteness the sole proof of its possessing that quality But because one thing may be the sole evidence of the existence of another thing it does not follow that the two are one and the same. The attribute whiteness it may be said is not the fact of receiving the sensation but something in the object itself a power inherent in it something in virtue of which the object produces the sensation And when we affirm that snow possesses the attribute whiteness we do not merely assert that the presence of snow produces in us that sensation but that it does so through and by reason of that power or quality For the purposes of logic it is not of material importance which of these opinions we adopt The full discussion of the subject belongs to the other department of scientific inquiry so often alluded to under the name of metaphysics but it may be said here that for the doctrine of the existence of a peculiar species of entities called qualities I can see no foundation except in a tendency of the human mind which is the cause of many delusions I mean the disposition wherever we meet with two names which are not precisely synonymous to suppose that they must be the names of two different things whereas in reality they may be names of the same thing viewed in two different lights or under different suppositions as to surrounding circumstances Because quality and sensation can not be put indiscriminately one for the other it is supposed that they can not both signify the same thing namely the impression or feeling with which we are affected through our senses by the presence of an object though there is at least no absurdity in supposing that this identical impression or feeling may be called a sensation when considered merely in itself and a quality when looked at in relation to any one of the numerous objects the presence of which to our organs excites in our minds that among various other sensations or feelings And if this be admissible as a supposition it rests with those who contend for an entity per se called a quality to show that their opinion is preferable or is any thing in fact but a lingering remnant of the old doctrine of occult causes the very absurdity which Molière so happily ridiculed when he made one of his pedantic physicians account for the fact that opium produces sleep by the maxim Because it has a soporific virtue It is evident that when the physician stated that opium has a soporific virtue he did not account for but merely asserted over again the fact that it produces sleep In like manner when we say that snow is white because it has the quality of whiteness we are only reasserting in more technical language the fact that it excites in us the sensation of white If it be said that the sensation must have some cause I answer its cause is the presence of the assemblage of phenomena which is termed the object When we have asserted that as often as the object is present and our organs in their normal state the sensation takes place we have stated all that we know about the matter There is no need after assigning a certain and intelligible cause to suppose an occult cause besides for the purpose of enabling the real cause to produce its effect If I am asked why does the presence of the object cause this sensation in me I can not tell I can only say that such is my nature and the nature of the object that the fact forms a part of the constitution of things And to this we must at last come even after interpolating the imaginary entity Whatever number of links the chain of causes and effects may consist of how any one link produces the one which is next to it remains equally inexplicable to us It is as easy to comprehend that the object should produce the sensation directly and at once as that it should produce the same sensation by the aid of something else called the power of producing it But as the difficulties which may be felt in adopting this view of the subject can not be removed without discussions transcending the bounds of our science I content myself with a passing indication and shall for the purposes of logic adopt a language compatible with either view of the nature of qualities I shall say what at least admits of no dispute that the quality of whiteness ascribed to the object snow is grounded on its exciting in us the sensation of white and adopting the language already used by the school logicians in the case of the kind of attributes called Relations I shall term the sensation of white the foundation of the quality whiteness For logical purposes the sensation is the only essential part of what is meant by the word the only part which we ever can be concerned in proving When that is proved the quality is proved if an object excites a sensation it has of course the power of exciting it IV Relations The qualities of a body we have said are the attributes grounded on the sensations which the presence of that particular body to our organs excites in our minds But when we ascribe to any object the kind of attribute called a Relation the foundation of the attribute must be something in which other objects are concerned besides itself and the percipient As there may with propriety be said to be a relation between any two things to which two correlative names are or may be given we may expect to discover what constitutes a relation in general if we enumerate the principal cases in which mankind have imposed correlative names and observe what these cases have in common What then is the character which is possessed in common by states of circumstances so heterogeneous and discordant as these one thing like another one thing unlike another one thing near another one thing far from another one thing before after along with another one thing greater equal less than another one thing the cause of another the effect of another one person the master servant child parent debtor creditor sovereign subject attorney client of another and so on Omitting for the present the case of Resemblance a relation which requires to be considered separately there seems to be one thing common to all these cases and only one that in each of them there exists or occurs or has existed or occurred or may be expected to exist or occur some fact or phenomenon into which the two things which are said to be related to each other both enter as parties concerned This fact or phenomenon is what the Aristotelian logicians called the fundamentum relationis Thus in the relation of greater and less between two magnitudes the fundamentum relationis is the fact that one of the two magnitudes could under certain conditions be included in without entirely filling the space occupied by the other magnitude In the relation of master and servant the fundamentum relationis is the fact that the one has undertaken or is compelled to perform certain services for the benefit and at the bidding of the other Examples might be indefinitely multiplied but it is already obvious that whenever two things are said to be related there is some fact or series of facts into which they both enter and that whenever any two things are involved in some one fact or series of facts we may ascribe to those two things a mutual relation grounded on the fact Even if they have nothing in common but what is common to all things that they are members of the universe we call that a relation and denominate them fellowcreatures fellowbeings or fellowdenizens of the universe But in proportion as the fact into which the two objects enter as parts is of a more special and peculiar or of a more complicated nature so also is the relation grounded upon it And there are as many conceivable relations as there are conceivable kinds of fact in which two things can be jointly concerned In the same manner therefore as a quality is an attribute grounded on the fact that a certain sensation or sensations are produced in us by the object so an attribute grounded on some fact into which the object enters jointly with another object is a relation between it and that other object But the fact in the latter case consists of the very same kind of elements as the fact in the former namely states of consciousness In the case for example of any legal relation as debtor and creditor principal and agent guardian and ward the fundamentum relationis consists entirely of thoughts feelings and volitions actual or contingent either of the persons themselves or of other persons concerned in the same series of transactions as for instance the intentions which would be formed by a judge in case a complaint were made to his tribunal of the infringement of any of the legal obligations imposed by the relation and the acts which the judge would perform in consequence acts being as we have already seen another word for intentions followed by an effect and that effect being but another word for sensations or some other feelings occasioned either to the agent himself or to somebody else There is no part of what the names expressive of the relation imply that is not resolvable into states of consciousness outward objects being no doubt supposed throughout as the causes by which some of those states of consciousness are excited and minds as the subjects by which all of them are experienced but neither the external objects nor the minds making their existence known otherwise than by the states of consciousness Cases of relation are not always so complicated as those to which we last alluded The simplest of all cases of relation are those expressed by the words antecedent and consequent and by the word simultaneous If we say for instance that dawn preceded sunrise the fact in which the two things dawn and sunrise were jointly concerned consisted only of the two things themselves no third thing entered into the fact or phenomenon at all Unless indeed we choose to call the succession of the two objects a third thing but their succession is not something added to the things themselves it is something involved in them Dawn and sunrise announce themselves to our consciousness by two successive sensations Our consciousness of the succession of these sensations is not a third sensation or feeling added to them we have not first the two feelings and then a feeling of their succession To have two feelings at all implies having them either successively or else simultaneously Sensations or other feelings being given succession and simultaneousness are the two conditions to the alternative of which they are subjected by the nature of our faculties and no one has been able or needs expect to analyse the matter any further In a somewhat similar position are two other sorts of relations Likeness and Unlikeness I have two sensations we will suppose them to be simple ones two sensations of white or one sensation of white and another of black I call the first two sensations like the last two unlike What is the fact or phenomenon constituting the fundamentum of this relation The two sensations first and then what we call a feeling of resemblance or of want of resemblance Let us confine ourselves to the former case Resemblance is evidently a feeling a state of the consciousness of the observer Whether the feeling of the resemblance of the two colours be a third state of consciousness which I have after having the two sensations of colour or whether like the feeling of their succession it is involved in the sensations themselves may be a matter of discussion But in either case these feelings of resemblance and of its opposite dissimilarity are parts of our nature and parts so far from being capable of analysis that they are presupposed in every attempt to analyse any of our other feelings Likeness and unlikeness therefore as well as antecedence sequence and simultaneousness must stand apart among relations as things sui generis They are attributes grounded on facts that is on states of consciousness but on states which are peculiar unresolvable and inexplicable But though likeness or unlikeness can not be resolved into any thing else complex cases of likeness or unlikeness can be resolved into simpler ones When we say of two things which consist of parts that they are like one another the likeness of the wholes does admit of analysis it is compounded of likenesses between the various parts respectively and of likeness in their arrangement Of how vast a variety of resemblances of parts must that resemblance be composed which induces us to say that a portrait or a landscape is like its original If one person mimics another with any success of how many simple likenesses must the general or complex likeness be compounded likeness in a succession of bodily postures likeness in voice or in the accents and intonations of the voice likeness in the choice of words and in the thoughts or sentiments expressed whether by word countenance or gesture All likeness and unlikeness of which we have any cognizance resolve themselves into likeness and unlikeness between states of our own or some other mind When we say that one body is like another since we know nothing of bodies but the sensations which they excite we mean really that there is a resemblance between the sensations excited by the two bodies or between some portions at least of those sensations If we say that two attributes are like one another since we know nothing of attributes except the sensations or states of feeling on which they are grounded we mean really that those sensations or states of feeling resemble each other We may also say that two relations are alike The fact of resemblance between relations is sometimes called analogy forming one of the numerous meanings of that word The relation in which Priam stood to Hector namely that of father and son resembles the relation in which Philip stood to Alexander resembles it so closely that they are called the same relation The relation in which Cromwell stood to England resembles the relation in which Napoleon stood to France though not so closely as to be called the same relation The meaning in both these instances must be that a resemblance existed between the facts which constituted the fundamentum relationis This resemblance may exist in all conceivable gradations from perfect indistinguishableness to something extremely slight When we say that a thought suggested to the mind of a person of genius is like a seed cast into the ground because the former produces a multitude of other thoughts and the latter a multitude of other seeds this is saying that between the relation of an inventive mind to a thought contained in it and the relation of a fertile soil to a seed contained in it there exists a resemblance the real resemblance being in the two fundamental relationis in each of which there occurs a germ producing by its development a multitude of other things similar to itself And as whenever two objects are jointly concerned in a phenomenon this constitutes a relation between those objects so if we suppose a second pair of objects concerned in a second phenomenon the slightest resemblance between the two phenomena is sufficient to admit of its being said that the two relations resemble provided of course the points of resemblance are found in those portions of the two phenomena respectively which are connoted by the relative names While speaking of resemblance it is necessary to take notice of an ambiguity of language against which scarcely any one is sufficiently on his guard Resemblance when it exists in the highest degree of all amounting to indistinguishableness is often called identity and the two similar things are said to be the same I say often not always for we do not say that two visible objects two persons for instance are the same because they are so much alike that one might be mistaken for the other but we constantly use this mode of expression when speaking of feelings as when I say that the sight of any object gives me the same sensation or emotion today that it did yesterday or the same which it gives to some other person This is evidently an incorrect application of the word same for the feeling which I had yesterday is gone never to return what I have today is another feeling exactly like the former perhaps but distinct from it and it is evident that two different persons can not be experiencing the same feeling in the sense in which we say that they are both sitting at the same table By a similar ambiguity we say that two persons are ill of the same disease that two persons hold the same office not in the sense in which we say that they are engaged in the same adventure or sailing in the same ship but in the sense that they fill offices exactly similar though perhaps in distant places Great confusion of ideas is often produced and many fallacies engendered in otherwise enlightened understandings by not being sufficiently alive to the fact in itself not always to be avoided that they use the same name to express ideas so different as those of identity and undistinguishable resemblance Among modern writers Archbishop Whately stands almost alone in having drawn attention to this distinction and to the ambiguity connected with it Several relations generally called by other names are really cases of resemblance As for example equality which is but another word for the exact resemblance commonly called identity considered as subsisting between things in respect of their quantity And this example forms a suitable transition to the third and last of the three heads under which as already remarked Attributes are commonly arranged V Quantity Let us imagine two things between which there is no difference that is no dissimilarity except in quantity alone for instance a gallon of water and more than a gallon of water A gallon of water like any other external object makes its presence known to us by a set of sensations which it excites Ten gallons of water are also an external object making its presence known to us in a similar manner and as we do not mistake ten gallons of water for a gallon of water it is plain that the set of sensations is more or less different in the two cases In like manner a gallon of water and a gallon of wine are two external objects making their presence known by two sets of sensations which sensations are different from each other In the first case however we say that the difference is in quantity in the last there is a difference in quality while the quantity of the water and of the wine is the same What is the real distinction between the two cases It is not within the province of Logic to analyse it nor to decide whether it is susceptible of analysis or not For us the following considerations are sufficient It is evident that the sensations I receive from the gallon of water and those I receive from the gallon of wine are not the same that is not precisely alike neither are they altogether unlike they are partly similar partly dissimilar and that in which they resemble is precisely that in which alone the gallon of water and the ten gallons do not resemble That in which the gallon of water and the gallon of wine are like each other and in which the gallon and the ten gallons of water are unlike each other is called their quantity This likeness and unlikeness I do not pretend to explain no more than any other kind of likeness or unlikeness But my object is to show that when we say of two things that they differ in quantity just as when we say that they differ in quality the assertion is always grounded on a difference in the sensations which they excite Nobody I presume will say that to see or to lift or to drink ten gallons of water does not include in itself a different set of sensations from those of seeing lifting or drinking one gallon or that to see or handle a footrule and to see or handle a yardmeasure made exactly like it are the same sensations I do not undertake to say what the difference in the sensations is Every body knows and nobody can tell no more than any one could tell what white is to a person who had never had the sensation But the difference so far as cognizable by our faculties lies in the sensations Whatever difference we say there is in the things themselves is in this as in all other cases grounded and grounded exclusively on a difference in the sensations excited by them Thus then all the attributes of bodies which are classed under Quality or Quantity are grounded on the sensations which we receive from those bodies and may be defined the powers which the bodies have of exciting those sensations And the same general explanation has been found to apply to most of the attributes usually classed under the head of Relation They too are grounded on some fact or phenomenon into which the related objects enter as parts that fact or phenomenon having no meaning and no existence to us except the series of sensations or other states of consciousness by which it makes itself known and the relation being simply the power or capacity which the object possesses of taking part along with the correlated object in the production of that series of sensations or states of consciousness We have been obliged indeed to recognize a somewhat different character in certain peculiar relations those of succession and simultaneity of likeness and unlikeness These not being grounded on any fact or phenomenon distinct from the related objects themselves do not admit of the same kind of analysis But these relations though not like other relations grounded on states of consciousness are themselves states of consciousness resemblance is nothing but our feeling of resemblance succession is nothing but our feeling of succession Or if this be disputed and we can not without transgressing the bounds of our science discuss it here at least our knowledge of these relations and even our possibility of knowledge is confined to those which subsist between sensations or other states of consciousness for though we ascribe resemblance or succession or simultaneity to objects and to attributes it is always in virtue of resemblance or succession or simultaneity in the sensations or states of consciousness which those objects excite and on which those attributes are grounded In the preceding investigation we have for the sake of simplicity considered bodies only and omitted minds But what we have said is applicable mutatis mutandis to the latter The attributes of minds as well as those of bodies are grounded on states of feeling or consciousness But in the case of a mind we have to consider its own states as well as those which it produces in other minds Every attribute of a mind consists either in being itself affected in a certain way or affecting other minds in a certain way Considered in itself we can predicate nothing of it but the series of its own feelings When we say of any mind that it is devout or superstitious or meditative or cheerful we mean that the ideas emotions or volitions implied in those words form a frequently recurring part of the series of feelings or states of consciousness which fill up the sentient existence of that mind In addition however to those attributes of a mind which are grounded on its own states of feeling attributes may also be ascribed to it in the same manner as to a body grounded on the feelings which it excites in other minds A mind does not indeed like a body excite sensations but it may excite thoughts or emotions The most important example of attributes ascribed on this ground is the employment of terms expressive of approbation or blame When for example we say of any character or in other words) of any mind that it is admirable we mean that the contemplation of it excites the sentiment of admiration and indeed somewhat more for the word implies that we not only feel admiration but approve that sentiment in ourselves In some cases under the semblance of a single attribute two are really predicated one of them a state of the mind itself the other a state with which other minds are affected by thinking of it As when we say of any one that he is generous The word generosity expresses a certain state of mind but being a term of praise it also expresses that this state of mind excites in us another mental state called approbation The assertion made therefore is twofold and of the following purport Certain feelings form habitually a part of this person’s sentient existence and the idea of those feelings of his excites the sentiment of approbation in ourselves or others As we thus ascribe attributes to minds on the ground of ideas and emotions so may we to bodies on similar grounds and not solely on the ground of sensations as in speaking of the beauty of a statue since this attribute is grounded on the peculiar feeling of pleasure which the statue produces in our minds which is not a sensation but an emotion Our survey of the varieties of Things which have been or which are capable of being named which have been or are capable of being either predicated of other Things or themselves made the subject of predications is now concluded Our enumeration commenced with Feelings These we scrupulously distinguished from the objects which excite them and from the organs by which they are or may be supposed to be conveyed Feelings are of four sorts Sensations Thoughts Emotions and Volitions What are called Perceptions are merely a particular case of Belief and Belief is a kind of thought Actions are merely volitions followed by an effect After Feelings we proceeded to Substances These are either Bodies or Minds Without entering into the grounds of the metaphysical doubts which have been raised concerning the existence of Matter and Mind as objective realities we stated as sufficient for us the conclusion in which the best thinkers are now for the most part agreed that all we can know of Matter is the sensations which it gives us and the order of occurrence of those sensations and that while the substance Body is the unknown cause of our sensations the substance Mind is the unknown recipient The only remaining class of Nameable Things is Attributes and these are of three kinds Quality Relation and Quantity Qualities like substances are known to us no otherwise than by the sensations or other states of consciousness which they excite and while in compliance with common usage we have continued to speak of them as a distinct class of Things we showed that in predicating them no one means to predicate any thing but those sensations or states of consciousness on which they may be said to be grounded and by which alone they can be defined or described Relations except the simple cases of likeness and unlikeness succession and simultaneity are similarly grounded on some fact or phenomenon that is on some series of sensations or states of consciousness more or less complicated The third species of Attribute Quantity is also manifestly grounded on something in our sensations or states of feeling since there is an indubitable difference in the sensations excited by a larger and a smaller bulk or by a greater or a less degree of intensity in any object of sense or of consciousness All attributes therefore are to us nothing but either our sensations and other states of feeling or something inextricably involved therein and to this even the peculiar and simple relations just adverted to are not exceptions Those peculiar relations however are so important and even if they might in strictness be classed among states of consciousness are so fundamentally distinct from any other of those states that it would be a vain subtlety to bring them under that common description and it is necessary that they should be classed apart As the result therefore of our analysis we obtain the following as an enumeration and classification of all Nameable Things 1st Feelings or States of Consciousness 2d The Minds which experience those feelings 3d The Bodies or external objects which excite certain of those feelings together with the powers or properties whereby they excite them these latter at least being included rather in compliance with common opinion and because their existence is taken for granted in the common language from which I can not prudently deviate than because the recognition of such powers or properties as real existences appears to be warranted by a sound philosophy 4th and last The Successions and Coexistences the Likenesses and Unlikenesses between feelings or states of consciousness Those relations when considered as subsisting between other things exist in reality only between the states of consciousness which those things if bodies excite if minds either excite or experience This until a better can be suggested may serve as a substitute for the Categories of Aristotle considered as a classification of Existences The practical application of it will appear when we commence the inquiry into the Import of Propositions in other words when we inquire what it is which the mind actually believes when it gives what is called its assent to a proposition These four classes comprising if the classification be correct all Nameable Things these or some of them must of course compose the signification of all names and of these or some of them is made up whatever we call a fact For distinction’s sake every fact which is solely composed of feelings or states of consciousness considered as such is often called a Psychological or Subjective fact while every fact which is composed either wholly or in part of something different from these that is of substances and attributes is called an Objective fact We may say then that every objective fact is grounded on a corresponding subjective one and has no meaning to us apart from the subjective fact which corresponds to it except as a name for the unknown and inscrutable process by which that subjective or psychological fact is brought to pass In treating of Propositions as already in treating of Names some considerations of a comparatively elementary nature respecting their form and varieties must be premised before entering upon that analysis of the import conveyed by them which is the real subject and purpose of this preliminary book A proposition we have before said is a portion of discourse in which a predicate is affirmed or denied of a subject A predicate and a subject are all that is necessarily required to make up a proposition but as we can not conclude from merely seeing two names put together that they are a predicate and a subject that is that one of them is intended to be affirmed or denied of the other it is necessary that there should be some mode or form of indicating that such is the intention some sign to distinguish a predication from any other kind of discourse This is sometimes done by a slight alteration of one of the words called an inflection as when we say Fire burns the change of the second word from burn to burns showing that we mean to affirm the predicate burn of the subject fire But this function is more commonly fulfilled by the word is when an affirmation is intended is not when a negation or by some other part of the verb to be The word which thus serves the purpose of a sign of predication is called as we formerly observed the copula It is important that there should be no indistinctness in our conception of the nature and office of the copula for confused notions respecting it are among the causes which have spread mysticism over the field of logic and perverted its speculations into logomachies It is apt to be supposed that the copula is something more than a mere sign of predication that it also signifies existence In the proposition Socrates is just it may seem to be implied not only that the quality just can be affirmed of Socrates but moreover that Socrates is that is to say exists This however only shows that there is an ambiguity in the word is a word which not only performs the function of the copula in affirmations but has also a meaning of its own in virtue of which it may itself be made the predicate of a proposition That the employment of it as a copula does not necessarily include the affirmation of existence appears from such a proposition as this A centaur is a fiction of the poets where it can not possibly be implied that a centaur exists since the proposition itself expressly asserts that the thing has no real existence Many volumes might be filled with the frivolous speculations concerning the nature of Being Ens Entitas Essentia and the like which have arisen from overlooking this double meaning of the word to be from supposing that when it signifies to exist and when it signifies to be some specified thing as to be a man to be Socrates to be seen or spoken of to be a phantom even to be a nonentity it must still at bottom answer to the same idea and that a meaning must be found for it which shall suit all these cases The fog which rose from this narrow spot diffused itself at an early period over the whole surface of metaphysics Yet it becomes us not to triumph over the great intellects of Plato and Aristotle because we are now able to preserve ourselves from many errors into which they perhaps inevitably fell The fireteaser of a modern steamengine produces by his exertions far greater effects than Milo of Crotona could but he is not therefore a stronger man The Greeks seldom knew any language but their own This rendered it far more difficult for them than it is for us to acquire a readiness in detecting ambiguities One of the advantages of having accurately studied a plurality of languages especially of those languages which eminent thinkers have used as the vehicle of their thoughts is the practical lesson we learn respecting the ambiguities of words by finding that the same word in one language corresponds on different occasions to different words in another When not thus exercised even the strongest understandings find it difficult to believe that things which have a common name have not in some respect or other a common nature and often expend much labour very unprofitably as was frequently done by the two philosophers just mentioned in vain attempts to discover in what this common nature consists But the habit once formed intellects much inferior are capable of detecting even ambiguities which are common to many languages and it is surprising that the one now under consideration though it exists in the modern languages as well as in the ancient should have been overlooked by almost all authors The quantity of futile speculation which had been caused by a misapprehension of the nature of the copula was hinted at by Hobbes but Mr James Mill was I believe the first who distinctly characterized the ambiguity and pointed out how many errors in the received systems of philosophy it has had to answer for It has indeed misled the moderns scarcely less than the ancients though their mistakes because our understandings are not yet so completely emancipated from their influence do not appear equally irrational We shall now briefly review the principal distinctions which exist among propositions and the technical terms most commonly in use to express those distinctions A proposition being a portion of discourse in which something is affirmed or denied of something the first division of propositions is into affirmative and negative An affirmative proposition is that in which the predicate is affirmed of the subject as Caesar is dead A negative proposition is that in which the predicate is denied of the subject as Caesar is not dead The copula in this last species of proposition consists of the words is not which are the sign of negation is being the sign of affirmation Some logicians among whom may be mentioned Hobbes state this distinction differently they recognize only one form of copula is and attach the negative sign to the predicate Caesar is dead and Caesar is not dead according to these writers are propositions agreeing not in the subject and predicate but in the subject only They do not consider dead but not dead to be the predicate of the second proposition and they accordingly define a negative proposition to be one in which the predicate is a negative name The point though not of much practical moment deserves notice as an example not infrequent in logic where by means of an apparent simplification but which is merely verbal matters are made more complex than before The notion of these writers was that they could get rid of the distinction between affirming and denying by treating every case of denying as the affirming of a negative name But what is meant by a negative name A name expressive of the absence of an attribute So that when we affirm a negative name what we are really predicating is absence and not presence we are asserting not that any thing is but that something is not to express which operation no word seems so proper as the word denying The fundamental distinction is between a fact and the nonexistence of that fact between seeing something and not seeing it between Caesar’s being dead and his not being dead and if this were a merely verbal distinction the generalization which brings both within the same form of assertion would be a real simplification the distinction however being real and in the facts it is the generalization confounding the distinction that is merely verbal and tends to obscure the subject by treating the difference between two kinds of truths as if it were only a difference between two kinds of words To put things together and to put them or keep them asunder will remain different operations whatever tricks we may play with language A remark of a similar nature may be applied to most of those distinctions among propositions which are said to have reference to their modality as difference of tense or time the sun did rise the sun is rising the sun will rise These differences like that between affirmation and negation might be glossed over by considering the incident of time as a mere modification of the predicate thus The sun is an object having risen The sun is an object now rising The sun is an object to rise hereafter But the simplification would be merely verbal Past present and future do not constitute so many different kinds of rising they are designations belonging to the event asserted to the sun’s rising today They affect not the predicate but the applicability of the predicate to the particular subject That which we affirm to be past present or future is not what the subject signifies nor what the predicate signifies but specifically and expressly what the predication signifies what is expressed only by the proposition as such and not by either or both of the terms Therefore the circumstance of time is properly considered as attaching to the copula which is the sign of predication and not to the predicate If the same can not be said of such modifications as these Caesar may be dead Caesar is perhaps dead it is possible that Caesar is dead it is only because these fall altogether under another head being properly assertions not of any thing relating to the fact itself but of the state of our own mind in regard to it namely our absence of disbelief of it Thus Caesar may be dead means I am not sure that Caesar is alive The next division of propositions is into Simple and Complex more aptly by Professor Bain termed Compound A simple proposition is that in which one predicate is affirmed or denied of one subject A compound proposition is that in which there is more than one predicate or more than one subject or both At first sight this division has the air of an absurdity a solemn distinction of things into one and more than one as if we were to divide horses into single horses and teams of horses And it is true that what is called a complex or compound proposition is often not a proposition at all but several propositions held together by a conjunction Such for example is this Caesar is dead and Brutus is alive or even this Caesar is dead but Brutus is alive There are here two distinct assertions and we might as well call a street a complex house as these two propositions a complex proposition It is true that the syncategorematic words and but have a meaning but that meaning is so far from making the two propositions one that it adds a third proposition to them All particles are abbreviations and generally abbreviations of propositions a kind of shorthand whereby something which to be expressed fully would have required a proposition or a series of propositions is suggested to the mind at once Thus the words Caesar is dead and Brutus is alive are equivalent to these Caesar is dead Brutus is alive it is desired that the two preceding propositions should be thought of together If the words were Caesar is dead but Brutus is alive the sense would be equivalent to the same three propositions together with a fourth between the two preceding propositions there exists a contrast viz either between the two facts themselves or between the feelings with which it is desired that they should be regarded In the instances cited the two propositions are kept visibly distinct each subject having its separate predicate and each predicate its separate subject For brevity however and to avoid repetition the propositions are often blended together as in this Peter and James preached at Jerusalem and in Galilee which contains four propositions Peter preached at Jerusalem Peter preached in Galilee James preached at Jerusalem James preached in Galilee We have seen that when the two or more propositions comprised in what is called a complex proposition are stated absolutely and not under any condition or proviso it is not a proposition at all but a plurality of propositions since what it expresses is not a single assertion but several assertions which if true when joined are true also when separated But there is a kind of proposition which though it contains a plurality of subjects and of predicates and may be said in one sense of the word to consist of several propositions contains but one assertion and its truth does not at all imply that of the simple propositions which compose it An example of this is when the simple propositions are connected by the particle or as either A is B or C is D or by the particle if as A is B if C is D In the former case the proposition is called disjunctive in the latter conditional the name hypothetical was originally common to both As has been well remarked by Archbishop Whately and others the disjunctive form is resolvable into the conditional every disjunctive proposition being equivalent to two or more conditional ones Either A is B or C is D means if A is not B C is D and if C is not D A is B All hypothetical propositions therefore though disjunctive in form are conditional in meaning and the words hypothetical and conditional may be as indeed they generally are used synonymously Propositions in which the assertion is not dependent on a condition are said in the language of logicians to be categorical A hypothetical proposition is not like the pretended complex propositions which we previously considered a mere aggregation of simple propositions The simple propositions which form part of the words in which it is couched form no part of the assertion which it conveys When we say If the Koran comes from God Mohammed is the prophet of God we do not intend to affirm either that the Koran does come from God or that Mohammed is really his prophet Neither of these simple propositions may be true and yet the truth of the hypothetical proposition may be indisputable What is asserted is not the truth of either of the propositions but the inferribility of the one from the other What then is the subject and what the predicate of the hypothetical proposition The Koran is not the subject of it nor is Mohammed for nothing is affirmed or denied either of the Koran or of Mohammed The real subject of the predication is the entire proposition Mohammed is the prophet of God and the affirmation is that this is a legitimate inference from the proposition The Koran comes from God The subject and predicate therefore of a hypothetical proposition are names of propositions The subject is some one proposition The predicate is a general relative name applicable to propositions of this form an inference from so and so A fresh instance is here afforded of the remark that particles are abbreviations since If A is B C is D is found to be an abbreviation of the following The proposition C is D is a legitimate inference from the proposition A is B The distinction therefore between hypothetical and categorical propositions is not so great as it at first appears In the conditional as well as in the categorical form one predicate is affirmed of one subject and no more but a conditional proposition is a proposition concerning a proposition the subject of the assertion is itself an assertion Nor is this a property peculiar to hypothetical propositions There are other classes of assertions concerning propositions Like other things a proposition has attributes which may be predicated of it The attribute predicated of it in a hypothetical proposition is that of being an inference from a certain other proposition But this is only one of many attributes that might be predicated We may say That the whole is greater than its part is an axiom in mathematics That the Holy Ghost proceeds from the Father alone is a tenet of the Greek Church The doctrine of the divine right of kings was renounced by Parliament at the Revolution The infallibility of the Pope has no countenance from Scripture In all these cases the subject of the predication is an entire proposition That which these different predicates are affirmed of is the proposition the whole is greater than its part the proposition the Holy Ghost proceeds from the Father alone the proposition kings have a divine right the proposition the Pope is infallible Seeing then that there is much less difference between hypothetical propositions and any others than one might be led to imagine from their form we should be at a loss to account for the conspicuous position which they have been selected to fill in treatises on logic if we did not remember that what they predicate of a proposition namely its being an inference from something else is precisely that one of its attributes with which most of all a logician is concerned The next of the common divisions of Propositions is into Universal Particular Indefinite and Singular a distinction founded on the degree of generality in which the name which is the subject of the proposition is to be understood The following are examples All men are mortal Universal Some men are mortal Particular Man is mortal Indefinite Julius Caesar is mortal Singular The proposition is Singular when the subject is an individual name The individual name needs not be a proper name The Founder of Christianity was crucified is as much a singular proposition as Christ was crucified When the name which is the subject of the proposition is a general name we may intend to affirm or deny the predicate either of all the things that the subject denotes or only of some When the predicate is affirmed or denied of all and each of the things denoted by the subject the proposition is universal when of some undefined portion of them only it is particular Thus All men are mortal Every man is mortal are universal propositions No man is immortal is also a universal proposition since the predicate immortal is denied of each and every individual denoted by the term man the negative proposition being exactly equivalent to the following Every man is notimmortal But some men are wise some men are not wise are particular propositions the predicate wise being in the one case affirmed and in the other denied not of each and every individual denoted by the term man but only of each and every one of some portion of those individuals without specifying what portion for if this were specified the proposition would be changed either into a singular proposition or into a universal proposition with a different subject as for instance all properly instructed men are wise There are other forms of particular propositions as Most men are imperfectly educated it being immaterial how large a portion of the subject the predicate is asserted of as long as it is left uncertain how that portion is to be distinguished from the rest When the form of the expression does not clearly show whether the general name which is the subject of the proposition is meant to stand for all the individuals denoted by it or only for some of them the proposition is by some logicians called Indefinite but this as Archbishop Whately observes is a solecism of the same nature as that committed by some grammarians when in their list of genders they enumerate the doubtful gender The speaker must mean to assert the proposition either as a universal or as a particular proposition though he has failed to declare which and it often happens that though the words do not show which of the two he intends the context or the custom of speech supplies the deficiency Thus when it is affirmed that Man is mortal nobody doubts that the assertion is intended of all human beings and the word indicative of universality is commonly omitted only because the meaning is evident without it In the proposition Wine is good it is understood with equal readiness though for somewhat different reasons that the assertion is not intended to be universal but particular As is observed by Professor Bain the chief examples of Indefinite propositions occur with names of material which are the subjects sometimes of universal and at other times of particular predication Food is chemically constituted by carbon oxygen etc’ is a proposition of universal quantity the meaning is all food all kinds of food Food is necessary to animal life’ is a case of particular quantity the meaning is some sort of food not necessarily all sorts Metal is requisite in order to strength’ does not mean all kinds of metal Gold will make a way’ means a portion of gold When a general name stands for each and every individual which it is a name of or in other words, which it denotes it is said by logicians to be distributed or taken distributively Thus in the proposition All men are mortal the subject Man is distributed because mortality is affirmed of each and every man The predicate Mortal is not distributed because the only mortals who are spoken of in the proposition are those who happen to be men while the word may for aught that appears and in fact does comprehend within it an indefinite number of objects besides men In the proposition Some men are mortal both the predicate and the subject are undistributed In the following No men have wings both the predicate and the subject are distributed Not only is the attribute of having wings denied of the entire class Man but that class is severed and cast out from the whole of the class Winged and not merely from some part of that class This phraseology which is of great service in stating and demonstrating the rules of the syllogism enables us to express very concisely the definitions of a universal and a particular proposition A universal proposition is that of which the subject is distributed a particular proposition is that of which the subject is undistributed There are many more distinctions among propositions than those we have here stated some of them of considerable importance But for explaining and illustrating these more suitable opportunities will occur in the sequel An inquiry into the nature of propositions must have one of two objects to analyse the state of mind called Belief or to analyse what is believed All language recognizes a difference between a doctrine or opinion and the fact of entertaining the opinion between assent and what is assented to Logic according to the conception here formed of it has no concern with the nature of the act of judging or believing the consideration of that act as a phenomenon of the mind belongs to another science Philosophers however from Descartes downward and especially from the era of Leibnitz and Locke have by no means observed this distinction and would have treated with great disrespect any attempt to analyse the import of Propositions unless founded on an analysis of the act of Judgment A proposition they would have said is but the expression in words of a Judgment The thing expressed not the mere verbal expression is the important matter When the mind assents to a proposition it judges Let us find out what the mind does when it judges and we shall know what propositions mean and not otherwise Conformably to these views almost all the writers on Logic in the last two centuries whether English German or French have made their theory of Propositions from one end to the other a theory of Judgments They considered a Proposition or a Judgment for they used the two words indiscriminately to consist in affirming or denying one idea of another To judge was to put two ideas together or to bring one idea under another or to compare two ideas or to perceive the agreement or disagreement between two ideas and the whole doctrine of Propositions together with the theory of Reasoning always necessarily founded on the theory of Propositions was stated as if Ideas or Conceptions or whatever other term the writer preferred as a name for mental representations generally constituted essentially the subjectmatter and substance of those operations It is of course true that in any case of judgment as for instance when we judge that gold is yellow a process takes place in our minds of which some one or other of these theories is a partially correct account We must have the idea of gold and the idea of yellow and these two ideas must be brought together in our mind But in the first place it is evident that this is only a part of what takes place for we may put two ideas together without any act of belief as when we merely imagine something such as a golden mountain or when we actually disbelieve for in order even to disbelieve that Mohammed was an apostle of God we must put the idea of Mohammed and that of an apostle of God together To determine what it is that happens in the case of assent or dissent besides putting two ideas together is one of the most intricate of metaphysical problems But whatever the solution may be we may venture to assert that it can have nothing whatever to do with the import of propositions for this reason that propositions except sometimes when the mind itself is the subject treated of are not assertions respecting our ideas of things but assertions respecting the things themselves In order to believe that gold is yellow I must indeed have the idea of gold and the idea of yellow and something having reference to those ideas must take place in my mind but my belief has not reference to the ideas it has reference to the things What I believe is a fact relating to the outward thing gold and to the impression made by that outward thing upon the human organs not a fact relating to my conception of gold which would be a fact in my mental history not a fact of external nature It is true that in order to believe this fact in external nature another fact must take place in my mind a process must be performed upon my ideas but so it must in every thing else that I do I can not dig the ground unless I have the idea of the ground and of a spade and of all the other things I am operating upon and unless I put those ideas together But it would be a very ridiculous description of digging the ground to say that it is putting one idea into another Digging is an operation which is performed upon the things themselves though it can not be performed unless I have in my mind the ideas of them And in like manner believing is an act which has for its subject the facts themselves though a previous mental conception of the facts is an indispensable condition When I say that fire causes heat do I mean that my idea of fire causes my idea of heat No I mean that the natural phenomenon fire causes the natural phenomenon heat When I mean to assert any thing respecting the ideas I give them their proper name I call them ideas as when I say that a child’s idea of a battle is unlike the reality or that the ideas entertained of the Deity have a great effect on the characters of mankind The notion that what is of primary importance to the logician in a proposition is the relation between the two ideas corresponding to the subject and predicate instead of the relation between the two phenomena which they respectively express seems to me one of the most fatal errors ever introduced into the philosophy of Logic and the principal cause why the theory of the science has made such inconsiderable progress during the last two centuries The treatises on Logic and on the branches of Mental Philosophy connected with Logic which have been produced since the intrusion of this cardinal error though sometimes written by men of extraordinary abilities and attainments almost always tacitly imply a theory that the investigation of truth consists in contemplating and handling our ideas or conceptions of things instead of the things themselves a doctrine tantamount to the assertion that the only mode of acquiring knowledge of nature is to study it at second hand as represented in our own minds Meanwhile inquiries into every kind of natural phenomena were incessantly establishing great and fruitful truths on most important subjects by processes upon which these views of the nature of Judgment and Reasoning threw no light and in which they afforded no assistance whatever No wonder that those who knew by practical experience how truths are arrived at should deem a science futile which consisted chiefly of such speculations What has been done for the advancement of Logic since these doctrines came into vogue has been done not by professed logicians but by discoverers in the other sciences in whose methods of investigation many principles of logic not previously thought of have successively come forth into light but who have generally committed the error of supposing that nothing whatever was known of the art of philosophizing by the old logicians because their modern interpreters have written to so little purpose respecting it We have to inquire then on the present occasion not into Judgment but judgments not into the act of believing but into the thing believed What is the immediate object of belief in a Proposition What is the matter of fact signified by it What is it to which when I assert the proposition I give my assent and call upon others to give theirs What is that which is expressed by the form of discourse called a Proposition and the conformity of which to fact constitutes the truth of the proposition One of the clearest and most consecutive thinkers whom this country or the world has produced I mean Hobbes has given the following answer to this question In every proposition says he what is signified is the belief of the speaker that the predicate is a name of the same thing of which the subject is a name and if it really is so the proposition is true Thus the proposition All men are living beings he would say is true because living being is a name of every thing of which man is a name All men are six feet high is not true because six feet high is not a name of every thing though it is of some things of which man is a name What is stated in this theory as the definition of a true proposition must be allowed to be a property which all true propositions possess The subject and predicate being both of them names of things if they were names of quite different things the one name could not consistently with its signification be predicated of the other If it be true that some men are coppercoloured it must be true and the proposition does really assert that among the individuals denoted by the name man there are some who are also among those denoted by the name coppercoloured If it be true that all oxen ruminate it must be true that all the individuals denoted by the name ox are also among those denoted by the name ruminating and whoever asserts that all oxen ruminate undoubtedly does assert that this relation subsists between the two names The assertion therefore which according to Hobbes is the only one made in any proposition really is made in every proposition and his analysis has consequently one of the requisites for being the true one We may go a step further it is the only analysis that is rigorously true of all propositions without exception What he gives as the meaning of propositions is part of the meaning of all propositions and the whole meaning of some This however only shows what an extremely minute fragment of meaning it is quite possible to include within the logical formula of a proposition It does not show that no proposition means more To warrant us in putting together two words with a copula between them it is really enough that the thing or things denoted by one of the names should be capable without violation of usage of being called by the other name also If then this be all the meaning necessarily implied in the form of discourse called a Proposition why do I object to it as the scientific definition of what a proposition means Because though the mere collocation which makes the proposition a proposition conveys no more than this scanty amount of meaning that same collocation combined with other circumstances that form combined with other matter does convey more and the proposition in those other circumstances does assert more than merely that relation between the two names The only propositions of which Hobbes’s principle is a sufficient account are that limited and unimportant class in which both the predicate and the subject are proper names For as has already been remarked proper names have strictly no meaning they are mere marks for individual objects and when a proper name is predicated of another proper name all the signification conveyed is that both the names are marks for the same object But this is precisely what Hobbes produces as a theory of predication in general His doctrine is a full explanation of such predications as these Hyde was Clarendon or Tully is Cicero It exhausts the meaning of those propositions But it is a sadly inadequate theory of any others That it should ever have been thought of as such can be accounted for only by the fact that Hobbes in common with the other Nominalists bestowed little or no attention upon the connotation of words and sought for their meaning exclusively in what they denote as if all names had been what none but proper names really are marks put upon individuals and as if there were no difference between a proper and a general name except that the first denotes only one individual and the last a greater number It has been seen however that the meaning of all names except proper names and that portion of the class of abstract names which are not connotative resides in the connotation When therefore we are analysing the meaning of any proposition in which the predicate and the subject or either of them are connotative names it is to the connotation of those terms that we must exclusively look and not to what they denote or in the language of Hobbes language so far correct are names of In asserting that the truth of a proposition depends on the conformity of import between its terms as for instance that the proposition Socrates is wise is a true proposition because Socrates and wise are names applicable to or as he expresses it names of the same person it is very remarkable that so powerful a thinker should not have asked himself the question But how came they to be names of the same person Surely not because such was the intention of those who invented the words When mankind fixed the meaning of the word wise they were not thinking of Socrates nor when his parents gave him the name of Socrates were they thinking of wisdom The names happen to fit the same person because of a certain fact which fact was not known nor in being when the names were invented If we want to know what the fact is we shall find the clue to it in the connotation of the names A bird or a stone a man or a wise man means simply an object having such and such attributes The real meaning of the word man is those attributes and not Smith Brown and the remainder of the individuals The word mortal in like manner connotes a certain attribute or attributes and when we say All men are mortal the meaning of the proposition is that all beings which possess the one set of attributes possess also the other If in our experience the attributes connoted by man are always accompanied by the attribute connoted by mortal it will follow as a consequence that the class man will be wholly included in the class mortal and that mortal will be a name of all things of which man is a name but why Those objects are brought under the name by possessing the attributes connoted by it but their possession of the attributes is the real condition on which the truth of the proposition depends not their being called by the name Connotative names do not precede but follow the attributes which they connote If one attribute happens to be always found in conjunction with another attribute the concrete names which answer to those attributes will of course be predicable of the same subjects and may be said in Hobbes’s language in the propriety of which on this occasion I fully concur to be two names for the same things But the possibility of a concurrent application of the two names is a mere consequence of the conjunction between the two attributes and was in most cases never thought of when the names were introduced and their signification fixed That the diamond is combustible was a proposition certainly not dreamed of when the words Diamond and Combustible first received their meaning and could not have been discovered by the most ingenious and refined analysis of the signification of those words It was found out by a very different process namely by exerting the senses and learning from them that the attribute of combustibility existed in the diamonds upon which the experiment was tried the number or character of the experiments being such that what was true of those individuals might be concluded to be true of all substances called by the name that is of all substances possessing the attributes which the name connotes The assertion therefore when analysed is that wherever we find certain attributes there will be found a certain other attribute which is not a question of the signification of names but of laws of nature the order existing among phenomena Although Hobbes’s theory of Predication has not in the terms in which he stated it met with a very favourable reception from subsequent thinkers a theory virtually identical with it and not by any means so perspicuously expressed may almost be said to have taken the rank of an established opinion The most generally received notion of Predication decidedly is that it consists in referring something to a class ie either placing an individual under a class or placing one class under another class Thus the proposition Man is mortal asserts according to this view of it that the class man is included in the class mortal Plato is a philosopher asserts that the individual Plato is one of those who compose the class philosopher If the proposition is negative then instead of placing something in a class it is said to exclude something from a class Thus if the following be the proposition The elephant is not carnivorous what is asserted according to this theory is that the elephant is excluded from the class carnivorous or is not numbered among the things comprising that class There is no real difference except in language between this theory of Predication and the theory of Hobbes For a class is absolutely nothing but an indefinite number of individuals denoted by a general name The name given to them in common is what makes them a class To refer any thing to a class therefore is to look upon it as one of the things which are to be called by that common name To exclude it from a class is to say that the common name is not applicable to it How widely these views of predication have prevailed is evident from this that they are the basis of the celebrated dictum de omni et nullo When the syllogism is resolved by all who treat of it into an inference that what is true of a class is true of all things whatever that belong to the class and when this is laid down by almost all professed logicians as the ultimate principle to which all reasoning owes its validity it is clear that in the general estimation of logicians the propositions of which reasonings are composed can be the expression of nothing but the process of dividing things into classes and referring every thing to its proper class This theory appears to me a signal example of a logical error very often committed in logic that of ¹ or explaining a thing by something which presupposes it When I say that snow is white I may and ought to be thinking of snow as a class because I am asserting a proposition as true of all snow but I am certainly not thinking of white objects as a class I am thinking of no white object whatever except snow but only of that and of the sensation of white which it gives me When indeed I have judged or assented to the propositions that snow is white and that several other things are also white I gradually begin to think of white objects as a class including snow and those other things But this is a conception which followed not preceded those judgments and therefore can not be given as an explanation of them Instead of explaining the effect by the cause this doctrine explains the cause by the effect and is I conceive founded on a latent misconception of the nature of classification There is a sort of language very generally prevalent in these discussions which seems to suppose that classification is an arrangement and grouping of definite and known individuals that when names were imposed mankind took into consideration all the individual objects in the universe distributed them into parcels or lists and gave to the objects of each list a common name repeating this operation toties quoties until they had invented all the general names of which language consists which having been once done if a question subsequently arises whether a certain general name can be truly predicated of a certain particular object we have only as it were to read the roll of the objects upon which that name was conferred and see whether the object about which the question arises is to be found among them The framers of language it would seem to be supposed have predetermined all the objects that are to compose each class and we have only to refer to the record of an antecedent decision So absurd a doctrine will be owned by nobody when thus nakedly stated but if the commonly received explanations of classification and naming do not imply this theory it requires to be shown how they admit of being reconciled with any other General names are not marks put upon definite objects classes are not made by drawing a line round a given number of assignable individuals The objects which compose any given class are perpetually fluctuating We may frame a class without knowing the individuals or even any of the individuals of which it may be composed we may do so while believing that no such individuals exist If by the meaning of a general name are to be understood the things which it is the name of no general name except by accident has a fixed meaning at all or ever long retains the same meaning The only mode in which any general name has a definite meaning is by being a name of an indefinite variety of things namely of all things known or unknown past present or future which possess certain definite attributes When by studying not the meaning of words but the phenomena of nature we discover that these attributes are possessed by some object not previously known to possess them as when chemists found that the diamond was combustible we include this new object in the class but it did not already belong to the class We place the individual in the class because the proposition is true the proposition is not true because the object is placed in the class It will appear hereafter in treating of reasoning how much the theory of that intellectual process has been vitiated by the influence of these erroneous notions and by the habit which they exemplify of assimilating all the operations of the human understanding which have truth for their object to processes of mere classification and naming Unfortunately the minds which have been entangled in this net are precisely those which have escaped the other cardinal error commented upon in the beginning of the present chapter Since the revolution which dislodged Aristotle from the schools logicians may almost be divided into those who have looked upon reasoning as essentially an affair of Ideas and those who have looked upon it as essentially an affair of Names Although however Hobbes’s theory of Predication according to the wellknown remark of Leibnitz and the avowal of Hobbes himself renders truth and falsity completely arbitrary with no standard but the will of men it must not be concluded that either Hobbes or any of the other thinkers who have in the main agreed with him did in fact consider the distinction between truth and error as less real or attached less importance to it than other people To suppose that they did so would argue total unacquaintance with their other speculations But this shows how little hold their doctrine possessed over their own minds No person at bottom ever imagined that there was nothing more in truth than propriety of expression than using language in conformity to a previous convention When the inquiry was brought down from generals to a particular case it has always been acknowledged that there is a distinction between verbal and real questions that some false propositions are uttered from ignorance of the meaning of words but that in others the source of the error is a misapprehension of things that a person who has not the use of language at all may form propositions mentally and that they may be untrue that is he may believe as matters of fact what are not really so This last admission can not be made in stronger terms than it is by Hobbes himself though he will not allow such erroneous belief to be called falsity but only error And he has himself laid down in other places doctrines in which the true theory of predication is by implication contained He distinctly says that general names are given to things on account of their attributes and that abstract names are the names of those attributes Abstract is that which in any subject denotes the cause of the concrete name And these causes of names are the same with the causes of our conceptions namely some power of action or affection of the thing conceived which some call the manner by which any thing works upon our senses but by most men they are called accidents It is strange that having gone so far he should not have gone one step further and seen that what he calls the cause of the concrete name is in reality the meaning of it and that when we predicate of any subject a name which is given because of an attribute or as he calls it an accident our object is not to affirm the name but by means of the name to affirm the attribute Let the predicate be as we have said a connotative term and to take the simplest case first let the subject be a proper name The summit of Chimborazo is white The word white connotes an attribute which is possessed by the individual object designated by the words summit of Chimborazo which attribute consists in the physical fact of its exciting in human beings the sensation which we call a sensation of white It will be admitted that by asserting the proposition we wish to communicate information of that physical fact and are not thinking of the names except as the necessary means of making that communication The meaning of the proposition therefore is that the individual thing denoted by the subject has the attributes connoted by the predicate If we now suppose the subject also to be a connotative name the meaning expressed by the proposition has advanced a step further in complication Let us first suppose the proposition to be universal as well as affirmative All men are mortal In this case as in the last what the proposition asserts or expresses a belief of is of course that the objects denoted by the subject man possess the attributes connoted by the predicate mortal But the characteristic of this case is that the objects are no longer individually designated They are pointed out only by some of their attributes they are the objects called men that is possessing the attributes connoted by the name man and the only thing known of them may be those attributes indeed as the proposition is general and the objects denoted by the subject are therefore indefinite in number most of them are not known individually at all The assertion therefore is not as before that the attributes which the predicate connotes are possessed by any given individual or by any number of individuals previously known as John Thomas etc but that those attributes are possessed by each and every individual possessing certain other attributes that whatever has the attributes connoted by the subject has also those connoted by the predicate that the latter set of attributes constantly accompany the former set Whatever has the attributes of man has the attribute of mortality mortality constantly accompanies the attributes of man If it be remembered that every attribute is grounded on some fact or phenomenon either of outward sense or of inward consciousness and that to possess an attribute is another phrase for being the cause of or forming part of the fact or phenomenon upon which the attribute is grounded we may add one more step to complete the analysis The proposition which asserts that one attribute always accompanies another attribute really asserts thereby no other thing than this that one phenomenon always accompanies another phenomenon insomuch that where we find the latter we have assurance of the existence of the former Thus in the proposition All men are mortal the word man connotes the attributes which we ascribe to a certain kind of living creatures on the ground of certain phenomena which they exhibit and which are partly physical phenomena namely the impressions made on our senses by their bodily form and structure and partly mental phenomena namely the sentient and intellectual life which they have of their own All this is understood when we utter the word man by any one to whom the meaning of the word is known Now when we say Man is mortal we mean that wherever these various physical and mental phenomena are all found there we have assurance that the other physical and mental phenomenon called death will not fail to take place The proposition does not affirm when for the connotation of the word mortal goes no further than to the occurrence of the phenomenon at some time or other leaving the particular time undecided We have already proceeded far enough not only to demonstrate the error of Hobbes but to ascertain the real import of by far the most numerous class of propositions The object of belief in a proposition when it asserts any thing more than the meaning of words is generally as in the cases which we have examined either the coexistence or the sequence of two phenomena At the very commencement of our inquiry we found that every act of belief implied two Things we have now ascertained what in the most frequent case these two things are namely two Phenomena in other words two states of consciousness and what it is which the proposition affirms or denies to subsist between them namely either succession or coexistence And this case includes innumerable instances which no one previous to reflection would think of referring to it Take the following example A generous person is worthy of honour Who would expect to recognize here a case of coexistence between phenomena But so it is The attribute which causes a person to be termed generous is ascribed to him on the ground of states of his mind and particulars of his conduct both are phenomena the former are facts of internal consciousness the latter so far as distinct from the former are physical facts or perceptions of the senses Worthy of honour admits of a similar analysis Honora as here used means a state of approving and admiring emotion followed on occasion by corresponding outward acts Worthy of honour connotes all this together with our approval of the act of showing honour All these are phenomena states of internal consciousness accompanied or followed by physical facts When we say A generous person is worthy of honour we affirm coexistence between the two complicated phenomena connoted by the two terms respectively We affirm that wherever and whenever the inward feelings and outward facts implied in the word generosity have place then and there the existence and manifestation of an inward feeling honour would be followed in our minds by another inward feeling approval After the analysis in a former chapter of the import of names many examples are not needed to illustrate the import of propositions When there is any obscurity or difficulty it does not lie in the meaning of the proposition but in the meaning of the names which compose it in the extremely complicated connotation of many words the immense multitude and prolonged series of facts which often constitute the phenomenon connoted by a name But where it is seen what the phenomenon is there is seldom any difficulty in seeing that the assertion conveyed by the proposition is the coexistence of one such phenomenon with another or the succession of one such phenomenon to another so that where the one is found we may calculate on finding the other though perhaps not conversely This however though the most common is not the only meaning which propositions are ever intended to convey In the first place sequences and coexistences are not only asserted respecting Phenomena we make propositions also respecting those hidden causes of phenomena which are named substances and attributes A substance however being to us nothing but either that which causes or that which is conscious of phenomena and the same being true mutatis mutandis of attributes no assertion can be made at least with a meaning concerning these unknown and unknowable entities except in virtue of the Phenomena by which alone they manifest themselves to our faculties When we say Socrates was contemporary with the Peloponnesian war the foundation of this assertion as of all assertions concerning substances is an assertion concerning the phenomena which they exhibit namely that the series of facts by which Socrates manifested himself to mankind and the series of mental states which constituted his sentient existence went on simultaneously with the series of facts known by the name of the Peloponnesian war Still the proposition as commonly understood does not assert that alone it asserts that the Thing in itself the noumenon Socrates was existing and doing or experiencing those various facts during the same time Coexistence and sequence therefore may be affirmed or denied not only between phenomena but between noumena or between a noumenon and phenomena And both of noumena and of phenomena we may affirm simple existence But what is a noumenon An unknown cause In affirming therefore the existence of a noumenon we affirm causation Here therefore are two additional kinds of fact capable of being asserted in a proposition Besides the propositions which assert Sequence or Coexistence there are some which assert simple Existence and others assert Causation which subject to the explanations which will follow in the Third Book must be considered provisionally as a distinct and peculiar kind of assertion To these four kinds of matteroffact or assertion must be added a fifth Resemblance This was a species of attribute which we found it impossible to analyse for which no fundamentum distinct from the objects themselves could be assigned Besides propositions which assert a sequence or coexistence between two phenomena there are therefore also propositions which assert resemblance between them as This colour is like that colour The heat of today is equal to the heat of yesterday It is true that such an assertion might with some plausibility be brought within the description of an affirmation of sequence by considering it as an assertion that the simultaneous contemplation of the two colours is followed by a specific feeling termed the feeling of resemblance But there would be nothing gained by encumbering ourselves especially in this place with a generalization which may be looked upon as strained Logic does not undertake to analyse mental facts into their ultimate elements Resemblance between two phenomena is more intelligible in itself than any explanation could make it and under any classification must remain specifically distinct from the ordinary cases of sequence and coexistence It is sometimes said that all propositions whatever of which the predicate is a general name do in point of fact, affirm or deny resemblance All such propositions affirm that a thing belongs to a class but things being classed together according to their resemblance every thing is of course classed with the things which it is supposed to resemble most and thence it may be said when we affirm that Gold is a metal or that Socrates is a man the affirmation intended is that gold resembles other metals and Socrates other men more nearly than they resemble the objects contained in any other of the classes coordinate with these There is some slight degree of foundation for this remark but no more than a slight degree The arrangement of things into classes such as the class metal or the class man is grounded indeed on a resemblance among the things which are placed in the same class but not on a mere general resemblance the resemblance it is grounded on consists in the possession by all those things of certain common peculiarities and those peculiarities it is which the terms connote and which the propositions consequently assert not the resemblance For though when I say Gold is a metal I say by implication that if there be any other metals it must resemble them yet if there were no other metals I might still assert the proposition with the same meaning as at present namely that gold has the various properties implied in the word metal just as it might be said Christians are men even if there were no men who were not Christians Propositions therefore in which objects are referred to a class because they possess the attributes constituting the class are so far from asserting nothing but resemblance that they do not properly speaking assert resemblance at all But we remarked some time ago and the reasons of the remark will be more fully entered into in a subsequent Book that there is sometimes a convenience in extending the boundaries of a class so as to include things which possess in a very inferior degree if in any some of the characteristic properties of the class provided they resemble that class more than any other insomuch that the general propositions which are true of the class will be nearer to being true of those things than any other equally general propositions For instance there are substances called metals which have very few of the properties by which metals are commonly recognized and almost every great family of plants or animals has a few anomalous genera or species on its borders which are admitted into it by a sort of courtesy and concerning which it has been matter of discussion to what family they properly belonged Now when the classname is predicated of any object of this description we do by so predicating it affirm resemblance and nothing more And in order to be scrupulously correct it ought to be said that in every case in which we predicate a general name we affirm not absolutely that the object possesses the properties designated by the name but that it either possesses those properties or if it does not at any rate resembles the things which do so more than it resembles any other things In most cases however it is unnecessary to suppose any such alternative the latter of the two grounds being very seldom that on which the assertion is made and when it is there is generally some slight difference in the form of the expression as This species or genus is considered or may be ranked as belonging to such and such a family we should hardly say positively that it does belong to it unless it possessed unequivocally the properties of which the classname is scientifically significant There is still another exceptional case in which though the predicate is the name of a class yet in predicating it we affirm nothing but resemblance the class being founded not on resemblance in any given particular but on general unanalysable resemblance The classes in question are those into which our simple sensations or other simple feelings are divided Sensations of white for instance are classed together not because we can take them to pieces and say they are alike in this and not alike in that but because we feel them to be alike altogether though in different degrees When therefore I say The colour I saw yesterday was a white colour or The sensation I feel is one of tightness in both cases the attribute I affirm of the colour or of the other sensation is mere resemblance simple likeness to sensations which I have had before and which have had those names bestowed upon them The names of feelings like other concrete general names are connotative but they connote a mere resemblance When predicated of any individual feeling the information they convey is that of its likeness to the other feelings which we have been accustomed to call by the same name Thus much may suffice in illustration of the kind of propositions in which the matteroffact asserted or denied is simple Resemblance Existence Coexistence Sequence Causation Resemblance one or other of these is asserted or denied in every proposition which is not merely verbal This fivefold division is an exhaustive classification of mattersoffact of all things that can be believed or tendered for belief of all questions that can be propounded and all answers that can be returned to them Professor Bain distinguishes two kinds of Propositions of Coexistence In the one kind account is taken of Place they may be described as propositions of Order in Place In the other kind the coexistence which is predicated is termed by Mr Bain Coinherence of Attributes This is a distinct variety of Propositions of Coexistence Instead of an arrangement in place with numerical intervals we have the concurrence of two or more attributes or powers in the same part or locality A mass of gold contains in every atom the concurring attributes that mark the substance weight hardness colour lustre incorrosibility etc An animal besides having parts situated in place has coinhering functions in the same parts exerted by the very same masses and molecules of its substance The Mind which affords no Propositions of Order in Place has coinhering functions We affirm mind to contain Feeling Will and Thought not in local separation but in commingling exercise The concurring properties of minerals of plants and of the bodily and the mental structure of animals are united in affirmations of coinherence The distinction is real and important But as has been seen an Attribute when it is any thing but a simple unanalysable Resemblance between the subject and some other things consists in causing impressions of some sort on consciousness Consequently the coinherence of two attributes is but the coexistence of the two states of consciousness implied in their meaning with the difference however that this coexistence is sometimes potential only the attribute being considered as in existence though the fact on which it is grounded may not be actually but only potentially present Snow for instance is with great convenience said to be white even in a state of total darkness because though we are not now conscious of the colour we shall be conscious of it as soon as morning breaks Coinherence of attributes is therefore still a case though a complex one of coexistence of states of consciousness a totally different thing however from Order in Place Being a part of simultaneity it belongs not to Place but to Time We may therefore and we shall sometimes find it a convenience instead of Coexistence and Sequence say for greater particularity Order in Place and Order in Time Order in Place being a specific mode of coexistence not necessary to be more particularly analysed here while the mere fact of coexistence whether between actual sensations or between the potentialities of causing them known by the name of attributes may be classed together with Sequence under the head of Order in Time In the foregoing inquiry into the import of propositions we have thought it necessary to analyse directly those alone in which the terms of the proposition or the predicate at least are concrete terms But in doing so we have indirectly analysed those in which the terms are abstract The distinction between an abstract term and its corresponding concrete does not turn upon any difference in what they are appointed to signify for the real signification of a concrete general name is as we have so often said its connotation and what the concrete term connotes forms the entire meaning of the abstract name Since there is nothing in the import of an abstract name which is not in the import of the corresponding concrete it is natural to suppose that neither can there be any thing in the import of a proposition of which the terms are abstract but what there is in some proposition which can be framed of concrete terms And this presumption a closer examination will confirm An abstract name is the name of an attribute or combination of attributes The corresponding concrete is a name given to things because of and in order to express their possessing that attribute or that combination of attributes When therefore we predicate of any thing a concrete name the attribute is what we in reality predicate of it But it has now been shown that in all propositions of which the predicate is a concrete name what is really predicated is one of five things Existence Coexistence Causation Sequence or Resemblance An attribute therefore is necessarily either an existence a coexistence a causation a sequence or a resemblance When a proposition consists of a subject and predicate which are abstract terms it consists of terms which must necessarily signify one or other of these things When we predicate of any thing an abstract name we affirm of the thing that it is one or other of these five things that it is a case of Existence or of Coexistence or of Causation or of Sequence or of Resemblance It is impossible to imagine any proposition expressed in abstract terms which can not be transformed into a precisely equivalent proposition in which the terms are concrete namely either the concrete names which connote the attributes themselves or the names of the fundamenta of those attributes the facts or phenomena on which they are grounded To illustrate the latter case let us take this proposition of which the subject only is an abstract name Thoughtlessness is dangerous Thoughtlessness is an attribute grounded on the facts which we call thoughtless actions and the proposition is equivalent to this Thoughtless actions are dangerous In the next example the predicate as well as the subject are abstract names Whiteness is a colour or The colour of snow is a whiteness These attributes being grounded on sensations the equivalent propositions in the concrete would be The sensation of white is one of the sensations called those of colour The sensation of sight caused by looking at snow is one of the sensations called sensations of white In these propositions as we have before seen the matteroffact asserted is a Resemblance In the following examples the concrete terms are those which directly correspond to the abstract names connoting the attribute which these denote Prudence is a virtue this may be rendered All prudent persons in so far as prudent are virtuous Courage is deserving of honour thus All courageous persons are deserving of honour in so far as they are courageous which is equivalent to this All courageous persons deserve an addition to the honour or a diminution of the disgrace which would attach to them on other grounds In order to throw still further light upon the import of propositions of which the terms are abstract we will subject one of the examples given above to a minuter analysis The proposition we shall select is the following Prudence is a virtue Let us substitute for the word virtue an equivalent but more definite expression such as a mental quality beneficial to society or a mental quality pleasing to God or whatever else we adopt as the definition of virtue What the proposition asserts is a sequence accompanied with causation namely that benefit to society or that the approval of God is consequent on and caused by prudence Here is a sequence but between what We understand the consequent of the sequence but we have yet to analyse the antecedent Prudence is an attribute and in connection with it two things besides itself are to be considered prudent persons who are the subjects of the attribute and prudential conduct which may be called the foundation of it Now is either of these the antecedent and first is it meant that the approval of God or benefit to society is attendant upon all prudent persons No except in so far as they are prudent for prudent persons who are scoundrels can seldom on the whole be beneficial to society nor can they be acceptable to a good being Is it upon prudential conduct then that divine approbation and benefit to mankind are supposed to be invariably consequent Neither is this the assertion meant when it is said that prudence is a virtue except with the same reservation as before and for the same reason namely that prudential conduct although in so far as it is prudential it is beneficial to society may yet by reason of some other of its qualities be productive of an injury outweighing the benefit and deserve a displeasure exceeding the approbation which would be due to the prudence Neither the substance therefore viz the person nor the phenomenon the conduct is an antecedent on which the other term of the sequence is universally consequent But the proposition Prudence is a virtue is a universal proposition What is it then upon which the proposition affirms the effects in question to be universally consequent Upon that in the person and in the conduct which causes them to be called prudent and which is equally in them when the action though prudent is wicked namely a correct foresight of consequences a just estimation of their importance to the object in view and repression of any unreflecting impulse at variance with the deliberate purpose These which are states of the person’s mind are the real antecedent in the sequence the real cause in the causation asserted by the proposition But these are also the real ground or foundation of the attribute Prudence since wherever these states of mind exist we may predicate prudence even before we know whether any conduct has followed And in this manner every assertion respecting an attribute may be transformed into an assertion exactly equivalent respecting the fact or phenomenon which is the ground of the attribute And no case can be assigned where that which is predicated of the fact or phenomenon does not belong to one or other of the five species formerly enumerated it is either simple Existence or it is some Sequence Coexistence Causation or Resemblance And as these five are the only things which can be affirmed so are they the only things which can be denied No horses are webfooted denies that the attributes of a horse ever coexist with webfeet It is scarcely necessary to apply the same analysis to Particular affirmations and negations Some birds are webfooted affirms that with the attributes connoted by bird the phenomenon webfeet is sometimes coexistent Some birds are not webfooted asserts that there are other instances in which this coexistence does not have place Any further explanation of a thing which if the previous exposition has been assented to is so obvious may here be spared As a preparation for the inquiry which is the proper object of Logic namely in what manner propositions are to be proved we have found it necessary to inquire what they contain which requires or is susceptible of proof or which is the same thing what they assert In the course of this preliminary investigation into the import of Propositions we examined the opinion of the Conceptualists that a proposition is the expression of a relation between two ideas and the doctrine of the extreme Nominalists that it is the expression of an agreement or disagreement between the meanings of two names We decided that as general theories both of these are erroneous and that though propositions may be made both respecting names and respecting ideas neither the one nor the other are the subjectmatter of Propositions considered generally We then examined the different kinds of Propositions and found that with the exception of those which are merely verbal they assert five different kinds of matters of fact namely Existence Order in Place Order in Time Causation and Resemblance that in every proposition one of these five is either affirmed or denied of some fact or phenomenon or of some object the unknown source of a fact or phenomenon In distinguishing however the different kinds of matters of fact asserted in propositions we reserved one class of propositions which do not relate to any matter of fact in the proper sense of the term at all but to the meaning of names Since names and their signification are entirely arbitrary such propositions are not strictly speaking susceptible of truth or falsity but only of conformity or disconformity to usage or convention and all the proof they are capable of is proof of usage proof that the words have been employed by others in the acceptation in which the speaker or writer desires to use them These propositions occupy however a conspicuous place in philosophy and their nature and characteristics are of as much importance in logic as those of any of the other classes of propositions previously adverted to If all propositions respecting the signification of words were as simple and unimportant as those which served us for examples when examining Hobbes’s theory of predication viz those of which the subject and predicate are proper names and which assert only that those names have or that they have not been conventionally assigned to the same individual there would be little to attract to such propositions the attention of philosophers But the class of merely verbal propositions embraces not only much more than these but much more than any propositions which at first sight present themselves as verbal comprehending a kind of assertions which have been regarded not only as relating to things but as having actually a more intimate relation with them than any other propositions whatever The student in philosophy will perceive that I allude to the distinction on which so much stress was laid by the schoolmen and which has been retained either under the same or under other names by most metaphysicians to the present day viz between what were called essential and what were called accidental propositions and between essential and accidental properties or attributes Almost all metaphysicians prior to Locke as well as many since his time have made a great mystery of Essential Predication and of predicates which are said to be of the essence of the subject The essence of a thing they said was that without which the thing could neither be nor be conceived to be Thus rationality was of the essence of man because without rationality man could not be conceived to exist The different attributes which made up the essence of the thing were called its essential properties and a proposition in which any of these were predicated of it was called an Essential Proposition and was considered to go deeper into the nature of the thing and to convey more important information respecting it than any other proposition could do All properties not of the essence of the thing were called its accidents were supposed to have nothing at all or nothing comparatively to do with its inmost nature and the propositions in which any of these were predicated of it were called Accidental Propositions A connection may be traced between this distinction which originated with the schoolmen and the wellknown dogmas of substantiae secundae or general substances and substantial forms doctrines which under varieties of language pervaded alike the Aristotelian and the Platonic schools and of which more of the spirit has come down to modern times than might be conjectured from the disuse of the phraseology The false views of the nature of classification and generalization which prevailed among the schoolmen and of which these dogmas were the technical expression afford the only explanation which can be given of their having misunderstood the real nature of those Essences which held so conspicuous a place in their philosophy They said truly that man can not be conceived without rationality But though man can not a being may be conceived exactly like a man in all points except that one quality and those others which are the conditions or consequences of it All therefore which is really true in the assertion that man can not be conceived without rationality is only that if he had not rationality he would not be reputed a man There is no impossibility in conceiving the thing nor for aught we know in its existing the impossibility is in the conventions of language which will not allow the thing even if it exist to be called by the name which is reserved for rational beings Rationality in short is involved in the meaning of the word man is one of the attributes connoted by the name The essence of man simply means the whole of the attributes connoted by the word and any one of those attributes taken singly is an essential property of man But these reflections so easy to us would have been difficult to persons who thought as most of the later Aristotelians did that objects were made what they were called that gold for instance was made gold not by the possession of certain properties to which mankind have chosen to attach that name but by participation in the nature of a general substance called gold in general which substance together with all the properties that belonged to it inhered in every individual piece of gold As they did not consider these universal substances to be attached to all general names but only to some they thought that an object borrowed only a part of its properties from a universal substance and that the rest belonged to it individually the former they called its essence and the latter its accidents The scholastic doctrine of essences long survived the theory on which it rested that of the existence of real entities corresponding to general terms and it was reserved for Locke at the end of the seventeenth century to convince philosophers that the supposed essences of classes were merely the signification of their names nor among the signal services which his writings rendered to philosophy was there one more needful or more valuable Now as the most familiar of the general names by which an object is designated usually connotes not one only but several attributes of the object each of which attributes separately forms also the bond of union of some class and the meaning of some general name we may predicate of a name which connotes a variety of attributes another name which connotes only one of these attributes or some smaller number of them than all In such cases the universal affirmative proposition will be true since whatever possesses the whole of any set of attributes must possess any part of that same set A proposition of this sort however conveys no information to any one who previously understood the whole meaning of the terms The propositions Every man is a corporeal being Every man is a living creature Every man is rational convey no knowledge to any one who was already aware of the entire meaning of the word man for the meaning of the word includes all this and that every man has the attributes connoted by all these predicates is already asserted when he is called a man Now of this nature are all the propositions which have been called essential They are in fact identical propositions It is true that a proposition which predicates any attribute even though it be one implied in the name is in most cases understood to involve a tacit assertion that there exists a thing corresponding to the name and possessing the attributes connoted by it and this implied assertion may convey information even to those who understood the meaning of the name But all information of this sort conveyed by all the essential propositions of which man can be made the subject is included in the assertion Men exist And this assumption of real existence is after all the result of an imperfection of language It arises from the ambiguity of the copula which in addition to its proper office of a mark to show that an assertion is made is also as formerly remarked a concrete word connoting existence The actual existence of the subject of the proposition is therefore only apparently not really implied in the predication if an essential one we may say A ghost is a disembodied spirit without believing in ghosts But an accidental or nonessential affirmation does imply the real existence of the subject because in the case of a nonexistent subject there is nothing for the proposition to assert Such a proposition as The ghost of a murdered person haunts the couch of the murderer can only have a meaning if understood as implying a belief in ghosts for since the signification of the word ghost implies nothing of the kind the speaker either means nothing or means to assert a thing which he wishes to be believed to have really taken place It will be hereafter seen that when any important consequences seem to follow as in mathematics from an essential proposition or, in other words, from a proposition involved in the meaning of a name what they really flow from is the tacit assumption of the real existence of the objects so named Apart from this assumption of real existence the class of propositions in which the predicate is of the essence of the subject that is in which the predicate connotes the whole or part of what the subject connotes but nothing besides answer no purpose but that of unfolding the whole or some part of the meaning of the name to those who did not previously know it Accordingly the most useful and in strictness the only useful kind of essential propositions are Definitions which to be complete should unfold the whole of what is involved in the meaning of the word defined that is when it is a connotative word the whole of what it connotes In defining a name however it is not usual to specify its entire connotation but so much only as is sufficient to mark out the objects usually denoted by it from all other known objects And sometimes a merely accidental property not involved in the meaning of the name answers this purpose equally well The various kinds of definition which these distinctions give rise to and the purposes to which they are respectively subservient will be minutely considered in the proper place According to the above view of essential propositions no proposition can be reckoned such which relates to an individual by name that is in which the subject is a proper name Individuals have no essences When the schoolmen talked of the essence of an individual they did not mean the properties implied in its name for the names of individuals imply no properties They regarded as of the essence of an individual whatever was of the essence of the species in which they were accustomed to place that individual ie of the class to which it was most familiarly referred and to which therefore they conceived that it by nature belonged Thus because the proposition Man is a rational being was an essential proposition they affirmed the same thing of the proposition Julius Caesar is a rational being This followed very naturally if genera and species were to be considered as entities distinct from but inhering in the individuals composing them If man was a substance inhering in each individual man the essence of man whatever that might mean was naturally supposed to accompany it to inhere in John Thompson and to form the common essence of Thompson and Julius Caesar It might then be fairly said that rationality being of the essence of Man was of the essence also of Thompson But if Man altogether be only the individual men and a name bestowed upon them in consequence of certain common properties what becomes of John Thompson’s essence A fundamental error is seldom expelled from philosophy by a single victory It retreats slowly defends every inch of ground and often after it has been driven from the open country retains a footing in some remote fastness The essences of individuals were an unmeaning figment arising from a misapprehension of the essences of classes yet even Locke when he extirpated the parent error could not shake himself free from that which was its fruit He distinguished two sorts of essences Real and Nominal His nominal essences were the essences of classes explained nearly as we have now explained them Nor is any thing wanting to render the third book of Locke’s Essay a nearly unexceptional treatise on the connotation of names except to free its language from the assumption of what are called Abstract Ideas which unfortunately is involved in the phraseology though not necessarily connected with the thoughts contained in that immortal Third Book But besides nominal essences he admitted real essences or essences of individual objects which he supposed to be the causes of the sensible properties of those objects We know not said he what these are and this acknowledgment rendered the fiction comparatively innocuous but if we did we could from them alone demonstrate the sensible properties of the object as the properties of the triangle are demonstrated from the definition of the triangle I shall have occasion to revert to this theory in treating of Demonstration and of the conditions under which one property of a thing admits of being demonstrated from another property It is enough here to remark that according to this definition the real essence of an object has in the progress of physics come to be conceived as nearly equivalent in the case of bodies to their corpuscular structure what it is now supposed to mean in the case of any other entities I would not take upon myself to define An essential proposition then is one which is purely verbal which asserts of a thing under a particular name only what is asserted of it in the fact of calling it by that name and which therefore either gives no information or gives it respecting the name not the thing Nonessential or accidental propositions on the contrary may be called Real Propositions in opposition to Verbal They predicate of a thing some fact not involved in the signification of the name by which the proposition speaks of it some attribute not connoted by that name Such are all propositions concerning things individually designated and all general or particular propositions in which the predicate connotes any attribute not connoted by the subject All these if true add to our knowledge they convey information not already involved in the names employed When I am told that all or even that some objects which have certain qualities or which stand in certain relations have also certain other qualities or stand in certain other relations I learn from this proposition a new fact a fact not included in my knowledge of the meaning of the words nor even of the existence of Things answering to the signification of those words It is this class of propositions only which are in themselves instructive or from which any instructive propositions can be inferred Nothing has probably contributed more to the opinion so long prevalent of the futility of the school logic than the circumstance that almost all the examples used in the common school books to illustrate the doctrine of predication and that of the syllogism consist of essential propositions They were usually taken either from the branches or from the main trunk of the Predicamental Tree which included nothing but what was of the essence of the species Omne corpus est substantia Omne animal est corpus Omnis homo est corpus Omnis homo est animal Omnis homo est rationalis and so forth It is far from wonderful that the syllogistic art should have been thought to be of no use in assisting correct reasoning when almost the only propositions which in the hands of its professed teachers it was employed to prove were such as every one assented to without proof the moment he comprehended the meaning of the words and stood exactly on a level in point of evidence with the premises from which they were drawn I have therefore throughout this work avoided the employment of essential propositions as examples except where the nature of the principle to be illustrated specifically required them With respect to propositions which do convey information which assert something of a Thing under a name that does not already presuppose what is about to be asserted there are two different aspects in which these or rather such of them as are general propositions may be considered we may either look at them as portions of speculative truth or as memoranda for practical use According as we consider propositions in one or the other of these lights their import may be conveniently expressed in one or in the other of two formulas According to the formula which we have hitherto employed and which is best adapted to express the import of the proposition as a portion of our theoretical knowledge All men are mortal means that the attributes of man are always accompanied by the attribute mortality No men are gods means that the attributes of man are never accompanied by the attributes or at least never by all the attributes signified by the word god But when the proposition is considered as a memorandum for practical use we shall find a different mode of expressing the same meaning better adapted to indicate the office which the proposition performs The practical use of a proposition is to apprise or remind us what we have to expect in any individual case which comes within the assertion contained in the proposition In reference to this purpose the proposition All men are mortal means that the attributes of man are evidence of are a mark of mortality an indication by which the presence of that attribute is made manifest No men are gods means that the attributes of man are a mark or evidence that some or all of the attributes understood to belong to a god are not there that where the former are we need not expect to find the latter These two forms of expression are at bottom equivalent but the one points the attention more directly to what a proposition means the latter to the manner in which it is to be used Now it is to be observed that Reasoning the subject to which we are next to proceed is a process into which propositions enter not as ultimate results but as means to the establishment of other propositions We may expect therefore that the mode of exhibiting the import of a general proposition which shows it in its application to practical use will best express the function which propositions perform in Reasoning And accordingly in the theory of Reasoning the mode of viewing the subject which considers a Proposition as asserting that one fact or phenomenon is a mark or evidence of another fact or phenomenon will be found almost indispensable For the purposes of that Theory the best mode of defining the import of a proposition is not the mode which shows most clearly what it is in itself but that which most distinctly suggests the manner in which it may be made available for advancing from it to other propositions In examining into the nature of general propositions we have adverted much less than is usual with logicians to the ideas of a Class and Classification ideas which since the Realist doctrine of General Substances went out of vogue have formed the basis of almost every attempt at a philosophical theory of general terms and general propositions We have considered general names as having a meaning quite independently of their being the names of classes That circumstance is in truth accidental it being wholly immaterial to the signification of the name whether there are many objects or only one to which it happens to be applicable or whether there be any at all God is as much a general term to the Christian or Jew as to the Polytheist and dragon hippogriff chimera mermaid ghost are as much so as if real objects existed corresponding to those names Every name the signification of which is constituted by attributes is potentially a name of an indefinite number of objects but it needs not be actually the name of any and if of any it may be the name of only one As soon as we employ a name to connote attributes the things be they more or fewer which happen to possess those attributes are constituted ipso facto a class But in predicating the name we predicate only the attributes and the fact of belonging to a class does not in many cases come into view at all Although however Predication does not presuppose Classification and though the theory of Names and of Propositions is not cleared up but only encumbered by intruding the idea of classification into it there is nevertheless a close connection between Classification and the employment of General Names By every general name which we introduce we create a class if there be any things real or imaginary to compose it that is any Things corresponding to the signification of the name Classes therefore mostly owe their existence to general language But general language also though that is not the most common case sometimes owes its existence to classes A general which is as much as to say a significant name is indeed mostly introduced because we have a signification to express by it because we need a word by means of which to predicate the attributes which it connotes But it is also true that a name is sometimes introduced because we have found it convenient to create a class because we have thought it useful for the regulation of our mental operations that a certain group of objects should be thought of together A naturalist for purposes connected with his particular science sees reason to distribute the animal or vegetable creation into certain groups rather than into any others and he requires a name to bind as it were each of his groups together It must not however be supposed that such names when introduced differ in any respect as to their mode of signification from other connotative names The classes which they denote are as much as any other classes constituted by certain common attributes and their names are significant of those attributes and of nothing else The names of Cuvier’s classes and orders Plantigrades Digitigrades etc are as much the expression of attributes as if those names had preceded instead of grown out of his classification of animals The only peculiarity of the case is that the convenience of classification was here the primary motive for introducing the names while in other cases the name is introduced as a means of predication and the formation of a class denoted by it is only an indirect consequence The principles which ought to regulate Classification as a logical process subservient to the investigation of truth can not be discussed to any purpose until a much later stage of our inquiry But of Classification as resulting from and implied in the fact of employing general language we can not forbear to treat here without leaving the theory of general names and of their employment in predication mutilated and formless This portion of the theory of general language is the subject of what is termed the doctrine of the Predicables a set of distinctions handed down from Aristotle and his follower Porphyry many of which have taken a firm root in scientific and some of them even in popular phraseology The predicables are a fivefold division of General Names not grounded as usual on a difference in their meaning that is in the attribute which they connote but on a difference in the kind of class which they denote We may predicate of a thing five different varieties of classname A genus of the thing A species A differentia A proprium An accidens It is to be remarked of these distinctions that they express not what the predicate is in its own meaning but what relation it bears to the subject of which it happens on the particular occasion to be predicated There are not some names which are exclusively genera and others which are exclusively species or differentiae but the same name is referred to one or another predicable according to the subject of which it is predicated on the particular occasion Animal for instance is a genus with respect to man or John a species with respect to Substance or Being Rectangular is one of the Differentiae of a geometrical square it is merely one of the Accidentia of the table at which I am writing The words genus species etc are therefore relative terms they are names applied to certain predicates to express the relation between them and some given subject a relation grounded as we shall see not on what the predicate connotes but on the class which it denotes and on the place which in some given classification that class occupies relatively to the particular subject Of these five names two Genus and Species are not only used by naturalists in a technical acceptation not precisely agreeing with their philosophical meaning but have also acquired a popular acceptation much more general than either In this popular sense any two classes one of which includes the whole of the other and more may be called a Genus and a Species Such for instance are Animal and Man Man and Mathematician Animal is a Genus Man and Brute are its two species or we may divide it into a greater number of species as man horse dog etc Biped or twofooted animal may also be considered a genus of which man and bird are two species Taste is a genus of which sweet taste sour taste salt taste etc are species Virtue is a genus justice prudence courage fortitude generosity etc are its species The same class which is a genus with reference to the subclasses or species included in it may be itself a species with reference to a more comprehensive or as it is often called a superior genus Man is a species with reference to animal but a genus with reference to the species Mathematician Animal is a genus divided into two species man and brute but animal is also a species which with another species vegetable makes up the genus organized being Biped is a genus with reference to man and bird but a species with respect to the superior genus animal Taste is a genus divided into species but also a species of the genus sensation Virtue a genus with reference to justice temperance etc is one of the species of the genus mental quality In this popular sense the words Genus and Species have passed into common discourse And it should be observed that in ordinary parlance not the name of the class but the class itself is said to be the genus or species not of course the class in the sense of each individual of the class but the individuals collectively considered as an aggregate whole the name by which the class is designated being then called not the genus or species but the generic or specific name And this is an admissible form of expression nor is it of any importance which of the two modes of speaking we adopt provided the rest of our language is consistent with it but if we call the class itself the genus we must not talk of predicating the genus We predicate of man the name mortal and by predicating the name we may be said in an intelligible sense to predicate what the name expresses the attribute mortality but in no allowable sense of the word predication do we predicate of man the class mortal We predicate of him the fact of belonging to the class By the Aristotelian logicians the terms genus and species were used in a more restricted sense They did not admit every class which could be divided into other classes to be a genus or every class which could be included in a larger class to be a species Animal was by them considered a genus man and brute coordinate species under that genus biped however would not have been admitted to be a genus with reference to man but a proprium or accidens only It was requisite according to their theory that genus and species should be of the essence of the subject Animal was of the essence of man biped was not And in every classification they considered some one class as the lowest or infima species Man for instance was a lowest species Any further divisions into which the class might be capable of being broken down as man into white black and red man or into priest and layman they did not admit to be species It has been seen however in the preceding chapter that the distinction between the essence of a class and the attributes or properties which are not of its essence a distinction which has given occasion to so much abstruse speculation and to which so mysterious a character was formerly and by many writers is still attached amounts to nothing more than the difference between those attributes of the class which are and those which are not involved in the signification of the classname As applied to individuals the word Essence we found has no meaning except in connection with the exploded tenets of the Realists and what the schoolmen chose to call the essence of an individual was simply the essence of the class to which that individual was most familiarly referred Is there no difference then save this merely verbal one between the classes which the schoolmen admitted to be genera or species and those to which they refused the title Is it an error to regard some of the differences which exist among objects as differences in kind genere or specie and others only as differences in the accidents Were the schoolmen right or wrong in giving to some of the classes into which things may be divided the name of kinds and considering others as secondary divisions grounded on differences of a comparatively superficial nature Examination will show that the Aristotelians did mean something by this distinction and something important but which being but indistinctly conceived was inadequately expressed by the phraseology of essences and the various other modes of speech to which they had recourse It is a fundamental principle in logic that the power of framing classes is unlimited as long as there is any even the smallest difference to found a distinction upon Take any attribute whatever and if some things have it and others have not we may ground on the attribute a division of all things into two classes and we actually do so the moment we create a name which connotes the attribute The number of possible classes therefore is boundless and there are as many actual classes either of real or of imaginary things as there are general names positive and negative together But if we contemplate any one of the classes so formed such as the class animal or plant or the class sulphur or phosphorus or the class white or red and consider in what particulars the individuals included in the class differ from those which do not come within it we find a very remarkable diversity in this respect between some classes and others There are some classes the things contained in which differ from other things only in certain particulars which may be numbered while others differ in more than can be numbered more even than we need ever expect to know Some classes have little or nothing in common to characterize them by except precisely what is connoted by the name white things for example are not distinguished by any common properties except whiteness or if they are it is only by such as are in some way dependent on or connected with whiteness But a hundred generations have not exhausted the common properties of animals or of plants of sulphur or of phosphorus nor do we suppose them to be exhaustible but proceed to new observations and experiments in the full confidence of discovering new properties which were by no means implied in those we previously knew While if any one were to propose for investigation the common properties of all things which are of the same colour the same shape or the same specific gravity the absurdity would be palpable We have no ground to believe that any such common properties exist except such as may be shown to be involved in the supposition itself or to be derivable from it by some law of causation It appears therefore that the properties on which we ground our classes sometimes exhaust all that the class has in common or contain it all by some mode of implication but in other instances we make a selection of a few properties from among not only a greater number but a number inexhaustible by us and to which as we know no bounds they may so far as we are concerned be regarded as infinite There is no impropriety in saying that of these two classifications the one answers to a much more radical distinction in the things themselves than the other does And if any one even chooses to say that the one classification is made by nature the other by us for our convenience he will be right provided he means no more than this Where a certain apparent difference between things though perhaps in itself of little moment answers to we know not what number of other differences pervading not only their known properties but properties yet undiscovered it is not optional but imperative to recognize this difference as the foundation of a specific distinction while on the contrary differences that are merely finite and determinate like those designated by the words white black or red may be disregarded if the purpose for which the classification is made does not require attention to those particular properties The differences however are made by nature in both cases while the recognition of those differences as grounds of classification and of naming is equally in both cases the act of man only in the one case the ends of language and of classification would be subverted if no notice were taken of the difference while in the other case the necessity of taking notice of it depends on the importance or unimportance of the particular qualities in which the difference happens to consist Now these classes distinguished by unknown multitudes of properties and not solely by a few determinate ones which are parted off from one another by an unfathomable chasm instead of a mere ordinary ditch with a visible bottom are the only classes which by the Aristotelian logicians were considered as genera or species Differences which extended only to a certain property or properties and there terminated they considered as differences only in the accidents of things but where any class differed from other things by an infinite series of differences known and unknown they considered the distinction as one of kind and spoke of it as being an essential difference which is also one of the current meanings of that vague expression at the present day Conceiving the schoolmen to have been justified in drawing a broad line of separation between these two kinds of classes and of classdistinctions I shall not only retain the division itself but continue to express it in their language According to that language the proximate or lowest Kind to which any individual is referable is called its species Conformably to this Isaac Newton would be said to be of the species man There are indeed numerous subclasses included in the class man to which Newton also belongs for example Christian and Englishman and Mathematician But these though distinct classes are not in our sense of the term distinct Kinds of men A Christian for example differs from other human beings but he differs only in the attribute which the word expresses namely belief in Christianity and whatever else that implies either as involved in the fact itself or connected with it through some law of cause and effect. We should never think of inquiring what properties unconnected with Christianity either as cause or effect are common to all Christians and peculiar to them while in regard to all Men physiologists are perpetually carrying on such an inquiry nor is the answer ever likely to be completed Man therefore we may call a species Christian or Mathematician we can not Note here that it is by no means intended to imply that there may not be different Kinds or logical species of man The various races and temperaments the two sexes and even the various ages may be differences of kind within our meaning of the term I do not say that they are so For in the progress of physiology it may almost be said to be made out that the differences which really exist between different races sexes etc follow as consequences under laws of nature from a small number of primary differences which can be precisely determined and which as the phrase is account for all the rest If this be so these are not distinctions in kind no more than Christian Jew Mussulman and Pagan a difference which also carries many consequences along with it And in this way classes are often mistaken for real Kinds which are afterward proved not to be so But if it turned out that the differences were not capable of being thus accounted for then Caucasian Mongolian Negro etc would be really different Kinds of human beings and entitled to be ranked as species by the logician though not by the naturalist For as already noticed the word species is used in a different signification in logic and in natural history By the naturalist organized beings are not usually said to be of different species if it is supposed that they have descended from the same stock That however is a sense artificially given to the word for the technical purposes of a particular science To the logician if a negro and a white man differ in the same manner however less in degree as a horse and a camel do that is if their differences are inexhaustible and not referable to any common cause they are different species whether they are descended from common ancestors or not But if their differences can all be traced to climate and habits or to some one or a few special differences in structure they are not in the logician’s view specifically distinct When the infima species or proximate Kind to which an individual belongs has been ascertained the properties common to that Kind include necessarily the whole of the common properties of every other real Kind to which the individual can be referable Let the individual for example be Socrates and the proximate Kind man Animal or living creature is also a real kind and includes Socrates but since it likewise includes man or in other words, since all men are animals the properties common to animals form a portion of the common properties of the subclass man And if there be any class which includes Socrates without including man that class is not a real Kind Let the class for example be flatnosed that being a class which includes Socrates without including all men To determine whether it is a real Kind we must ask ourselves this question Have all flatnosed animals in addition to whatever is implied in their flat noses any common properties other than those which are common to all animals whatever If they had if a flat nose were a mark or index to an indefinite number of other peculiarities not deducible from the former by an ascertainable law then out of the class man we might cut another class flatnosed man which according to our definition would be a Kind But if we could do this man would not be as it was assumed to be the proximate Kind Therefore the properties of the proximate Kind do comprehend those whether known or unknown of all other Kinds to which the individual belongs which was the point we undertook to prove And hence every other Kind which is predicable of the individual will be to the proximate Kind in the relation of a genus according to even the popular acceptation of the terms genus and species that is it will be a larger class including it and more We are now able to fix the logical meaning of these terms Every class which is a real Kind that is which is distinguished from all other classes by an indeterminate multitude of properties not derivable from one another is either a genus or a species A Kind which is not divisible into other Kinds can not be a genus because it has no species under it but it is itself a species both with reference to the individuals below and to the genera above Species Predicabilis and Species Subjicibilis But every Kind which admits of division into real Kinds as animal into mammal bird fish etc or bird into various species of birds is a genus to all below it a species to all genera in which it is itself included And here we may close this part of the discussion and pass to the three remaining predicables Differentia Proprium and Accidens To begin with Differentia This word is correlative with the words genus and species and as all admit it signifies the attribute which distinguishes a given species from every other species of the same genus This is so far clear but we may still ask which of the distinguishing attributes it signifies For we have seen that every Kind and a species must be a Kind is distinguished from other Kinds not by any one attribute but by an indefinite number Man for instance is a species of the genus animal Rational or rationality for it is of no consequence here whether we use the concrete or the abstract form is generally assigned by logicians as the Differentia and doubtless this attribute serves the purpose of distinction but it has also been remarked of man that he is a cooking animal the only animal that dresses its food This therefore is another of the attributes by which the species man is distinguished from other species of the same genus would this attribute serve equally well for a differentia The Aristotelians say No having laid it down that the differentia must like the genus and species be of the essence of the subject And here we lose even that vestige of a meaning grounded in the nature of the things themselves which may be supposed to be attached to the word essence when it is said that genus and species must be of the essence of the thing There can be no doubt that when the schoolmen talked of the essences of things as opposed to their accidents they had confusedly in view the distinction between differences of kind and the differences which are not of kind they meant to intimate that genera and species must be Kinds Their notion of the essence of a thing was a vague notion of a something which makes it what it is ie which makes it the Kind of thing that it is which causes it to have all that variety of properties which distinguish its Kind But when the matter came to be looked at more closely nobody could discover what caused the thing to have all those properties nor even that there was any thing which caused it to have them Logicians however not liking to admit this and being unable to detect what made the thing to be what it was satisfied themselves with what made it to be what it was called Of the innumerable properties known and unknown that are common to the class man a portion only and of course a very small portion are connoted by its name these few however will naturally have been thus distinguished from the rest either for their greater obviousness or for greater supposed importance These properties then which were connoted by the name logicians seized upon and called them the essence of the species and not stopping there they affirmed them in the case of the infima species to be the essence of the individual too for it was their maxim that the species contained the whole essence of the thing Metaphysics that fertile field of delusion propagated by language does not afford a more signal instance of such delusion On this account it was that rationality being connoted by the name man was allowed to be a differentia of the class but the peculiarity of cooking their food not being connoted was relegated to the class of accidental properties The distinction therefore between Differentia Proprium and Accidens is not grounded in the nature of things but in the connotation of names and we must seek it there if we wish to find what it is From the fact that the genus includes the species in other words denotes more than the species or is predicable of a greater number of individuals it follows that the species must connote more than the genus It must connote all the attributes which the genus connotes or there would be nothing to prevent it from denoting individuals not included in the genus And it must connote something besides otherwise it would include the whole genus Animal denotes all the individuals denoted by man and many more Man therefore must connote all that animal connotes otherwise there might be men who are not animals and it must connote something more than animal connotes otherwise all animals would be men This surplus of connotation this which the species connotes over and above the connotation of the genus is the Differentia or specific difference or to state the same proposition in other words the Differentia is that which must be added to the connotation of the genus to complete the connotation of the species The word man for instance exclusively of what it connotes in common with animal also connotes rationality and at least some approximation to that external form which we all know but which as we have no name for it considered in itself we are content to call the human The Differentia or specific difference therefore of man as referred to the genus animal is that outward form and the possession of reason The Aristotelians said the possession of reason without the outward form But if they adhered to this they would have been obliged to call the Houyhnhnms men The question never arose and they were never called upon to decide how such a case would have affected their notion of essentiality However this may be they were satisfied with taking such a portion of the differentia as sufficed to distinguish the species from all other existing things though by so doing they might not exhaust the connotation of the name And here to prevent the notion of differentia from being restricted within too narrow limits it is necessary to remark that a species even as referred to the same genus will not always have the same differentia but a different one according to the principle and purpose which preside over the particular classification For example a naturalist surveys the various kinds of animals and looks out for the classification of them most in accordance with the order in which for zoological purposes he considers it desirable that we should think of them With this view he finds it advisable that one of his fundamental divisions should be into warmblooded and coldblooded animals or into animals which breathe with lungs and those which breathe with gills or into carnivorous and frugivorous or graminivorous or into those which walk on the flat part and those which walk on the extremity of the foot a distinction on which two of Cuvier’s families are founded In doing this the naturalist creates as many new classes which are by no means those to which the individual animal is familiarly and spontaneously referred nor should we ever think of assigning to them so prominent a position in our arrangement of the animal kingdom unless for a preconceived purpose of scientific convenience And to the liberty of doing this there is no limit In the examples we have given most of the classes are real Kinds since each of the peculiarities is an index to a multitude of properties belonging to the class which it characterizes but even if the case were otherwise if the other properties of those classes could all be derived by any process known to us from the one peculiarity on which the class is founded even then if these derivative properties were of primary importance for the purposes of the naturalist he would be warranted in founding his primary divisions on them If however practical convenience is a sufficient warrant for making the main demarcations in our arrangement of objects run in lines not coinciding with any distinction of Kind and so creating genera and species in the popular sense which are not genera or species in the rigorous sense at all ˆ fortiori must we be warranted when our genera and species are real genera and species in marking the distinction between them by those of their properties which considerations of practical convenience most strongly recommend If we cut a species out of a given genus the species man for instance out of the genus animal with an intention on our part that the peculiarity by which we are to be guided in the application of the name man should be rationality then rationality is the differentia of the species man Suppose however that being naturalists we for the purposes of our particular study cut out of the genus animal the same species man but with an intention that the distinction between man and all other species of animal should be not rationality but the possession of four incisors in each jaw tusks solitary and erect posture It is evident that the word man when used by us as naturalists no longer connotes rationality but connotes the three other properties specified for that which we have expressly in view when we impose a name assuredly forms part of the meaning of that name We may therefore lay it down as a maxim that wherever there is a Genus and a Species marked out from that genus by an assignable differentia the name of the species must be connotative and must connote the differentia but the connotation may be special not involved in the signification of the term as ordinarily used but given to it when employed as a term of art or science The word Man in common use connotes rationality and a certain form but does not connote the number or character of the teeth in the Linnaean system it connotes the number of incisor and canine teeth but does not connote rationality nor any particular form The word man has therefore two different meanings though not commonly considered as ambiguous because it happens in both cases to denote the same individual objects But a case is conceivable in which the ambiguity would become evident we have only to imagine that some new kind of animal were discovered having Linnaeus’s three characteristics of humanity but not rational or not of the human form In ordinary parlance these animals would not be called men but in natural history they must still be called so by those if any there should be who adhere to the Linnaean classification and the question would arise whether the word should continue to be used in two senses or the classification be given up and the technical sense of the term be abandoned along with it Words not otherwise connotative may in the mode just adverted to acquire a special or technical connotation Thus the word whiteness as we have so often remarked connotes nothing it merely denotes the attribute corresponding to a certain sensation but if we are making a classification of colours and desire to justify or even merely to point out the particular place assigned to whiteness in our arrangement we may define it the colour produced by the mixture of all the simple rays and this fact though by no means implied in the meaning of the word whiteness as ordinarily used but only known by subsequent scientific investigation is part of its meaning in the particular essay or treatise and becomes the differentia of the species The differentia therefore of a species may be defined to be that part of the connotation of the specific name whether ordinary or special and technical which distinguishes the species in question from all other species of the genus to which on the particular occasion we are referring it Having disposed of Genus Species and Differentia we shall not find much difficulty in attaining a clear conception of the distinction between the other two predicables as well as between them and the first three In the Aristotelian phraseology Genus and Differentia are of the essence of the subject by which as we have seen is really meant that the properties signified by the genus and those signified by the differentia form part of the connotation of the name denoting the species Proprium and Accidens on the other hand form no part of the essence but are predicated of the species only accidentally Both are Accidents in the wider sense in which the accidents of a thing are opposed to its essence though in the doctrine of the Predicables Accidens is used for one sort of accident only Proprium being another sort Proprium continue the schoolmen is predicated accidentally indeed but necessarily or as they further explain it signifies an attribute which is not indeed part of the essence but which flows from or is a consequence of the essence and is therefore inseparably attached to the species eg the various properties of a triangle which though no part of its definition must necessarily be possessed by whatever comes under that definition Accidens on the contrary has no connection whatever with the essence but may come and go and the species still remain what it was before If a species could exist without its Propria it must be capable of existing without that on which its Propria are necessarily consequent and therefore without its essence without that which constitutes it a species But an Accidens whether separable or inseparable from the species in actual experience may be supposed separated without the necessity of supposing any other alteration or at least without supposing any of the essential properties of the species to be altered since with them an Accidens has no connection A Proprium therefore of the species may be defined any attribute which belongs to all the individuals included in the species and which though not connoted by the specific name either ordinarily if the classification we are considering be for ordinary purposes or specially if it be for a special purpose yet follows from some attribute which the name either ordinarily or specially connotes One attribute may follow from another in two ways and there are consequently two kinds of Proprium It may follow as a conclusion follows premises or it may follow as an effect follows a cause Thus the attribute of having the opposite sides equal which is not one of those connoted by the word Parallelogram nevertheless follows from those connoted by it namely from having the opposite sides straight lines and parallel and the number of sides four The attribute therefore of having the opposite sides equal is a Proprium of the class parallelogram and a Proprium of the first kind which follows from the connoted attributes by way of demonstration The attribute of being capable of understanding language is a Proprium of the species man since without being connoted by the word it follows from an attribute which the word does connote viz from the attribute of rationality But this is a Proprium of the second kind which follows by way of causation How it is that one property of a thing follows or can be inferred from another under what conditions this is possible and what is the exact meaning of the phrase are among the questions which will occupy us in the two succeeding Books At present it needs only be said that whether a Proprium follows by demonstration or by causation it follows necessarily that is to say its not following would be inconsistent with some law which we regard as a part of the constitution either of our thinking faculty or of the universe Under the remaining predicable Accidens are included all attributes of a thing which are neither involved in the signification of the name whether ordinarily or as a term of art nor have so far as we know any necessary connection with attributes which are so involved They are commonly divided into Separable and Inseparable Accidents Inseparable accidents are those which although we know of no connection between them and the attributes constitutive of the species and although therefore so far as we are aware they might be absent without making the name inapplicable and the species a different species are yet never in fact known to be absent A concise mode of expressing the same meaning is that inseparable accidents are properties which are universal to the species but not necessary to it Thus blackness is an attribute of a crow and as far as we know a universal one But if we were to discover a race of white birds in other respects resembling crows we should not say These are not crows we should say These are white crows Crow therefore does not connote blackness nor from any of the attributes which it does connote whether as a word in popular use or as a term of art could blackness be inferred Not only therefore can we conceive a white crow but we know of no reason why such an animal should not exist Since however none but black crows are known to exist blackness in the present state of our knowledge ranks as an accident but an inseparable accident of the species crow Separable Accidents are those which are found in point of fact, to be sometimes absent from the species which are not only not necessary but not even universal They are such as do not belong to every individual of the species but only to some individuals or if to all not at all times Thus the colour of a European is one of the separable accidents of the species man because it is not an attribute of all human creatures Being born is also speaking in the logical sense a separable accident of the species man because though an attribute of all human beings it is so only at one particular time A fortiori those attributes which are not constant even in the same individual as to be in one or in another place to be hot or cold sitting or walking must be ranked as separable accidents One necessary part of the theory of Names and of Propositions remains to be treated of in this place the theory of Definitions As being the most important of the class of propositions which we have characterized as purely verbal they have already received some notice in the chapter preceding the last But their fuller treatment was at that time postponed because definition is so closely connected with classification that until the nature of the latter process is in some measure understood the former can not be discussed to much purpose The simplest and most correct notion of a Definition is a proposition declaratory of the meaning of a word namely either the meaning which it bears in common acceptation or that which the speaker or writer for the particular purposes of his discourse intends to annex to it The definition of a word being the proposition which enunciates its meaning words which have no meaning are unsusceptible of definition Proper names therefore can not be defined A proper name being a mere mark put upon an individual and of which it is the characteristic property to be destitute of meaning its meaning can not of course be declared though we may indicate by language as we might indicate still more conveniently by pointing with the finger upon what individual that particular mark has been or is intended to be put It is no definition of John Thomson to say he is the son of General Thomson for the name John Thomson does not express this Neither is it any definition of John Thomson to say he is the man now crossing the street These propositions may serve to make known who is the particular man to whom the name belongs but that may be done still more unambiguously by pointing to him which however has not been esteemed one of the modes of definition In the case of connotative names the meaning as has been so often observed is the connotation and the definition of a connotative name is the proposition which declares its connotation This might be done either directly or indirectly The direct mode would be by a proposition in this form Man or whatsoever the word may be is a name connoting such and such attributes or is a name which when predicated of any thing signifies the possession of such and such attributes by that thing Or thus Man is every thing which possesses such and such attributes Man is every thing which possesses corporeity organization life rationality and certain peculiarities of external form This form of definition is the most precise and least equivocal of any but it is not brief enough and is besides too technical for common discourse The more usual mode of declaring the connotation of a name is to predicate of it another name or names of known signification which connote the same aggregation of attributes This may be done either by predicating of the name intended to be defined another connotative name exactly synonymous as Man is a human being which is not commonly accounted a definition at all or by predicating two or more connotative names which make up among them the whole connotation of the name to be defined In this last case again we may either compose our definition of as many connotative names as there are attributes each attribute being connoted by one as Man is a corporeal organized animated rational being shaped so and so or we employ names which connote several of the attributes at once as Man is a rational animal shaped so and so The definition of a name according to this view of it is the sum total of all the essential propositions which can be framed with that name for their subject All propositions the truth of which is implied in the name all those which we are made aware of by merely hearing the name are included in the definition if complete and may be evolved from it without the aid of any other premises whether the definition expresses them in two or three words or in a larger number It is therefore not without reason that Condillac and other writers have affirmed a definition to be an analysis To resolve any complex whole into the elements of which it is compounded is the meaning of analysis and this we do when we replace one word which connotes a set of attributes collectively by two or more which connote the same attributes singly or in smaller groups From this however the question naturally arises in what manner are we to define a name which connotes only a single attribute for instance white which connotes nothing but whiteness rational which connotes nothing but the possession of reason It might seem that the meaning of such names could only be declared in two ways by a synonymous term if any such can be found or in the direct way already alluded to White is a name connoting the attribute whiteness Let us see however whether the analysis of the meaning of the name that is the breaking down of that meaning into several parts admits of being carried farther Without at present deciding this question as to the word white it is obvious that in the case of rational some further explanation may be given of its meaning than is contained in the proposition Rational is that which possesses the attribute of reason since the attribute reason itself admits of being defined And here we must turn our attention to the definitions of attributes or rather of the names of attributes that is of abstract names In regard to such names of attributes as are connotative and express attributes of those attributes there is no difficulty like other connotative names they are defined by declaring their connotation Thus the word fault may be defined a quality productive of evil or inconvenience Sometimes again the attribute to be defined is not one attribute but a union of several we have only therefore to put together the names of all the attributes taken separately and we obtain the definition of the name which belongs to them all taken together a definition which will correspond exactly to that of the corresponding concrete name For as we define a concrete name by enumerating the attributes which it connotes and as the attributes connoted by a concrete name form the entire signification of the corresponding abstract name the same enumeration will serve for the definition of both Thus if the definition of a human being be this a being corporeal animated rational shaped so and so the definition of humanity will be corporeity and animal life combined with rationality and with such and such a shape When on the other hand the abstract name does not express a complication of attributes but a single attribute we must remember that every attribute is grounded on some fact or phenomenon from which and which alone it derives its meaning To that fact or phenomenon called in a former chapter the foundation of the attribute we must therefore have recourse for its definition Now the foundation of the attribute may be a phenomenon of any degree of complexity consisting of many different parts either coexistent or in succession To obtain a definition of the attribute we must analyse the phenomenon into these parts Eloquence for example is the name of one attribute only but this attribute is grounded on external effects of a complicated nature flowing from acts of the person to whom we ascribe the attribute and by resolving this phenomenon of causation into its two parts the cause and the effect we obtain a definition of eloquence viz the power of influencing the feelings by speech or writing A name therefore whether concrete or abstract admits of definition provided we are able to analyse that is to distinguish into parts the attribute or set of attributes which constitute the meaning both of the concrete name and of the corresponding abstract if a set of attributes by enumerating them if a single attribute by dissecting the fact or phenomenon whether of perception or of internal consciousness which is the foundation of the attribute But further even when the fact is one of our simple feelings or states of consciousness and therefore unsusceptible of analysis the names both of the object and of the attribute still admit of definition or rather would do so if all our simple feelings had names Whiteness may be defined the property or power of exciting the sensation of white A white object may be defined an object which excites the sensation of white The only names which are unsusceptible of definition because their meaning is unsusceptible of analysis are the names of the simple feelings themselves These are in the same condition as proper names They are not indeed like proper names unmeaning for the words sensation of white signify that the sensation which I so denominate resembles other sensations which I remember to have had before and to have called by that name But as we have no words by which to recall those former sensations except the very word which we seek to define or some other which being exactly synonymous with it requires definition as much words can not unfold the signification of this class of names and we are obliged to make a direct appeal to the personal experience of the individual whom we address Having stated what seems to be the true idea of a Definition I proceed to examine some opinions of philosophers and some popular conceptions on the subject which conflict more or less with that idea The only adequate definition of a name is as already remarked one which declares the facts and the whole of the facts which the name involves in its signification But with most persons the object of a definition does not embrace so much they look for nothing more in a definition than a guide to the correct use of the term a protection against applying it in a manner inconsistent with custom and convention Any thing therefore is to them a sufficient definition of a term which will serve as a correct index to what the term denotes though not embracing the whole and sometimes perhaps not even any part of what it connotes This gives rise to two sorts of imperfect or unscientific definition Essential but incomplete Definitions and Accidental Definitions or Descriptions In the former a connotative name is defined by a part only of its connotation in the latter by something which forms no part of the connotation at all An example of the first kind of imperfect definitions is the following Man is a rational animal It is impossible to consider this as a complete definition of the word Man since as before remarked if we adhered to it we should be obliged to call the Houyhnhnms men but as there happen to be no Houyhnhnms this imperfect definition is sufficient to mark out and distinguish from all other things the objects at present denoted by man all the beings actually known to exist of whom the name is predicable Though the word is defined by some only among the attributes which it connotes not by all it happens that all known objects which possess the enumerated attributes possess also those which are omitted so that the field of predication which the word covers and the employment of it which is conformable to usage are as well indicated by the inadequate definition as by an adequate one Such definitions however are always liable to be overthrown by the discovery of new objects in nature Definitions of this kind are what logicians have had in view when they laid down the rule that the definition of a species should be per genus et differentiam Differentia being seldom taken to mean the whole of the peculiarities constitutive of the species but some one of those peculiarities only a complete definition would be per genus et differentias rather than differentiam It would include with the name of the superior genus not merely some attribute which distinguishes the species intended to be defined from all other species of the same genus but all the attributes implied in the name of the species which the name of the superior genus has not already implied The assertion however that a definition must of necessity consist of a genus and differentiae is not tenable It was early remarked by logicians that the summum genus in any classification having no genus superior to itself could not be defined in this manner Yet we have seen that all names except those of our elementary feelings are susceptible of definition in the strictest sense by setting forth in words the constituent parts of the fact or phenomenon of which the connotation of every word is ultimately composed Although the first kind of imperfect definition which defines a connotative term by a part only of what it connotes but a part sufficient to mark out correctly the boundaries of its denotation has been considered by the ancients and by logicians in general as a complete definition it has always been deemed necessary that the attributes employed should really form part of the connotation for the rule was that the definition must be drawn from the essence of the class and this would not have been the case if it had been in any degree made up of attributes not connoted by the name The second kind of imperfect definition therefore in which the name of a class is defined by any of its accidents that is by attributes which are not included in its connotation has been rejected from the rank of genuine Definition by all logicians and has been termed Description This kind of imperfect definition however takes its rise from the same cause as the other namely the willingness to accept as a definition any thing which whether it expounds the meaning of the name or not enables us to discriminate the things denoted by the name from all other things and consequently to employ the term in predication without deviating from established usage This purpose is duly answered by stating any no matter what of the attributes which are common to the whole of the class and peculiar to it or any combination of attributes which happens to be peculiar to it though separately each of those attributes may be common to it with some other things It is only necessary that the definition or description thus formed should be convertible with the name which it professes to define that is should be exactly coextensive with it being predicable of every thing of which it is predicable and of nothing of which it is not predicable though the attributes specified may have no connection with those which mankind had in view when they formed or recognized the class and gave it a name The following are correct definitions of Man according to this test Man is a mammiferous animal having by nature two hands for the human species answers to this description and no other animal does Man is an animal who cooks his food Man is a featherless biped What would otherwise be a mere description may be raised to the rank of a real definition by the peculiar purpose which the speaker or writer has in view As was seen in the preceding chapter it may for the ends of a particular art or science or for the more convenient statement of an author’s particular doctrines be advisable to give to some general name without altering its denotation a special connotation different from its ordinary one When this is done a definition of the name by means of the attributes which make up the special connotation though in general a mere accidental definition or description becomes on the particular occasion and for the particular purpose a complete and genuine definition This actually occurs with respect to one of the preceding examples Man is a mammiferous animal having two hands which is the scientific definition of man considered as one of the species in Cuvier’s distribution of the animal kingdom In cases of this sort though the definition is still a declaration of the meaning which in the particular instance the name is appointed to convey it can not be said that to state the meaning of the word is the purpose of the definition The purpose is not to expound a name but a classification The special meaning which Cuvier assigned to the word Man quite foreign to its ordinary meaning though involving no change in the denotation of the word was incidental to a plan of arranging animals into classes on a certain principle that is according to a certain set of distinctions And since the definition of Man according to the ordinary connotation of the word though it would have answered every other purpose of a definition would not have pointed out the place which the species ought to occupy in that particular classification he gave the word a special connotation that he might be able to define it by the kind of attributes on which for reasons of scientific convenience he had resolved to found his division of animated nature Scientific definitions whether they are definitions of scientific terms or of common terms used in a scientific sense are almost always of the kind last spoken of their main purpose is to serve as the landmarks of scientific classification And since the classifications in any science are continually modified as scientific knowledge advances the definitions in the sciences are also constantly varying A striking instance is afforded by the words Acid and Alkali especially the former As experimental discovery advanced the substances classed with acids have been constantly multiplying and by a natural consequence the attributes connoted by the word have receded and become fewer At first it connoted the attributes of combining with an alkali to form a neutral substance called a salt being compounded of a base and oxygen causticity to the taste and touch fluidity etc The true analysis of muriatic acid into chlorine and hydrogen caused the second property composition from a base and oxygen to be excluded from the connotation The same discovery fixed the attention of chemists upon hydrogen as an important element in acids and more recent discoveries having led to the recognition of its presence in sulphuric nitric and many other acids where its existence was not previously suspected there is now a tendency to include the presence of this element in the connotation of the word But carbonic acid silica sulphurous acid have no hydrogen in their composition that property can not therefore be connoted by the term unless those substances are no longer to be considered acids Causticity and fluidity have long since been excluded from the characteristics of the class by the inclusion of silica and many other substances in it and the formation of neutral bodies by combination with alkalis together with such electrochemical peculiarities as this is supposed to imply are now the only differentiae which form the fixed connotation of the word Acid as a term of chemical science What is true of the definition of any term of science is of course true of the definition of a science itself and accordingly as observed in the Introductory Chapter of this work the definition of a science must necessarily be progressive and provisional Any extension of knowledge or alteration in the current opinions respecting the subjectmatter may lead to a change more or less extensive in the particulars included in the science and its composition being thus altered it may easily happen that a different set of characteristics will be found better adapted as differentiae for defining its name In the same manner in which a special or technical definition has for its object to expound the artificial classification out of which it grows the Aristotelian logicians seem to have imagined that it was also the business of ordinary definition to expound the ordinary and what they deemed the natural classification of things namely the division of them into Kinds and to show the place which each Kind occupies as superior collateral or subordinate among other Kinds This notion would account for the rule that all definition must necessarily be per genus et differentiam and would also explain why a single differentia was deemed sufficient But to expound or express in words a distinction of Kind has already been shown to be an impossibility the very meaning of a Kind is that the properties which distinguish it do not grow out of one another and can not therefore be set forth in words even by implication otherwise than by enumerating them all and all are not known nor are ever likely to be so It is idle therefore to look to this as one of the purposes of a definition while if it be only required that the definition of a Kind should indicate what kinds include it or are included by it any definitions which expound the connotation of the names will do this for the name of each class must necessarily connote enough of its properties to fix the boundaries of the class If the definition therefore be a full statement of the connotation it is all that a definition can be required to be Of the two incomplete and popular modes of definition and in what they differ from the complete or philosophical mode enough has now been said We shall next examine an ancient doctrine once generally prevalent and still by no means exploded which I regard as the source of a great part of the obscurity hanging over some of the most important processes of the understanding in the pursuit of truth According to this the definitions of which we have now treated are only one of two sorts into which definitions may be divided viz definitions of names and definitions of things The former are intended to explain the meaning of a term the latter the nature of a thing the last being incomparably the most important This opinion was held by the ancient philosophers and by their followers with the exception of the Nominalists but as the spirit of modern metaphysics until a recent period has been on the whole a Nominalist spirit the notion of definitions of things has been to a certain extent in abeyance still continuing however to breed confusion in logic by its consequences indeed rather than by itself Yet the doctrine in its own proper form now and then breaks out and has appeared among other places where it was scarcely to be expected in a justly admired word Archbishop Whately’s Logic In a review of that work published by me in the Westminster Review for January 1828 and containing some opinions which I no longer entertain I find the following observations on the question now before us observations with which my present view of that question is still sufficiently in accordance The distinction between nominal and real definitions between definitions of words and what are called definitions of things though conformable to the ideas of most of the Aristotelian logicians can not as it appears to us be maintained We apprehend that no definition is ever intended to explain and unfold the nature of a thing’ It is some confirmation of our opinion that none of those writers who have thought that there were definitions of things have ever succeeded in discovering any criterion by which the definition of a thing can be distinguished from any other proposition relating to the thing The definition they say unfolds the nature of the thing but no definition can unfold its whole nature and every proposition in which any quality whatever is predicated of the thing unfolds some part of its nature The true state of the case we take to be this All definitions are of names and of names only but in some definitions it is clearly apparent that nothing is intended except to explain the meaning of the word while in others besides explaining the meaning of the word it is intended to be implied that there exists a thing corresponding to the word Whether this be or be not implied in any given case can not be collected from the mere form of the expression A centaur is an animal with the upper parts of a man and the lower parts of a horse’ and A triangle is a rectilinear figure with three sides’ are in form expressions precisely similar although in the former it is not implied that any thing conformable to the term really exists while in the latter it is as may be seen by substituting in both definitions the word means for is In the first expression A centaur means an animal’ etc the sense would remain unchanged in the second A triangle means’ etc the meaning would be altered since it would be obviously impossible to deduce any of the truths of geometry from a proposition expressive only of the manner in which we intend to employ a particular sign There are therefore expressions commonly passing for definitions which include in themselves more than the mere explanation of the meaning of a term But it is not correct to call an expression of this sort a peculiar kind of definition Its difference from the other kind consists in this that it is not a definition but a definition and something more The definition above given of a triangle obviously comprises not one but two propositions perfectly distinguishable The one is There may exist a figure bounded by three straight lines’ the other And this figure may be termed a triangle’ The former of these propositions is not a definition at all the latter is a mere nominal definition or explanation of the use and application of a term The first is susceptible of truth or falsehood and may therefore be made the foundation of a train of reasoning The latter can neither be true nor false the only character it is susceptible of is that of conformity or disconformity to the ordinary usage of language There is a real distinction then between definitions of names and what are erroneously called definitions of things but it is that the latter along with the meaning of a name covertly asserts a matter of fact This covert assertion is not a definition but a postulate The definition is a mere identical proposition which gives information only about the use of language and from which no conclusions affecting matters of fact can possibly be drawn The accompanying postulate on the other hand affirms a fact which may lead to consequences of every degree of importance It affirms the actual or possible existence of Things possessing the combination of attributes set forth in the definition and this if true may be foundation sufficient on which to build a whole fabric of scientific truth We have already made and shall often have to repeat the remark that the philosophers who overthrew Realism by no means got rid of the consequences of Realism but retained long afterward in their own philosophy numerous propositions which could only have a rational meaning as part of a Realistic system It had been handed down from Aristotle and probably from earlier times as an obvious truth that the science of Geometry is deduced from definitions This so long as a definition was considered to be a proposition unfolding the nature of the thing did well enough But Hobbes followed and rejected utterly the notion that a definition declares the nature of the thing or does any thing but state the meaning of a name yet he continued to affirm as broadly as any of his predecessors that the principia or original premises of mathematics and even of all science are definitions producing the singular paradox that systems of scientific truth nay all truths whatever at which we arrive by reasoning are deduced from the arbitrary conventions of mankind concerning the signification of words To save the credit of the doctrine that definitions are the premises of scientific knowledge the proviso is sometimes added that they are so only under a certain condition namely that they be framed conformably to the phenomena of nature that is that they ascribe such meanings to terms as shall suit objects actually existing But this is only an instance of the attempt so often made to escape from the necessity of abandoning old language after the ideas which it expresses have been exchanged for contrary ones From the meaning of a name we are told it is possible to infer physical facts provided the name has corresponding to it an existing thing But if this proviso be necessary from which of the two is the inference really drawn From the existence of a thing having the properties or from the existence of a name meaning them Take for instance any of the definitions laid down as premises in Euclid’s Elements the definition let us say of a circle This being analysed consists of two propositions the one an assumption with respect to a matter of fact the other a genuine definition A figure may exist having all the points in the line which bounds it equally distant from a single point within it Any figure possessing this property is called a circle Let us look at one of the demonstrations which are said to depend on this definition and observe to which of the two propositions contained in it the demonstration really appeals About the centre A describe the circle B C D Here is an assumption that a figure such as the definition expresses may be described which is no other than the postulate or covert assumption involved in the socalled definition But whether that figure be called a circle or not is quite immaterial The purpose would be as well answered in all respects except brevity were we to say Through the point B draw a line returning into itself of which every point shall be at an equal distance from the point A By this the definition of a circle would be got rid of and rendered needless but not the postulate implied in it without that the demonstration could not stand The circle being now described let us proceed to the consequence Since B C D is a circle the radius B A is equal to the radius C A B A is equal to C A not because B C D is a circle but because B C D is a figure with the radii equal Our warrant for assuming that such a figure about the centre A with the radius B A may be made to exist is the postulate Whether the admissibility of these postulates rests on intuition or on proof may be a matter of dispute but in either case they are the premises on which the theorems depend and while these are retained it would make no difference in the certainty of geometrical truths though every definition in Euclid and every technical term therein defined were laid aside It is perhaps superfluous to dwell at so much length on what is so nearly selfevident but when a distinction obvious as it may appear has been confounded and by powerful intellects it is better to say too much than too little for the purpose of rendering such mistakes impossible in future I will therefore detain the reader while I point out one of the absurd consequences flowing from the supposition that definitions as such are the premises in any of our reasonings except such as relate to words only If this supposition were true we might argue correctly from true premises and arrive at a false conclusion We should only have to assume as a premise the definition of a nonentity or rather of a name which has no entity corresponding to it Let this for instance be our definition A dragon is a serpent breathing flame This proposition considered only as a definition is indisputably correct A dragon is a serpent breathing flame the word means that The tacit assumption indeed if there were any such understood assertion of the existence of an object with properties corresponding to the definition would in the present instance be false Out of this definition we may carve the premises of the following syllogism A dragon is a thing which breathes flame A dragon is a serpent From which the conclusion is Therefore some serpent or serpents breathe flame an unexceptionable syllogism in the first mode of the third figure in which both premises are true and yet the conclusion false which every logician knows to be an absurdity The conclusion being false and the syllogism correct the premises can not be true But the premises considered as parts of a definition are true Therefore the premises considered as parts of a definition can not be the real ones The real premises must be A dragon is a really existing thing which breathes flame A dragon is a really existing serpent which implied premises being false the falsity of the conclusion presents no absurdity If we would determine what conclusion follows from the same ostensible premises when the tacit assumption of real existence is left out let us according to the recommendation in a previous page substitute means for is We then have Dragon is a word meaning a thing which breathes flame Dragon is a word meaning a serpent From which the conclusion is Some word or words which mean a serpent also mean a thing which breathes flame where the conclusion as well as the premises is true and is the only kind of conclusion which can ever follow from a definition namely a proposition relating to the meaning of words There is still another shape into which we may transform this syllogism We may suppose the middle term to be the designation neither of a thing nor of a name but of an idea We then have The idea of a dragon is an idea of a thing which breathes flame The idea of a dragon is an idea of a serpent Therefore there is an idea of a serpent which is an idea of a thing breathing flame Here the conclusion is true and also the premises but the premises are not definitions They are propositions affirming that an idea existing in the mind includes certain ideal elements The truth of the conclusion follows from the existence of the psychological phenomenon called the idea of a dragon and therefore still from the tacit assumption of a matter of fact When as in this last syllogism the conclusion is a proposition respecting an idea the assumption on which it depends may be merely that of the existence of an idea But when the conclusion is a proposition concerning a Thing the postulate involved in the definition which stands as the apparent premise is the existence of a thing conformable to the definition and not merely of an idea conformable to it This assumption of real existence we always convey the impression that we intend to make when we profess to define any name which is already known to be a name of really existing objects On this account it is that the assumption was not necessarily implied in the definition of a dragon while there was no doubt of its being included in the definition of a circle One of the circumstances which have contributed to keep up the notion that demonstrative truths follow from definitions rather than from the postulates implied in those definitions is that the postulates even in those sciences which are considered to surpass all others in demonstrative certainty are not always exactly true It is not true that a circle exists or can be described which has all its radii exactly equal Such accuracy is ideal only it is not found in nature still less can it be realized by art People had a difficulty therefore in conceiving that the most certain of all conclusions could rest on premises which instead of being certainly true are certainly not true to the full extent asserted This apparent paradox will be examined when we come to treat of Demonstration where we shall be able to show that as much of the postulate is true as is required to support as much as is true of the conclusion Philosophers however to whom this view had not occurred or whom it did not satisfy have thought it indispensable that there should be found in definitions something more certain or at least more accurately true than the implied postulate of the real existence of a corresponding object And this something they flattered themselves they had found when they laid it down that a definition is a statement and analysis not of the mere meaning of a word nor yet of the nature of a thing but of an idea Thus the proposition A circle is a plane figure bounded by a line all the points of which are at an equal distance from a given point within it was considered by them not as an assertion that any real circle has that property which would not be exactly true but that we conceive a circle as having it that our abstract idea of a circle is an idea of a figure with its radii exactly equal Conformably to this it is said that the subjectmatter of mathematics and of every other demonstrative science is not things as they really exist but abstractions of the mind A geometrical line is a line without breadth but no such line exists in nature it is a notion merely suggested to the mind by its experience of nature The definition it is said is a definition of this mental line not of any actual line and it is only of the mental line not of any line existing in nature that the theorems of geometry are accurately true Allowing this doctrine respecting the nature of demonstrative truth to be correct which in a subsequent place I shall endeavour to prove that it is not even on that supposition the conclusions which seem to follow from a definition do not follow from the definition as such but from an implied postulate Even if it be true that there is no object in nature answering to the definition of a line and that the geometrical properties of lines are not true of any lines in nature but only of the idea of a line the definition at all events postulates the real existence of such an idea it assumes that the mind can frame or rather has framed the notion of length without breadth and without any other sensible property whatever To me indeed it appears that the mind can not form any such notion it can not conceive length without breadth it can only in contemplating objects attend to their length exclusively of their other sensible qualities and so determine what properties may be predicated of them in virtue of their length alone If this be true the postulate involved in the geometrical definition of a line is the real existence not of length without breadth but merely of length that is of long objects This is quite enough to support all the truths of geometry since every property of a geometrical line is really a property of all physical objects in so far as possessing length But even what I hold to be the false doctrine on the subject leaves the conclusion that our reasonings are grounded on the matters of fact postulated in definitions and not on the definitions themselves entirely unaffected and accordingly this conclusion is one which I have in common with Dr Whewell in his Philosophy of the Inductive Sciences though on the nature of demonstrative truth Dr Whewell’s opinions are greatly at variance with mine And here as in many other instances I gladly acknowledge that his writings are eminently serviceable in clearing from confusion the initial steps in the analysis of the mental processes even where his views respecting the ultimate analysis are such as though with unfeigned respect I can not but regard as fundamentally erroneous Although according to the opinion here presented Definitions are properly of names only and not of things it does not follow from this that definitions are arbitrary How to define a name may not only be an inquiry of considerable difficulty and intricacy but may involve considerations going deep into the nature of the things which are denoted by the name Such for instance are the inquiries which form the subjects of the most important of Plato’s Dialogues as What is rhetoric the topic of the Gorgias or What is justice that of the Republic Such also is the question scornfully asked by Pilate What is truth and the fundamental question with speculative moralists in all ages What is virtue It would be a mistake to represent these difficult and noble inquiries as having nothing in view beyond ascertaining the conventional meaning of a name They are inquiries not so much to determine what is as what should be the meaning of a name which like other practical questions of terminology requires for its solution that we should enter and sometimes enter very deeply into the properties not merely of names but of the things named Although the meaning of every concrete general name resides in the attributes which it connotes the objects were named before the attributes as appears from the fact that in all languages abstract names are mostly compounds or other derivatives of the concrete names which correspond to them Connotative names therefore were after proper names the first which were used and in the simpler cases no doubt a distinct connotation was present to the minds of those who first used the name and was distinctly intended by them to be conveyed by it The first person who used the word white as applied to snow or to any other object knew no doubt very well what quality he intended to predicate and had a perfectly distinct conception in his mind of the attribute signified by the name But where the resemblances and differences on which our classifications are founded are not of this palpable and easily determinable kind especially where they consist not in any one quality but in a number of qualities the effects of which being blended together are not very easily discriminated and referred each to its true source it often happens that names are applied to nameable objects with no distinct connotation present to the minds of those who apply them They are only influenced by a general resemblance between the new object and all or some of the old familiar objects which they have been accustomed to call by that name This as we have seen is the law which even the mind of the philosopher must follow in giving names to the simple elementary feelings of our nature but where the things to be named are complex wholes a philosopher is not content with noticing a general resemblance he examines what the resemblance consists in and he only gives the same name to things which resemble one another in the same definite particulars The philosopher therefore habitually employs his general names with a definite connotation But language was not made and can only in some small degree be mended by philosophers In the minds of the real arbiters of language general names especially where the classes they denote can not be brought before the tribunal of the outward senses to be identified and discriminated connote little more than a vague gross resemblance to the things which they were earliest or have been most accustomed to call by those names When for instance ordinary persons predicate the words just or unjust of any action noble or mean of any sentiment expression or demeanour statesman or charlatan of any personage figuring in politics do they mean to affirm of those various subjects any determinate attributes of whatever kind No they merely recognize as they think some likeness more or less vague and loose between these and some other things which they have been accustomed to denominate or to hear denominated by those appellations Language as Sir James Mackintosh used to say of governments is not made but grows A name is not imposed at once and by previous purpose upon a class of objects but is first applied to one thing and then extended by a series of transitions to another and another By this process as has been remarked by several writers and illustrated with great force and clearness by Dugald Stewart in his Philosophical Essays a name not unfrequently passes by successive links of resemblance from one object to another until it becomes applied to things having nothing in common with the first things to which the name was given which however do not for that reason drop the name so that it at last denotes a confused huddle of objects having nothing whatever in common and connotes nothing not even a vague and general resemblance When a name has fallen into this state in which by predicating it of any object we assert literally nothing about the object it has become unfit for the purposes either of thought or of the communication of thought and can only be made serviceable by stripping it of some part of its multifarious denotation and confining it to objects possessed of some attributes in common which it may be made to connote Such are the inconveniences of a language which is not made but grows Like the governments which are in a similar case it may be compared to a road which is not made but has made itself it requires continual mending in order to be passable From this it is already evident why the question respecting the definition of an abstract name is often one of so much difficulty The question What is justice is in other words What is the attribute which mankind mean to predicate when they call an action just To which the first answer is that having come to no precise agreement on the point they do not mean to predicate distinctly any attribute at all Nevertheless all believe that there is some common attribute belonging to all the actions which they are in the habit of calling just The question then must be whether there is any such common attribute and in the first place whether mankind agree sufficiently with one another as to the particular actions which they do or do not call just to render the inquiry what quality those actions have in common a possible one if so whether the actions really have any quality in common and if they have what it is Of these three the first alone is an inquiry into usage and convention the other two are inquiries into matters of fact And if the second question whether the actions form a class at all has been answered negatively there remains a fourth often more arduous than all the rest namely how best to form a class artificially which the name may denote And here it is fitting to remark that the study of the spontaneous growth of languages is of the utmost importance to those who would logically remodel them The classifications rudely made by established language when retouched as they almost all require to be by the hands of the logician are often themselves excellently suited to his purposes As compared with the classifications of a philosopher they are like the customary law of a country which has grown up as it were spontaneously compared with laws methodized and digested into a code the former are a far less perfect instrument than the latter but being the result of a long though unscientific course of experience they contain a mass of materials which may be made very usefully available in the formation of the systematic body of written law In like manner the established grouping of objects under a common name even when founded only on a gross and general resemblance is evidence in the first place that the resemblance is obvious and therefore considerable and in the next place that it is a resemblance which has struck great numbers of persons during a series of years and ages Even when a name by successive extensions has come to be applied to things among which there does not exist this gross resemblance common to them all still at every step in its progress we shall find such a resemblance And these transitions of the meaning of words are often an index to real connections between the things denoted by them which might otherwise escape the notice of thinkers of those at least who from using a different language or from any difference in their habitual associations have fixed their attention in preference on some other aspect of the things The history of philosophy abounds in examples of such oversights committed for want of perceiving the hidden link that connected together the seemingly disparate meanings of some ambiguous word Whenever the inquiry into the definition of the name of any real object consists of any thing else than a mere comparison of authorities we tacitly assume that a meaning must be found for the name compatible with its continuing to denote if possible all but at any rate the greater or the more important part of the things of which it is commonly predicated The inquiry therefore into the definition is an inquiry into the resemblances and differences among those things whether there be any resemblance running through them all if not through what portion of them such a general resemblance can be traced and finally what are the common attributes the possession of which gives to them all or to that portion of them the character of resemblance which has led to their being classed together When these common attributes have been ascertained and specified the name which belongs in common to the resembling objects acquires a distinct instead of a vague connotation and by possessing this distinct connotation becomes susceptible of definition In giving a distinct connotation to the general name the philosopher will endeavour to fix upon such attributes as while they are common to all the things usually denoted by the name are also of greatest importance in themselves either directly or from the number the conspicuousness or the interesting character of the consequences to which they lead He will select as far as possible such differentiae as lead to the greatest number of interesting propria For these rather than the more obscure and recondite qualities on which they often depend give that general character and aspect to a set of objects which determine the groups into which they naturally fall But to penetrate to the more hidden agreement on which these obvious and superficial agreements depend is often one of the most difficult of scientific problems As it is among the most difficult so it seldom fails to be among the most important And since upon the result of this inquiry respecting the causes of the properties of a class of things there incidentally depends the question what shall be the meaning of a word some of the most profound and most valuable investigations which philosophy presents to us have been introduced by and have offered themselves under the guise of inquiries into the definition of a name In the preceding Book we have been occupied not with the nature of Proof but with the nature of Assertion the import conveyed by a Proposition whether that Proposition be true or false not the means by which to discriminate true from false Propositions The proper subject however of Logic is Proof Before we could understand what Proof is it was necessary to understand what that is to which proof is applicable what that is which can be a subject of belief or disbelief of affirmation or denial what in short the different kinds of Propositions assert This preliminary inquiry we have prosecuted to a definite result Assertion in the first place relates either to the meaning of words or to some property of the things which words signify Assertions respecting the meaning of words among which definitions are the most important hold a place and an indispensable one in philosophy but as the meaning of words is essentially arbitrary this class of assertions are not susceptible of truth or falsity nor therefore of proof or disproof Assertions respecting Things or what may be called Real Propositions in contradistinction to verbal ones are of various sorts We have analysed the import of each sort and have ascertained the nature of the things they relate to and the nature of what they severally assert respecting those things We found that whatever be the form of the proposition and whatever its nominal subject or predicate the real subject of every proposition is some one or more facts or phenomena of consciousness or some one or more of the hidden causes or powers to which we ascribe those facts and that what is predicated or asserted either in the affirmative or negative of those phenomena or those powers is always either Existence Order in Place Order in Time Causation or Resemblance This then is the theory of the Import of Propositions reduced to its ultimate elements but there is another and a less abstruse expression for it which though stopping short in an earlier stage of the analysis is sufficiently scientific for many of the purposes for which such a general expression is required This expression recognizes the commonly received distinction between Subject and Attribute and gives the following as the analysis of the meaning of propositions Every Proposition asserts that some given subject does or does not possess some attribute or that some attribute is or is not either in all or in some portion of the subjects in which it is met with conjoined with some other attribute We shall now for the present take our leave of this portion of our inquiry and proceed to the peculiar problem of the Science of Logic namely how the assertions of which we have analysed the import are proved or disproved such of them at least as not being amenable to direct consciousness or intuition are appropriate subjects of proof We say of a fact or statement that it is proved when we believe its truth by reason of some other fact or statement from which it is said to follow Most of the propositions whether affirmative or negative universal particular or singular which we believe are not believed on their own evidence but on the ground of something previously assented to from which they are said to be inferred To infer a proposition from a previous proposition or propositions to give credence to it or claim credence for it as a conclusion from something else is to reason in the most extensive sense of the term There is a narrower sense in which the name reasoning is confined to the form of inference which is termed ratiocination and of which the syllogism is the general type The reasons for not conforming to this restricted use of the term were stated in an earlier stage of our inquiry and additional motives will be suggested by the considerations on which we are now about to enter In proceeding to take into consideration the cases in which inferences can legitimately be drawn we shall first mention some cases in which the inference is apparent not real and which require notice chiefly that they may not be confounded with cases of inference properly so called This occurs when the proposition ostensibly inferred from another appears on analysis to be merely a repetition of the same or part of the same assertion which was contained in the first All the cases mentioned in books of Logic as examples of equipollency or equivalence of propositions are of this nature Thus if we were to argue No man is incapable of reason for every man is rational or All men are mortal for no man is exempt from death it would be plain that we were not proving the proposition but only appealing to another mode of wording it which may or may not be more readily comprehensible by the hearer or better adapted to suggest the real proof but which contains in itself no shadow of proof Another case is where from a universal proposition we affect to infer another which differs from it only in being particular as All A is B therefore Some A is B No A is B therefore Some A is not B This too is not to conclude one proposition from another but to repeat a second time something which had been asserted at first with the difference that we do not here repeat the whole of the previous assertion but only an indefinite part of it A third case is where the antecedent having affirmed a predicate of a given subject the consequent affirms of the same subject something already connoted by the former predicate as Socrates is a man therefore Socrates is a living creature where all that is connoted by living creature was affirmed of Socrates when he was asserted to be a man If the propositions are negative we must invert their order thus Socrates is not a living creature therefore he is not a man for if we deny the less the greater which includes it is already denied by implication These therefore are not really cases of inference and yet the trivial examples by which in manuals of Logic the rules of the syllogism are illustrated are often of this illchosen kind formal demonstrations of conclusions to which whoever understands the terms used in the statement of the data has already and consciously assented The most complex case of this sort of apparent inference is what is called the Conversion of propositions which consists in turning the predicate into a subject and the subject into a predicate and framing out of the same terms thus reversed another proposition which must be true if the former is true Thus from the particular affirmative proposition Some A is B we may infer that Some B is A From the universal negative No A is B we may conclude that No B is A From the universal affirmative proposition All A is B it can not be inferred that all B is A though all water is liquid it is not implied that all liquid is water but it is implied that some liquid is so and hence the proposition All A is B is legitimately convertible into Some B is A This process which converts a universal proposition into a particular is termed conversion per accidens From the proposition Some A is not B we can not even infer that some B is not A though some men are not Englishmen it does not follow that some Englishmen are not men The only mode usually recognized of converting a particular negative proposition is in the form Some A is not B therefore something which is not B is A and this is termed conversion by contraposition In this case however the predicate and subject are not merely reversed but one of them is changed Instead of A and B the terms of the new proposition are a thing which is not B and A The original proposition Some A is not B is first changed into a proposition equipollent with it Some A is a thing which is not B and the proposition being now no longer a particular negative but a particular affirmative admits of conversion in the first mode or as it is called simple conversion In all these cases there is not really any inference there is in the conclusion no new truth nothing but what was already asserted in the premises and obvious to whoever apprehends them The fact asserted in the conclusion is either the very same fact or part of the fact asserted in the original proposition This follows from our previous analysis of the Import of Propositions When we say for example that some lawful sovereigns are tyrants what is the meaning of the assertion That the attributes connoted by the term lawful sovereign and the attributes connoted by the term tyrant sometimes coexist in the same individual Now this is also precisely what we mean when we say that some tyrants are lawful sovereigns which therefore is not a second proposition inferred from the first any more than the English translation of Euclid’s Elements is a collection of theorems different from and consequences of those contained in the Greek original Again if we assert that no great general is a rash man we mean that the attributes connoted by great general and those connoted by rash never coexist in the same subject which is also the exact meaning which would be expressed by saying that no rash man is a great general When we say that all quadrupeds are warmblooded we assert not only that the attributes connoted by quadruped and those connoted by warmblooded sometimes coexist but that the former never exist without the latter now the proposition Some warmblooded creatures are quadrupeds expresses the first half of this meaning dropping the latter half and therefore has been already affirmed in the antecedent proposition All quadrupeds are warmblooded But that all warmblooded creatures are quadrupeds or, in other words, that the attributes connoted by warmblooded never exist without those connoted by quadruped has not been asserted and can not be inferred In order to reassert in an inverted form the whole of what was affirmed in the proposition All quadrupeds are warmblooded we must convert it by contraposition thus Nothing which is not warmblooded is a quadruped This proposition and the one from which it is derived are exactly equivalent and either of them may be substituted for the other for to say that when the attributes of a quadruped are present those of a warmblooded creature are present is to say that when the latter are absent the former are absent In a manual for young students it would be proper to dwell at greater length on the conversion and equipollency of propositions For though that can not be called reasoning or inference which is a mere reassertion in different words of what had been asserted before there is no more important intellectual habit nor any the cultivation of which falls more strictly within the province of the art of logic than that of discerning rapidly and surely the identity of an assertion when disguised under diversity of language That important chapter in logical treatises which relates to the Opposition of Propositions and the excellent technical language which logic provides for distinguishing the different kinds or modes of opposition are of use chiefly for this purpose Such considerations as these that contrary propositions may both be false but can not both be true that subcontrary propositions may both be true but can not both be false that of two contradictory propositions one must be true and the other false that of two subalternate propositions the truth of the universal proves the truth of the particular and the falsity of the particular proves the falsity of the universal but not vic versa are apt to appear at first sight very technical and mysterious but when explained seem almost too obvious to require so formal a statement since the same amount of explanation which is necessary to make the principles intelligible would enable the truths which they convey to be apprehended in any particular case which can occur In this respect however these axioms of logic are on a level with those of mathematics That things which are equal to the same thing are equal to one another is as obvious in any particular case as it is in the general statement and if no such general maxim had ever been laid down the demonstrations in Euclid would never have halted for any difficulty in stepping across the gap which this axiom at present serves to bridge over Yet no one has ever censured writers on geometry for placing a list of these elementary generalizations at the head of their treatises as a first exercise to the learner of the faculty which will be required in him at every step that of apprehending a general truth And the student of logic in the discussion even of such truths as we have cited above acquires habits of circumspect interpretation of words and of exactly measuring the length and breadth of his assertions which are among the most indispensable conditions of any considerable mental attainment and which it is one of the primary objects of logical discipline to cultivate Having noticed in order to exclude from the province of Reasoning or Inference properly so called the cases in which the progression from one truth to another is only apparent the logical consequent being a mere repetition of the logical antecedent we now pass to those which are cases of inference in the proper acceptation of the term those in which we set out from known truths to arrive at others really distinct from them Reasoning in the extended sense in which I use the term and in which it is synonymous with Inference is popularly said to be of two kinds reasoning from particulars to generals and reasoning from generals to particulars the former being called Induction the latter Ratiocination or Syllogism It will presently be shown that there is a third species of reasoning which falls under neither of these descriptions and which nevertheless is not only valid but is the foundation of both the others It is necessary to observe that the expressions reasoning from particulars to generals and reasoning from generals to particulars are recommended by brevity rather than by precision and do not adequately mark without the aid of a commentary the distinction between Induction in the sense now adverted to and Ratiocination The meaning intended by these expressions is that Induction is inferring a proposition from propositions less general than itself and Ratiocination is inferring a proposition from propositions equally or more general When from the observation of a number of individual instances we ascend to a general proposition or when by combining a number of general propositions we conclude from them another proposition still more general the process which is substantially the same in both instances is called Induction When from a general proposition not alone for from a single proposition nothing can be concluded which is not involved in the terms but by combining it with other propositions we infer a proposition of the same degree of generality with itself or a less general proposition or a proposition merely individual the process is Ratiocination When in short the conclusion is more general than the largest of the premises the argument is commonly called Induction when less general or equally general it is Ratiocination As all experience begins with individual cases and proceeds from them to generals it might seem most conformable to the natural order of thought that Induction should be treated of before we touch upon Ratiocination It will however be advantageous in a science which aims at tracing our acquired knowledge to its sources that the inquirer should commence with the latter rather than with the earlier stages of the process of constructing our knowledge and should trace derivative truths backward to the truths from which they are deduced and on which they depend for their evidence before attempting to point out the original spring from which both ultimately take their rise The advantages of this order of proceeding in the present instance will manifest themselves as we advance in a manner superseding the necessity of any further justification or explanation Of Induction therefore we shall say no more at present than that it at least is without doubt a process of real inference The conclusion in an induction embraces more than is contained in the premises The principle or law collected from particular instances the general proposition in which we embody the result of our experience covers a much larger extent of ground than the individual experiments which form its basis A principle ascertained by experience is more than a mere summing up of what has been specifically observed in the individual cases which have been examined it is a generalization grounded on those cases and expressive of our belief that what we there found true is true in an indefinite number of cases which we have not examined and are never likely to examine The nature and grounds of this inference and the conditions necessary to make it legitimate will be the subject of discussion in the Third Book but that such inference really takes place is not susceptible of question In every induction we proceed from truths which we knew to truths which we did not know from facts certified by observation to facts which we have not observed and even to facts not capable of being now observed future facts for example but which we do not hesitate to believe on the sole evidence of the induction itself Induction then is a real process of Reasoning or Inference Whether and in what sense as much can be said of the Syllogism remains to be determined by the examination into which we are about to enter The analysis of the Syllogism has been so accurately and fully performed in the common manuals of Logic that in the present work which is not designed as a manual it is sufficient to recapitulate memoria causa the leading results of that analysis as a foundation for the remarks to be afterward made on the functions of the Syllogism and the place which it holds in science To a legitimate syllogism it is essential that there should be three and no more than three propositions namely the conclusion or proposition to be proved and two other propositions which together prove it and which are called the premises It is essential that there should be three and no more than three terms namely the subject and predicate of the conclusion and another called the middle term which must be found in both premises since it is by means of it that the other two terms are to be connected together The predicate of the conclusion is called the major term of the syllogism the subject of the conclusion is called the minor term As there can be but three terms the major and minor terms must each be found in one and only one of the premises together with the middle term which is in them both The premise which contains the middle term and the major term is called the major premise that which contains the middle term and the minor term is called the minor premise Syllogisms are divided by some logicians into three figures by others into four according to the position of the middle term which may either be the subject in both premises the predicate in both or the subject in one and the predicate in the other The most common case is that in which the middle term is the subject of the major premise and the predicate of the minor This is reckoned as the first figure When the middle term is the predicate in both premises the syllogism belongs to the second figure when it is the subject in both to the third In the fourth figure the middle term is the subject of the minor premise and the predicate of the major Those writers who reckon no more than three figures include this case in the first Each figure is divided into moods according to what are called the quantity and quality of the propositions that is according as they are universal or particular affirmative or negative The following are examples of all the legitimate moods that is all those in which the conclusion correctly follows from the premises A is the minor term C the major B the middle term FIRST FIGURE All B is C No B is CAll B is CNo B is C All A is B All A is B Some A is B Some A is B thereforethereforetherefore therefore All A is C No A is CSome A is C Some A is not C SECOND FIGURE No C is BAll C is B No C is B All C is B All A is B No A is BSome A is B Some A is not B thereforethereforetherefore therefore No A is CNo A is CSome A is not C Some A is not C THIRD FIGURE All B isNo B is C Some B is All B isSome B is No B is C C C C not C All B isAll B isAll B isSome B is All B isSome B is A A A A A A therefore therefore therefore therefore therefore therefore Some A is Some A is Some A is Some A is Some A is Some A is C not C C C not C not C FOURTH FIGURE All C is BAll C is B Some C is B No C is BNo C is B All B is ANo B is AAll B is AAll B is A Some B is A therefore thereforetherefore thereforetherefore Some A is C Some A isSome A is C Some A isSome A is not C not Cnot C In these exemplars or blank forms for making syllogisms no place is assigned to singular propositions not of course because such propositions are not used in ratiocination but because their predicate being affirmed or denied of the whole of the subject they are ranked for the purposes of the syllogism with universal propositions Thus these two syllogisms All men are mortal All men are mortal All kings are men Socrates is a man therefore therefore All kings are mortal Socrates is mortal are arguments precisely similar and are both ranked in the first mood of the first figure The reasons why syllogisms in any of the above forms are legitimate that is why if the premises are true the conclusion must inevitably be so and why this is not the case in any other possible mood that is in any other combination of universal and particular affirmative and negative propositions any person taking interest in these inquiries may be presumed to have either learned from the commonschool books of the syllogistic logic or to be capable of discovering for himself The reader may however be referred for every needful explanation to Archbishop Whately’s Elements of Logic where he will find stated with philosophical precision and explained with remarkable perspicuity the whole of the common doctrine of the syllogism All valid ratiocination all reasoning by which from general propositions previously admitted other propositions equally or less general are inferred may be exhibited in some of the above forms The whole of Euclid for example might be thrown without difficulty into a series of syllogisms regular in mood and figure Though a syllogism framed according to any of these formulae is a valid argument all correct ratiocination admits of being stated in syllogisms of the first figure alone The rules for throwing an argument in any of the other figures into the first figure are called rules for the reduction of syllogisms It is done by the conversion of one or other or both of the premises Thus an argument in the first mood of the second figure as No C is B All A is B therefore No A is C may be reduced as follows The proposition No C is B being a universal negative admits of simple conversion and may be changed into No B is C which as we showed is the very same assertion in other words the same fact differently expressed This transformation having been effected the argument assumes the following form No B is C All A is B therefore No A is C which is a good syllogism in the second mood of the first figure Again an argument in the first mood of the third figure must resemble the following All B is C All B is A therefore Some A is C where the minor premise All B is A conformably to what was laid down in the last chapter respecting universal affirmatives does not admit of simple conversion but may be converted per accidens thus Some A is B which though it does not express the whole of what is asserted in the proposition All B is A expresses as was formerly shown part of it and must therefore be true if the whole is true We have then as the result of the reduction the following syllogism in the third mood of the first figure All B is C Some A is B from which it obviously follows that Some A is C In the same manner or in a manner on which after these examples it is not necessary to enlarge every mood of the second third and fourth figures may be reduced to some one of the four moods of the first In other words every conclusion which can be proved in any of the last three figures may be proved in the first figure from the same premises with a slight alteration in the mere manner of expressing them Every valid ratiocination therefore may be stated in the first figure that is in one of the following forms Every B is C No B is C All A is BAll A is B Some A is B Some A is B therefore therefore All A is CNo A is C Some A is C Some A is not C Or if more significant symbols are preferred To prove an affirmative the argument must admit of being stated in this form All animals are mortal All menSome menSocrates are animals therefore All menSome menSocrates are mortal To prove a negative the argument must be capable of being expressed in this form No one who is capable of selfcontrol is necessarily vicious No one who is capable of selfcontrol is necessarily vicious All negroesSome negroesMr A’s negro are capable of selfcontrol therefore No negroes areSome negroes are notMr A’s negro is not necessarily vicious Though all ratiocination admits of being thrown into one or the other of these forms and sometimes gains considerably by the transformation both in clearness and in the obviousness of its consequence there are no doubt cases in which the argument falls more naturally into one of the other three figures and in which its conclusiveness is more apparent at the first glance in those figures than when reduced to the first Thus if the proposition were that pagans may be virtuous and the evidence to prove it were the example of Aristides a syllogism in the third figure Aristides was virtuous Aristides was a pagan therefore Some pagan was virtuous would be a more natural mode of stating the argument and would carry conviction more instantly home than the same ratiocination strained into the first figure thus Aristides was virtuous Some pagan was Aristides therefore Some pagan was virtuous A German philosopher Lambert whose Neues Organon published in the year 1764 contains among other things one of the most elaborate and complete expositions which had ever been made of the syllogistic doctrine has expressly examined what sort of arguments fall most naturally and suitably into each of the four figures and his investigation is characterized by great ingenuity and clearness of thought The argument however is one and the same, in whichever figure it is expressed since as we have already seen the premises of a syllogism in the second third or fourth figure and those of the syllogism in the first figure to which it may be reduced are the same premises in every thing except language or at least as much of them as contributes to the proof of the conclusion is the same We are therefore at liberty in conformity with the general opinion of logicians to consider the two elementary forms of the first figure as the universal types of all correct ratiocination the one when the conclusion to be proved is affirmative the other when it is negative even though certain arguments may have a tendency to clothe themselves in the forms of the second third and fourth figures which however can not possibly happen with the only class of arguments which are of firstrate scientific importance those in which the conclusion is a universal affirmative such conclusions being susceptible of proof in the first figure alone On examining then these two general formulae we find that in both of them one premise the major is a universal proposition and according as this is affirmative or negative the conclusion is so too All ratiocination therefore starts from a general proposition principle or assumption a proposition in which a predicate is affirmed or denied of an entire class that is in which some attribute or the negation of some attribute is asserted of an indefinite number of objects distinguished by a common characteristic and designated in consequence by a common name The other premise is always affirmative and asserts that something which may be either an individual a class or part of a class belongs to or is included in the class respecting which something was affirmed or denied in the major premise It follows that the attribute affirmed or denied of the entire class may if that affirmation or denial was correct be affirmed or denied of the object or objects alleged to be included in the class and this is precisely the assertion made in the conclusion Whether or not the foregoing is an adequate account of the constituent parts of the syllogism will be presently considered but as far as it goes it is a true account It has accordingly been generalized and erected into a logical maxim on which all ratiocination is said to be founded insomuch that to reason and to apply the maxim are supposed to be one and the same thing The maxim is That whatever can be affirmed or denied of a class may be affirmed or denied of every thing included in the class This axiom supposed to be the basis of the syllogistic theory is termed by logicians the dictum de omni et nullo This maxim however when considered as a principle of reasoning appears suited to a system of metaphysics once indeed generally received but which for the last two centuries has been considered as finally abandoned though there have not been wanting in our own day attempts at its revival So long as what are termed Universals were regarded as a peculiar kind of substances having an objective existence distinct from the individual objects classed under them the dictum de omni conveyed an important meaning because it expressed the intercommunity of nature which it was necessary on that theory that we should suppose to exist between those general substances and the particular substances which were subordinated to them That every thing predicable of the universal was predicable of the various individuals contained under it was then no identical proposition but a statement of what was conceived as a fundamental law of the universe The assertion that the entire nature and properties of the substantia secunda formed part of the nature and properties of each of the individual substances called by the same name that the properties of Man for example were properties of all men was a proposition of real significance when man did not mean all men but something inherent in men and vastly superior to them in dignity Now however when it is known that a class a universal a genus or species is not an entity per se but neither more nor less than the individual substances themselves which are placed in the class and that there is nothing real in the matter except those objects a common name given to them and common attributes indicated by the name what I should be glad to know do we learn by being told that whatever can be affirmed of a class may be affirmed of every object contained in the class The class is nothing but the objects contained in it and the dictum de omni merely amounts to the identical proposition that whatever is true of certain objects is true of each of those objects If all ratiocination were no more than the application of this maxim to particular cases the syllogism would indeed be what it has so often been declared to be solemn trifling The dictum de omni is on a par with another truth which in its time was also reckoned of great importance Whatever is is To give any real meaning to the dictum de omni we must consider it not as an axiom but as a definition we must look upon it as intended to explain in a circuitous and paraphrastic manner the meaning of the word class An error which seemed finally refuted and dislodged from thought often needs only put on a new suit of phrases to be welcomed back to its old quarters and allowed to repose unquestioned for another cycle of ages Modern philosophers have not been sparing in their contempt for the scholastic dogma that genera and species are a peculiar kind of substances which general substances being the only permanent things while the individual substances comprehended under them are in a perpetual flux knowledge which necessarily imports stability can only have relation to those general substances or universals and not to the facts or particulars included under them Yet though nominally rejected this very doctrine whether disguised under the Abstract Ideas of Locke whose speculations however it has less vitiated than those of perhaps any other writer who has been infected with it under the ultranominalism of Hobbes and Condillac or the ontology of the later German schools has never ceased to poison philosophy Once accustomed to consider scientific investigation as essentially consisting in the study of universals men did not drop this habit of thought when they ceased to regard universals as possessing an independent existence and even those who went the length of considering them as mere names could not free themselves from the notion that the investigation of truth consisted entirely or partly in some kind of conjuration or juggle with those names When a philosopher adopted fully the Nominalist view of the signification of general language retaining along with it the dictum de omni as the foundation of all reasoning two such premises fairly put together were likely if he was a consistent thinker to land him in rather startling conclusions Accordingly it has been seriously held by writers of deserved celebrity that the process of arriving at new truths by reasoning consists in the mere substitution of one set of arbitrary signs for another a doctrine which they suppose to derive irresistible confirmation from the example of algebra If there were any process in sorcery or necromancy more preternatural than this I should be much surprised The culminating point of this philosophy is the noted aphorism of Condillac that a science is nothing or scarcely any thing but une langue bien faite in other words that the one sufficient rule for discovering the nature and properties of objects is to name them properly as if the reverse were not the truth that it is impossible to name them properly except in proportion as we are already acquainted with their nature and properties Can it be necessary to say that none not even the most trivial knowledge with respect to Things ever was or could be originally got at by any conceivable manipulation of mere names as such and that what can be learned from names is only what somebody who used the names knew before Philosophical analysis confirms the indication of common sense that the function of names is but that of enabling us to remember and to communicate our thoughts That they also strengthen even to an incalculable extent the power of thought itself is most true but they do this by no intrinsic and peculiar virtue they do it by the power inherent in an artificial memory an instrument of which few have adequately considered the immense potency As an artificial memory language truly is what it has so often been called an instrument of thought but it is one thing to be the instrument and another to be the exclusive subject upon which the instrument is exercised We think indeed to a considerable extent by means of names but what we think of are the things called by those names and there can not be a greater error than to imagine that thought can be carried on with nothing in our mind but names or that we can make the names think for us Those who considered the dictum de omni as the foundation of the syllogism looked upon arguments in a manner corresponding to the erroneous view which Hobbes took of propositions Because there are some propositions which are merely verbal Hobbes in order apparently that his definition might be rigorously universal defined a proposition as if no propositions declared any thing except the meaning of words If Hobbes was right if no further account than this could be given of the import of propositions no theory could be given but the commonly received one of the combination of propositions in a syllogism If the minor premise asserted nothing more than that something belongs to a class and if the major premise asserted nothing of that class except that it is included in another class the conclusion would only be that what was included in the lower class is included in the higher and the result therefore nothing except that the classification is consistent with itself But we have seen that it is no sufficient account of the meaning of a proposition to say that it refers something to or excludes something from a class Every proposition which conveys real information asserts a matter of fact dependent on the laws of nature and not on classification It asserts that a given object does or does not possess a given attribute or it asserts that two attributes or sets of attributes do or do not constantly or occasionally coexist Since such is the purport of all propositions which convey any real knowledge and since ratiocination is a mode of acquiring real knowledge any theory of ratiocination which does not recognize this import of propositions can not we may be sure be the true one Applying this view of propositions to the two premises of a syllogism we obtain the following results The major premise which as already remarked is always universal asserts that all things which have a certain attribute or attributes have or have not along with it a certain other attribute or attributes The minor premise asserts that the thing or set of things which are the subject of that premise have the firstmentioned attribute and the conclusion is that they have or that they have not the second Thus in our former example All men are mortal Socrates is a man therefore Socrates is mortal the subject and predicate of the major premise are connotative terms denoting objects and connoting attributes The assertion in the major premise is that along with one of the two sets of attributes we always find the other that the attributes connoted by man never exist unless conjoined with the attribute called mortality The assertion in the minor premise is that the individual named Socrates possesses the former attributes and it is concluded that he possesses also the attribute mortality Or if both the premises are general propositions as All men are mortal All kings are men therefore All kings are mortal the minor premise asserts that the attributes denoted by kingship only exist in conjunction with those signified by the word man The major asserts as before that the lastmentioned attributes are never found without the attribute of mortality The conclusion is that wherever the attributes of kingship are found that of mortality is found also If the major premise were negative as No men are omnipotent it would assert not that the attributes connoted by man never exist without but that they never exist with those connoted by omnipotent from which together with the minor premise it is concluded that the same incompatibility exists between the attribute omnipotence and those constituting a king In a similar manner we might analyse any other example of the syllogism If we generalize this process and look out for the principle or law involved in every such inference and presupposed in every syllogism the propositions of which are any thing more than merely verbal we find not the unmeaning dictum de omni et nullo but a fundamental principle or rather two principles strikingly resembling the axioms of mathematics The first which is the principle of affirmative syllogisms is that things which coexist with the same thing coexist with one another or still more precisely a thing which coexists with another thing which other coexists with a third thing also coexists with that third thing The second is the principle of negative syllogisms and is to this effect that a thing which coexists with another thing with which other a third thing does not coexist is not coexistent with that third thing These axioms manifestly relate to facts and not to conventions and one or other of them is the ground of the legitimacy of every argument in which facts and not conventions are the matter treated of It remains to translate this exposition of the syllogism from the one into the other of the two languages in which we formerly remarked that all propositions and of course therefore all combinations of propositions might be expressed We observed that a proposition might be considered in two different lights as a portion of our knowledge of nature or as a memorandum for our guidance Under the former or speculative aspect an affirmative general proposition is an assertion of a speculative truth viz that whatever has a certain attribute has a certain other attribute Under the other aspect it is to be regarded not as a part of our knowledge but as an aid for our practical exigencies by enabling us when we see or learn that an object possesses one of the two attributes to infer that it possesses the other thus employing the first attribute as a mark or evidence of the second Thus regarded every syllogism comes within the following general formula Attribute A is a mark of attribute B The given object has the mark A therefore The given object has the attribute B Referred to this type the arguments which we have lately cited as specimens of the syllogism will express themselves in the following manner The attributes of man are a mark of the attribute mortality Socrates has the attributes of man therefore Socrates has the attribute mortality And again The attributes of man are a mark of the attribute mortality The attributes of a king are a mark of the attributes of man therefore The attributes of a king are a mark of the attribute mortality And lastly The attributes of man are a mark of the absence of the attribute omnipotence The attributes of a king are a mark of the attributes of man therefore The attributes of a king are a mark of the absence of the attribute signified by the word omnipotent or are evidence of the absence of that attribute To correspond with this alteration in the form of the syllogisms the axioms on which the syllogistic process is founded must undergo a corresponding transformation In this altered phraseology both those axioms may be brought under one general expression namely that whatever has any mark has that which it is a mark of Or when the minor premise as well as the major is universal we may state it thus Whatever is a mark of any mark is a mark of that which this last is a mark of To trace the identity of these axioms with those previously laid down may be left to the intelligent reader We shall find as we proceed the great convenience of the phraseology into which we have last thrown them and which is better adapted than any I am acquainted with to express with precision and force what is aimed at and actually accomplished in every case of the ascertainment of a truth by ratiocination We have shown what is the real nature of the truths with which the Syllogism is conversant in contradistinction to the more superficial manner in which their import is conceived in the common theory and what are the fundamental axioms on which its probative force or conclusiveness depends We have now to inquire whether the syllogistic process that of reasoning from generals to particulars is or is not a process of inference a progress from the known to the unknown a means of coming to a knowledge of something which we did not know before Logicians have been remarkably unanimous in their mode of answering this question It is universally allowed that a syllogism is vicious if there be any thing more in the conclusion than was assumed in the premises But this is in fact to say that nothing ever was or can be proved by syllogism which was not known or assumed to be known before Is ratiocination then not a process of inference And is the syllogism to which the word reasoning has so often been represented to be exclusively appropriate not really entitled to be called reasoning at all This seems an inevitable consequence of the doctrine admitted by all writers on the subject that a syllogism can prove no more than is involved in the premises Yet the acknowledgment so explicitly made has not prevented one set of writers from continuing to represent the syllogism as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths whether of science or of daily life which we believe while those who have avoided this inconsistency and followed out the general theorem respecting the logical value of the syllogism to its legitimate corollary have been led to impute uselessness and frivolity to the syllogistic theory itself on the ground of the petitio principii which they allege to be inherent in every syllogism As I believe both these opinions to be fundamentally erroneous I must request the attention of the reader to certain considerations without which any just appreciation of the true character of the syllogism and the functions it performs in philosophy appears to me impossible but which seem to have been either overlooked or insufficiently adverted to both by the defenders of the syllogistic theory and by its assailants It must be granted that in every syllogism considered as an argument to prove the conclusion there is a petitio principii When we say All men are mortal Socrates is a man therefore Socrates is mortal it is unanswerably urged by the adversaries of the syllogistic theory that the proposition Socrates is mortal is presupposed in the more general assumption All men are mortal that we can not be assured of the mortality of all men unless we are already certain of the mortality of every individual man that if it be still doubtful whether Socrates or any other individual we choose to name be mortal or not the same degree of uncertainty must hang over the assertion All men are mortal that the general principle instead of being given as evidence of the particular case can not itself be taken for true without exception until every shadow of doubt which could affect any case comprised with it is dispelled by evidence aliund and then what remains for the syllogism to prove That in short no reasoning from generals to particulars can as such prove any thing since from a general principle we can not infer any particulars but those which the principle itself assumes as known This doctrine appears to me irrefragable and if logicians though unable to dispute it have usually exhibited a strong disposition to explain it away this was not because they could discover any flaw in the argument itself but because the contrary opinion seemed to rest on arguments equally indisputable In the syllogism last referred to for example or in any of those which we previously constructed is it not evident that the conclusion may to the person to whom the syllogism is presented be actually and bona fide a new truth Is it not matter of daily experience that truths previously unthought of facts which have not been and can not be directly observed are arrived at by way of general reasoning We believe that the Duke of Wellington is mortal We do not know this by direct observation so long as he is not yet dead If we were asked how this being the case we know the duke to be mortal we should probably answer Because all men are so Here therefore we arrive at the knowledge of a truth not as yet susceptible of observation by a reasoning which admits of being exhibited in the following syllogism All men are mortal The Duke of Wellington is a man therefore The Duke of Wellington is mortal And since a large portion of our knowledge is thus acquired logicians have persisted in representing the syllogism as a process of inference or proof though none of them has cleared up the difficulty which arises from the inconsistency between that assertion and the principle that if there be any thing in the conclusion which was not already asserted in the premises the argument is vicious For it is impossible to attach any serious scientific value to such a mere salvo as the distinction drawn between being involved by implication in the premises and being directly asserted in them When Archbishop Whately says that the object of reasoning is merely to expand and unfold the assertions wrapped up as it were and implied in those with which we set out and to bring a person to perceive and acknowledge the full force of that which he has admitted he does not I think meet the real difficulty requiring to be explained namely how it happens that a science like geometry can be all wrapped up in a few definitions and axioms Nor does this defence of the syllogism differ much from what its assailants urge against it as an accusation when they charge it with being of no use except to those who seek to press the consequences of an admission into which a person has been entrapped without having considered and understood its full force When you admitted the major premise you asserted the conclusion but says Archbishop Whately you asserted it by implication merely this however can here only mean that you asserted it unconsciously that you did not know you were asserting it but if so the difficulty revives in this shape Ought you not to have known Were you warranted in asserting the general proposition without having satisfied yourself of the truth of every thing which it fairly includes And if not is not the syllogistic art prima facie what its assailants affirm it to be a contrivance for catching you in a trap and holding you fast in it From this difficulty there appears to be but one issue The proposition that the Duke of Wellington is mortal is evidently an inference it is got at as a conclusion from something else but do we in reality conclude it from the proposition All men are mortal I answer no The error committed is I conceive that of overlooking the distinction between two parts of the process of philosophizing the inferring part and the registering part and ascribing to the latter the functions of the former The mistake is that of referring a person to his own notes for the origin of his knowledge If a person is asked a question and is at the moment unable to answer it he may refresh his memory by turning to a memorandum which he carries about with him But if he were asked how the fact came to his knowledge he would scarcely answer because it was set down in his notebook unless the book was written like the Koran with a quill from the wing of the angel Gabriel Assuming that the proposition The Duke of Wellington is mortal is immediately an inference from the proposition All men are mortal whence do we derive our knowledge of that general truth Of course from observation Now all which man can observe are individual cases From these all general truths must be drawn and into these they may be again resolved for a general truth is but an aggregate of particular truths a comprehensive expression by which an indefinite number of individual facts are affirmed or denied at once But a general proposition is not merely a compendious form for recording and preserving in the memory a number of particular facts all of which have been observed Generalization is not a process of mere naming it is also a process of inference From instances which we have observed we feel warranted in concluding that what we found true in those instances holds in all similar ones past present and future however numerous they may be We then by that valuable contrivance of language which enables us to speak of many as if they were one record all that we have observed together with all that we infer from our observations in one concise expression and have thus only one proposition instead of an endless number to remember or to communicate The results of many observations and inferences and instructions for making innumerable inferences in unforeseen cases are compressed into one short sentence When therefore we conclude from the death of John and Thomas and every other person we ever heard of in whose case the experiment had been fairly tried that the Duke of Wellington is mortal like the rest we may indeed pass through the generalization All men are mortal as an intermediate stage but it is not in the latter half of the process the descent from all men to the Duke of Wellington that the inference resides The inference is finished when we have asserted that all men are mortal What remains to be performed afterward is merely deciphering our own notes Archbishop Whately has contended that syllogizing or reasoning from generals to particulars is not agreeably to the vulgar idea a peculiar mode of reasoning but the philosophical analysis of the mode in which all men reason and must do so if they reason at all With the deference due to so high an authority I can not help thinking that the vulgar notion is in this case the more correct If from our experience of John Thomas etc who once were living but are now dead we are entitled to conclude that all human beings are mortal we might surely without any logical inconsequence have concluded at once from those instances that the Duke of Wellington is mortal The mortality of John Thomas and others is after all the whole evidence we have for the mortality of the Duke of Wellington Not one iota is added to the proof by interpolating a general proposition Since the individual cases are all the evidence we can possess evidence which no logical form into which we choose to throw it can make greater than it is and since that evidence is either sufficient in itself or if insufficient for the one purpose can not be sufficient for the other I am unable to see why we should be forbidden to take the shortest cut from these sufficient premises to the conclusion and constrained to travel the high priori road by the arbitrary fiat of logicians I can not perceive why it should be impossible to journey from one place to another unless we march up a hill and then march down again It may be the safest road and there may be a restingplace at the top of the hill affording a commanding view of the surrounding country but for the mere purpose of arriving at our journey’s end our taking that road is perfectly optional it is a question of time trouble and danger Not only may we reason from particulars to particulars without passing through generals but we perpetually do so reason All our earliest inferences are of this nature From the first dawn of intelligence we draw inferences but years elapse before we learn the use of general language The child who having burned his fingers avoids to thrust them again into the fire has reasoned or inferred though he has never thought of the general maxim Fire burns He knows from memory that he has been burned and on this evidence believes when he sees a candle that if he puts his finger into the flame of it he will be burned again He believes this in every case which happens to arise but without looking in each instance beyond the present case He is not generalizing he is inferring a particular from particulars In the same way also brutes reason There is no ground for attributing to any of the lower animals the use of signs of such a nature as to render general propositions possible But those animals profit by experience and avoid what they have found to cause them pain in the same manner though not always with the same skill as a human creature Not only the burned child but the burned dog dreads the fire I believe that in point of fact, when drawing inferences from our personal experience and not from maxims handed down to us by books or tradition we much oftener conclude from particulars to particulars directly than through the intermediate agency of any general proposition We are constantly reasoning from ourselves to other people or from one person to another without giving ourselves the trouble to erect our observations into general maxims of human or external nature When we conclude that some person will on some given occasion feel or act so and so we sometimes judge from an enlarged consideration of the manner in which human beings in general or persons of some particular character are accustomed to feel and act but much oftener from merely recollecting the feelings and conduct of the same person in some previous instance or from considering how we should feel or act ourselves It is not only the village matron who when called to a consultation upon the case of a neighbour’s child pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her Lucy We all where we have no definite maxims to steer by guide ourselves in the same way and if we have an extensive experience and retain its impressions strongly we may acquire in this manner a very considerable power of accurate judgment which we may be utterly incapable of justifying or of communicating to others Among the higher order of practical intellects there have been many of whom it was remarked how admirably they suited their means to their ends without being able to give any sufficient reasons for what they did and applied or seemed to apply recondite principles which they were wholly unable to state This is a natural consequence of having a mind stored with appropriate particulars and having been long accustomed to reason at once from these to fresh particulars without practicing the habit of stating to one’s self or to others the corresponding general propositions An old warrior on a rapid glance at the outlines of the ground is able at once to give the necessary orders for a skilful arrangement of his troops though if he has received little theoretical instruction and has seldom been called upon to answer to other people for his conduct he may never have had in his mind a single general theorem respecting the relation between ground and array But his experience of encampments in circumstances more or less similar has left a number of vivid unexpressed ungeneralised analogies in his mind the most appropriate of which instantly suggesting itself determines him to a judicious arrangement The skill of an uneducated person in the use of weapons or of tools is of a precisely similar nature The savage who executes unerringly the exact throw which brings down his game or his enemy in the manner most suited to his purpose under the operation of all the conditions necessarily involved the weight and form of the weapon the direction and distance of the object the action of the wind etc owes this power to a long series of previous experiments the results of which he certainly never framed into any verbal theorems or rules The same thing may generally be said of any other extraordinary manual dexterity Not long ago a Scotch manufacturer procured from England at a high rate of wages a working dyer famous for producing very fine colours with the view of teaching to his other workmen the same skill The workman came but his mode of proportioning the ingredients in which lay the secret of the effects he produced was by taking them up in handfuls while the common method was to weigh them The manufacturer sought to make him turn his handling system into an equivalent weighing system that the general principle of his peculiar mode of proceeding might be ascertained This however the man found himself quite unable to do and therefore could impart his skill to nobody He had from the individual cases of his own experience established a connection in his mind between fine effects of colour and tactual perceptions in handling his dyeing materials and from these perceptions he could in any particular case infer the means to be employed and the effects which would be produced but could not put others in possession of the grounds on which he proceeded from having never generalized them in his own mind or expressed them in language Almost every one knows Lord Mansfield’s advice to a man of practical good sense who being appointed governor of a colony had to preside in its courts of justice without previous judicial practice or legal education The advice was to give his decision boldly for it would probably be right but never to venture on assigning reasons for they would almost infallibly be wrong In cases like this which are of no uncommon occurrence it would be absurd to suppose that the bad reason was the source of the good decision Lord Mansfield knew that if any reason were assigned it would be necessarily an afterthought the judge being in fact guided by impressions from past experience without the circuitous process of framing general principles from them and that if he attempted to frame any such he would assuredly fail Lord Mansfield however would not have doubted that a man of equal experience who had also a mind stored with general propositions derived by legitimate induction from that experience would have been greatly preferable as a judge to one however sagacious who could not be trusted with the explanation and justification of his own judgments The cases of men of talent performing wonderful things they know not how are examples of the rudest and most spontaneous form of the operations of superior minds It is a defect in them and often a source of errors not to have generalized as they went on but generalization though a help the most important indeed of all helps is not an essential Even the scientifically instructed who possess in the form of general propositions a systematic record of the results of the experience of mankind need not always revert to those general propositions in order to apply that experience to a new case It is justly remarked by Dugald Stewart that though the reasonings in mathematics depend entirely on the axioms it is by no means necessary to our seeing the conclusiveness of the proof that the axioms should be expressly adverted to When it is inferred that AB is equal to CD because each of them is equal to EF the most uncultivated understanding as soon as the propositions were understood would assent to the inference without having ever heard of the general truth that things which are equal to the same thing are equal to one another This remark of Stewart consistently followed out goes to the root as I conceive of the philosophy of ratiocination and it is to be regretted that he himself stopped short at a much more limited application of it He saw that the general propositions on which a reasoning is said to depend may in certain cases be altogether omitted without impairing its probative force But he imagined this to be a peculiarity belonging to axioms and argued from it that axioms are not the foundations or first principles of geometry from which all the other truths of the science are synthetically deduced as the laws of motion and of the composition of forces in dynamics the equal mobility of fluids in hydrostatics the laws of reflection and refraction in optics are the first principles of those sciences but are merely necessary assumptions selfevident indeed and the denial of which would annihilate all demonstration but from which as premises nothing can be demonstrated In the present as in many other instances this thoughtful and elegant writer has perceived an important truth but only by halves Finding in the case of geometrical axioms that general names have not any talismanic virtue for conjuring new truths out of the well where they lie hid and not seeing that this is equally true in every other case of generalization he contended that axioms are in their nature barren of consequences and that the really fruitful truths the real first principles of geometry are the definitions that the definition for example of the circle is to the properties of the circle what the laws of equilibrium and of the pressure of the atmosphere are to the rise of the mercury in the Torricellian tube Yet all that he had asserted respecting the function to which the axioms are confined in the demonstrations of geometry holds equally true of the definitions Every demonstration in Euclid might be carried on without them This is apparent from the ordinary process of proving a proposition of geometry by means of a diagram What assumption in fact do we set out from to demonstrate by a diagram any of the properties of the circle Not that in all circles the radii are equal but only that they are so in the circle ABC As our warrant for assuming this we appeal it is true to the definition of a circle in general but it is only necessary that the assumption be granted in the case of the particular circle supposed From this which is not a general but a singular proposition combined with other propositions of a similar kind some of which when generalized are called definitions and other axioms we prove that a certain conclusion is true not of all circles but of the particular circle ABC or at least would be so if the facts precisely accorded with our assumptions The enunciation as it is called that is the general theorem which stands at the head of the demonstration is not the proposition actually demonstrated One instance only is demonstrated but the process by which this is done is a process which when we consider its nature we perceive might be exactly copied in an indefinite number of other instances in every instance which conforms to certain conditions The contrivance of general language furnishing us with terms which connote these conditions we are able to assert this indefinite multitude of truths in a single expression and this expression is the general theorem By dropping the use of diagrams and substituting in the demonstrations general phrases for the letters of the alphabet we might prove the general theorem directly that is we might demonstrate all the cases at once and to do this we must of course employ as our premises the axioms and definitions in their general form But this only means that if we can prove an individual conclusion by assuming an individual fact then in whatever case we are warranted in making an exactly similar assumption we may draw an exactly similar conclusion The definition is a sort of notice to ourselves and others what assumptions we think ourselves entitled to make And so in all cases the general propositions whether called definitions axioms or laws of nature which we lay down at the beginning of our reasonings are merely abridged statements in a kind of shorthand of the particular facts which as occasion arises we either think we may proceed on as proved or intend to assume In any one demonstration it is enough if we assume for a particular case suitably selected what by the statement of the definition or principle we announce that we intend to assume in all cases which may arise The definition of the circle therefore is to one of Euclid’s demonstrations exactly what according to Stewart the axioms are that is the demonstration does not depend on it but yet if we deny it the demonstration fails The proof does not rest on the general assumption but on a similar assumption confined to the particular case that case however being chosen as a specimen or paradigm of the whole class of cases included in the theorem there can be no ground for making the assumption in that case which does not exist in every other and to deny the assumption as a general truth is to deny the right of making it in the particular instance There are undoubtedly the most ample reasons for stating both the principles and the theorems in their general form and these will be explained presently so far as explanation is requisite But that unpractised learners even in making use of one theorem to demonstrate another reason rather from particular to particular than from the general proposition is manifest from the difficulty they find in applying a theorem to a case in which the configuration of the diagram is extremely unlike that of the diagram by which the original theorem was demonstrated A difficulty which except in cases of unusual mental power long practice can alone remove and removes chiefly by rendering us familiar with all the configurations consistent with the general conditions of the theorem From the considerations now adduced the following conclusions seem to be established All inference is from particulars to particulars General propositions are merely registers of such inferences already made and short formulae for making more The major premise of a syllogism consequently is a formula of this description and the conclusion is not an inference drawn from the formula but an inference drawn according to the formula the real logical antecedent or premise being the particular facts from which the general proposition was collected by induction Those facts and the individual instances which supplied them may have been forgotten but a record remains not indeed descriptive of the facts themselves but showing how those cases may be distinguished respecting which the facts when known were considered to warrant a given inference According to the indications of this record we draw our conclusion which is to all intents and purposes a conclusion from the forgotten facts For this it is essential that we should read the record correctly and the rules of the syllogism are a set of precautions to insure our doing so This view of the functions of the syllogism is confirmed by the consideration of precisely those cases which might be expected to be least favourable to it namely those in which ratiocination is independent of any previous induction We have already observed that the syllogism in the ordinary course of our reasoning is only the latter half of the process of traveling from premises to a conclusion There are however some peculiar cases in which it is the whole process Particulars alone are capable of being subjected to observation and all knowledge which is derived from observation begins therefore of necessity in particulars but our knowledge may in cases of certain descriptions be conceived as coming to us from other sources than observation It may present itself as coming from testimony which on the occasion and for the purpose in hand is accepted as of an authoritative character and the information thus communicated may be conceived to comprise not only particular facts but general propositions as when a scientific doctrine is accepted without examination on the authority of writers or a theological doctrine on that of Scripture Or the generalization may not be in the ordinary sense an assertion at all but a command a law not in the philosophical but in the moral and political sense of the term an expression of the desire of a superior that we or any number of other persons shall conform our conduct to certain general instructions So far as this asserts a fact namely a volition of the legislator that fact is an individual fact and the proposition therefore is not a general proposition But the description therein contained of the conduct which it is the will of the legislator that his subjects should observe is general The proposition asserts not that all men are any thing but that all men shall do something In both these cases the generalities are the original data and the particulars are elicited from them by a process which correctly resolves itself into a series of syllogisms The real nature however of the supposed deductive process is evident enough The only point to be determined is whether the authority which declared the general proposition intended to include this case in it and whether the legislator intended his command to apply to the present case among others or not This is ascertained by examining whether the case possesses the marks by which as those authorities have signified the cases which they meant to certify or to influence may be known The object of the inquiry is to make out the witness’s or the legislator’s intention through the indication given by their words This is a question as the Germans express it of hermeneutics The operation is not a process of inference but a process of interpretation In this last phrase we have obtained an expression which appears to me to characterize more aptly than any other the functions of the syllogism in all cases When the premises are given by authority the function of Reasoning is to ascertain the testimony of a witness or the will of a legislator by interpreting the signs in which the one has intimated his assertion and the other his command In like manner when the premises are derived from observation the function of Reasoning is to ascertain what we or our predecessors formerly thought might be inferred from the observed facts and to do this by interpreting a memorandum of ours or of theirs The memorandum reminds us that from evidence more or less carefully weighed it formerly appeared that a certain attribute might be inferred wherever we perceive a certain mark The proposition All men are mortal for instance shows that we have had experience from which we thought it followed that the attributes connoted by the term man are a mark of mortality But when we conclude that the Duke of Wellington is mortal we do not infer this from the memorandum but from the former experience All that we infer from the memorandum is our own previous belief or that of those who transmitted to us the proposition concerning the inferences which that former experience would warrant This view of the nature of the syllogism renders consistent and intelligible what otherwise remains obscure and confused in the theory of Archbishop Whately and other enlightened defenders of the syllogistic doctrine respecting the limits to which its functions are confined They affirm in as explicit terms as can be used that the sole office of general reasoning is to prevent inconsistency in our opinions to prevent us from assenting to any thing the truth of which would contradict something to which we had previously on good grounds given our assent And they tell us that the sole ground which a syllogism affords for assenting to the conclusion is that the supposition of its being false combined with the supposition that the premises are true would lead to a contradiction in terms Now this would be but a lame account of the real grounds which we have for believing the facts which we learn from reasoning in contradistinction to observation The true reason why we believe that the Duke of Wellington will die is that his fathers and our fathers and all other persons who were contemporary with them have died Those facts are the real premises of the reasoning But we are not led to infer the conclusion from those premises by the necessity of avoiding any verbal inconsistency There is no contradiction in supposing that all those persons have died and that the Duke of Wellington may notwithstanding live forever But there would be a contradiction if we first on the ground of those same premises made a general assertion including and covering the case of the Duke of Wellington and then refused to stand to it in the individual case There is an inconsistency to be avoided between the memorandum we make of the inferences which may be justly drawn in future cases and the inferences we actually draw in those cases when they arise With this view we interpret our own formula precisely as a judge interprets a law in order that we may avoid drawing any inferences not conformable to our former intention as a judge avoids giving any decision not conformable to the legislator’s intention The rules for this interpretation are the rules of the syllogism and its sole purpose is to maintain consistency between the conclusions we draw in every particular case and the previous general directions for drawing them whether those general directions were framed by ourselves as the result of induction or were received by us from an authority competent to give them In the above observations it has I think been shown that though there is always a process of reasoning or inference where a syllogism is used the syllogism is not a correct analysis of that process of reasoning or inference which is on the contrary when not a mere inference from testimony an inference from particulars to particulars authorized by a previous inference from particulars to generals and substantially the same with it of the nature therefore of Induction But while these conclusions appear to me undeniable I must yet enter a protest as strong as that of Archbishop Whately himself against the doctrine that the syllogistic art is useless for the purposes of reasoning The reasoning lies in the act of generalization not in interpreting the record of that act but the syllogistic form is an indispensable collateral security for the correctness of the generalization itself It has already been seen that if we have a collection of particulars sufficient for grounding an induction we need not frame a general proposition we may reason at once from those particulars to other particulars But it is to be remarked withal that whenever from a set of particular cases we can legitimately draw any inference we may legitimately make our inference a general one If from observation and experiment we can conclude to one new case so may we to an indefinite number If that which has held true in our past experience will therefore hold in time to come it will hold not merely in some individual case but in all cases of some given description Every induction therefore which suffices to prove one fact proves an indefinite multitude of facts the experience which justifies a single prediction must be such as will suffice to bear out a general theorem This theorem it is extremely important to ascertain and declare in its broadest form of generality and thus to place before our minds in its full extent the whole of what our evidence must prove if it proves any thing This throwing of the whole body of possible inferences from a given set of particulars into one general expression operates as a security for their being just inferences in more ways than one First the general principle presents a larger object to the imagination than any of the singular propositions which it contains A process of thought which leads to a comprehensive generality is felt as of greater importance than one which terminates in an insulated fact and the mind is even unconsciously led to bestow greater attention upon the process and to weigh more carefully the sufficiency of the experience appealed to for supporting the inference grounded upon it There is another and a more important advantage In reasoning from a course of individual observations to some new and unobserved case which we are but imperfectly acquainted with or we should not be inquiring into it and in which since we are inquiring into it we probably feel a peculiar interest there is very little to prevent us from giving way to negligence or to any bias which may affect our wishes or our imagination and under that influence accepting insufficient evidence as sufficient But if instead of concluding straight to the particular case we place before ourselves an entire class of facts the whole contents of a general proposition every tittle of which is legitimately inferable from our premises if that one particular conclusion is so there is then a considerable likelihood that if the premises are insufficient and the general inference therefore groundless it will comprise within it some fact or facts the reverse of which we already know to be true and we shall thus discover the error in our generalization by a reductio ad impossibile Thus if during the reign of Marcus Aurelius a subject of the Roman empire under the bias naturally given to the imagination and expectations by the lives and characters of the Antonines had been disposed to expect that Commodus would be a just ruler supposing him to stop there he might only have been undeceived by sad experience But if he reflected that this expectation could not be justifiable unless from the same evidence he was warranted in concluding some general proposition as for instance that all Roman emperors are just rulers he would immediately have thought of Nero Domitian and other instances which showing the falsity of the general conclusion and therefore the insufficiency of the premises would have warned him that those premises could not prove in the instance of Commodus what they were inadequate to prove in any collection of cases in which his was included The advantage in judging whether any controverted inference is legitimate of referring to a parallel case is universally acknowledged But by ascending to the general proposition we bring under our view not one parallel case only but all possible parallel cases at once all cases to which the same set of evidentiary considerations are applicable When therefore we argue from a number of known cases to another case supposed to be analogous it is always possible and generally advantageous to divert our argument into the circuitous channel of an induction from those known cases to a general proposition and a subsequent application of that general proposition to the unknown case This second part of the operation which as before observed is essentially a process of interpretation will be resolvable into a syllogism or a series of syllogisms the majors of which will be general propositions embracing whole classes of cases every one of which propositions must be true in all its extent if the argument is maintainable If therefore any fact fairly coming within the range of one of these general propositions and consequently asserted by it is known or suspected to be other than the proposition asserts it to be this mode of stating the argument causes us to know or to suspect that the original observations which are the real grounds of our conclusion are not sufficient to support it And in proportion to the greater chance of our detecting the inconclusiveness of our evidence will be the increased reliance we are entitled to place in it if no such evidence of defect shall appear The value therefore of the syllogistic form and of the rules for using it correctly does not consist in their being the form and the rules according to which our reasonings are necessarily or even usually made but in their furnishing us with a mode in which those reasonings may always be represented and which is admirably calculated if they are inconclusive to bring their inconclusiveness to light An induction from particulars to generals followed by a syllogistic process from those generals to other particulars is a form in which we may always state our reasonings if we please It is not a form in which we must reason but it is a form in which we may reason and into which it is indispensable to throw our reasoning when there is any doubt of its validity though when the case is familiar and little complicated and there is no suspicion of error we may and do reason at once from the known particular cases to unknown ones These are the uses of syllogism as a mode of verifying any given argument Its ulterior uses as respects the general course of our intellectual operations hardly require illustration being in fact the acknowledged uses of general language They amount substantially to this that the inductions may be made once for all a single careful interrogation of experience may suffice and the result may be registered in the form of a general proposition which is committed to memory or to writing and from which afterward we have only to syllogize The particulars of our experiments may then be dismissed from the memory in which it would be impossible to retain so great a multitude of details while the knowledge which those details afforded for future use and which would otherwise be lost as soon as the observations were forgotten or as their record became too bulky for reference is retained in a commodious and immediately available shape by means of general language Against this advantage is to be set the countervailing inconvenience that inferences originally made on insufficient evidence become consecrated and as it were hardened into general maxims and the mind cleaves to them from habit after it has outgrown any liability to be misled by similar fallacious appearances if they were now for the first time presented but having forgotten the particulars it does not think of revising its own former decision An inevitable drawback which however considerable in itself forms evidently but a small setoff against the immense benefits of general language The use of the syllogism is in truth no other than the use of general propositions in reasoning We can reason without them in simple and obvious cases we habitually do so minds of great sagacity can do it in cases not simple and obvious provided their experience supplies them with instances essentially similar to every combination of circumstances likely to arise But other minds and the same minds where they have not the same preeminent advantages of personal experience are quite helpless without the aid of general propositions wherever the case presents the smallest complication and if we made no general propositions few persons would get much beyond those simple inferences which are drawn by the more intelligent of the brutes Though not necessary to reasoning general propositions are necessary to any considerable progress in reasoning It is therefore natural and indispensable to separate the process of investigation into two parts and obtain general formulae for determining what inferences may be drawn before the occasion arises for drawing the inferences The work of drawing them is then that of applying the formulae and the rules of syllogism are a system of securities for the correctness of the application To complete the series of considerations connected with the philosophical character of the syllogism it is requisite to consider since the syllogism is not the universal type of the reasoning process what is the real type This resolves itself into the question what is the nature of the minor premise and in what manner it contributes to establish the conclusion for as to the major we now fully understand that the place which it nominally occupies in our reasonings properly belongs to the individual facts or observations of which it expresses the general result the major itself being no real part of the argument but an intermediate haltingplace for the mind interposed by an artifice of language between the real premises and the conclusion by way of a security which it is in a most material degree for the correctness of the process The minor however being an indispensable part of the syllogistic expression of an argument without doubt either is or corresponds to an equally indispensable part of the argument itself and we have only to inquire what part It is perhaps worth while to notice here a speculation of a philosopher to whom mental science is much indebted but who though a very penetrating was a very hasty thinker and whose want of due circumspection rendered him fully as remarkable for what he did not see as for what he saw I allude to Dr Thomas Brown whose theory of ratiocination is peculiar He saw the petitio principii which is inherent in every syllogism if we consider the major to be itself the evidence by which the conclusion is proved instead of being what in fact it is an assertion of the existence of evidence sufficient to prove any conclusion of a given description Seeing this Dr Brown not only failed to see the immense advantage in point of security for correctness which is gained by interposing this step between the real evidence and the conclusion but he thought it incumbent on him to strike out the major altogether from the reasoning process without substituting any thing else and maintained that our reasonings consist only of the minor premise and the conclusion Socrates is a man therefore Socrates is mortal thus actually suppressing as an unnecessary step in the argument the appeal to former experience The absurdity of this was disguised from him by the opinion he adopted that reasoning is merely analysing our own general notions or abstract ideas and that the proposition Socrates is mortal is evolved from the proposition Socrates is a man simply by recognizing the notion of mortality as already contained in the notion we form of a man After the explanations so fully entered into on the subject of propositions much further discussion can not be necessary to make the radical error of this view of ratiocination apparent If the word man connoted mortality if the meaning of mortal were involved in the meaning of man we might undoubtedly evolve the conclusion from the minor alone because the minor would have already asserted it But if as is in fact the case the word man does not connote mortality how does it appear that in the mind of every person who admits Socrates to be a man the idea of man must include the idea of mortality Dr Brown could not help seeing this difficulty and in order to avoid it was led contrary to his intention to reestablish under another name that step in the argument which corresponds to the major by affirming the necessity of previously perceiving the relation between the idea of man and the idea of mortal If the reasoner has not previously perceived this relation he will not says Dr Brown infer because Socrates is a man that Socrates is mortal But even this admission though amounting to a surrender of the doctrine that an argument consists of the minor and the conclusion alone will not save the remainder of Dr Brown’s theory The failure of assent to the argument does not take place merely because the reasoner for want of due analysis does not perceive that his idea of man includes the idea of mortality it takes place much more commonly because in his mind that relation between the two ideas has never existed And in truth it never does exist except as the result of experience Consenting for the sake of the argument to discuss the question on a supposition of which we have recognized the radical incorrectness namely that the meaning of a proposition relates to the ideas of the things spoken of and not to the things themselves I must yet observe that the idea of man as a universal idea the common property of all rational creatures can not involve any thing but what is strictly implied in the name If any one includes in his own private idea of man as no doubt is always the case some other attributes such for instance as mortality he does so only as the consequence of experience after having satisfied himself that all men possess that attribute so that whatever the idea contains in any person’s mind beyond what is included in the conventional signification of the word has been added to it as the result of assent to a proposition while Dr Brown’s theory requires us to suppose on the contrary that assent to the proposition is produced by evolving through an analytic process this very element out of the idea This theory therefore may be considered as sufficiently refuted and the minor premise must be regarded as totally insufficient to prove the conclusion except with the assistance of the major or of that which the major represents namely the various singular propositions expressive of the series of observations of which the generalization called the major premise is the result In the argument then which proves that Socrates is mortal one indispensable part of the premises will be as follows My father and my father’s father A B C and an indefinite number of other persons were mortal which is only an expression in different words of the observed fact that they have died This is the major premise divested of the petitio principii and cut down to as much as is really known by direct evidence In order to connect this proposition with the conclusion Socrates is mortal the additional link necessary is such a proposition as the following Socrates resembles my father and my father’s father and the other individuals specified This proposition we assert when we say that Socrates is a man By saying so we likewise assert in what respect he resembles them namely in the attributes connoted by the word man And we conclude that he further resembles them in the attribute mortality We have thus obtained what we were seeking a universal type of the reasoning process We find it resolvable in all cases into the following elements Certain individuals have a given attribute an individual or individuals resemble the former in certain other attributes therefore they resemble them also in the given attribute This type of ratiocination does not claim like the syllogism to be conclusive from the mere form of the expression nor can it possibly be so That one proposition does or does not assert the very fact which was already asserted in another may appear from the form of the expression that is from a comparison of the language but when the two propositions assert facts which are bona fide different whether the one fact proves the other or not can never appear from the language but must depend on other considerations Whether from the attributes in which Socrates resembles those men who have heretofore died it is allowable to infer that he resembles them also in being mortal is a question of Induction and is to be decided by the principles or canons which we shall hereafter recognize as tests of the correct performance of that great mental operation Meanwhile however it is certain as before remarked that if this inference can be drawn as to Socrates it can be drawn as to all others who resemble the observed individuals in the same attributes in which he resembles them that is to express the thing concisely of all mankind If therefore the argument be admissible in the case of Socrates we are at liberty once for all to treat the possession of the attributes of man as a mark or satisfactory evidence of the attribute of mortality This we do by laying down the universal proposition All men are mortal and interpreting this as occasion arises in its application to Socrates and others By this means we establish a very convenient division of the entire logical operation into two steps first that of ascertaining what attributes are marks of mortality and secondly whether any given individuals possess those marks And it will generally be advisable in our speculations on the reasoning process to consider this double operation as in fact taking place and all reasoning as carried on in the form into which it must necessarily be thrown to enable us to apply to it any test of its correct performance Although therefore all processes of thought in which the ultimate premises are particulars whether we conclude from particulars to a general formula or from particulars to other particulars according to that formula are equally Induction we shall yet conformably to usage consider the name Induction as more peculiarly belonging to the process of establishing the general proposition and the remaining operation which is substantially that of interpreting the general proposition we shall call by its usual name Deduction And we shall consider every process by which any thing is inferred respecting an unobserved case as consisting of an Induction followed by a Deduction because although the process needs not necessarily be carried on in this form it is always susceptible of the form and must be thrown into it when assurance of scientific accuracy is needed and desired The theory of the syllogism laid down in the preceding pages has obtained among other important adhesions three of peculiar value those of Sir John Herschel Dr Whewell and Mr Bailey Sir John Herschel considering the doctrine though not strictly a discovery having been anticipated by Berkeley to be one of the greatest steps which have yet been made in the philosophy of Logic When we consider to quote the further words of the same authority the inveteracy of the habits and prejudices which it has cast to the winds there is no cause for misgiving in the fact that other thinkers no less entitled to consideration have formed a very different estimate of it Their principal objection can not be better or more succinctly stated than by borrowing a sentence from Archbishop Whately In every case where an inference is drawn from Induction unless that name is to be given to a mere random guess without any grounds at all we must form a judgment that the instance or instances adduced are sufficient to authorize the conclusion that it is allowable to take these instances as a sample warranting an inference respecting the whole class and the expression of this judgment in words it has been said by several of my critics is the major premise I quite admit that the major is an affirmation of the sufficiency of the evidence on which the conclusion rests That it is so is the very essence of my own theory And whoever admits that the major premise is only this adopts the theory in its essentials But I can not concede that this recognition of the sufficiency of the evidence that is of the correctness of the induction is a part of the induction itself unless we ought to say that it is a part of every thing we do to satisfy ourselves that it has been done rightly We conclude from known instances to unknown by the impulse of the generalizing propensity and until after a considerable amount of practice and mental discipline the question of the sufficiency of the evidence is only raised by a retrospective act turning back upon our own footsteps and examining whether we were warranted in doing what we have provisionally done To speak of this reflex operation as part of the original one requiring to be expressed in words in order that the verbal formula may correctly represent the psychological process appears to me false psychology We review our syllogistic as well as our inductive processes and recognize that they have been correctly performed but logicians do not add a third premise to the syllogism to express this act of recognition A careful copyist verifies his transcript by collating it with the original and if no error appears he recognizes that the transcript has been correctly made But we do not call the examination of the copy a part of the act of copying The conclusion in an induction is inferred from the evidence itself and not from a recognition of the sufficiency of the evidence as I infer that my friend is walking toward me because I see him and not because I recognize that my eyes are open and that eyesight is a means of knowledge In all operations which require care it is good to assure ourselves that the process has been performed accurately but the testing of the process is not the process itself and besides may have been omitted altogether and yet the process be correct It is precisely because that operation is omitted in ordinary unscientific reasoning that there is any thing gained in certainty by throwing reasoning into the syllogistic form To make sure as far as possible that it shall not be omitted we make the testing operation a part of the reasoning process itself We insist that the inference from particulars to particulars shall pass through a general proposition But this is a security for good reasoning not a condition of all reasoning and in some cases not even a security Our most familiar inferences are all made before we learn the use of general propositions and a person of untutored sagacity will skilfully apply his acquired experience to adjacent cases though he would bungle grievously in fixing the limits of the appropriate general theorem But though he may conclude rightly he never properly speaking knows whether he has done so or not he has not tested his reasoning Now this is precisely what forms of reasoning do for us We do not need them to enable us to reason but to enable us to know whether we reason correctly In still further answer to the objection it may be added that even when the test has been applied and the sufficiency of the evidence recognized if it is sufficient to support the general proposition it is sufficient also to support an inference from particulars to particulars without passing through the general proposition The inquirer who has logically satisfied himself that the conditions of legitimate induction were realized in the cases A B C would be as much justified in concluding directly to the Duke of Wellington as in concluding to all men The general conclusion is never legitimate unless the particular one would be so too and in no sense intelligible to me can the particular conclusion be said to be drawn from the general one Whenever there is ground for drawing any conclusion at all from particular instances there is ground for a general conclusion but that this general conclusion should be actually drawn however useful can not be an indispensable condition of the validity of the inference in the particular case A man gives away sixpence by the same power by which he disposes of his whole fortune but it is not necessary to the legality of the smaller act that he should make a formal assertion of his right to the greater one Some additional remarks in reply to minor objections are appended The preceding considerations enable us to understand the true nature of what is termed by recent writers Formal Logic and the relation between it and Logic in the widest sense Logic as I conceive it is the entire theory of the ascertainment of reasoned or inferred truth Formal Logic therefore which Sir William Hamilton from his own point of view and Archbishop Whately from his have represented as the whole of Logic properly so called is really a very subordinate part of it not being directly concerned with the process of Reasoning or Inference in the sense in which that process is a part of the Investigation of Truth What then is Formal Logic The name seems to be properly applied to all that portion of doctrine which relates to the equivalence of different modes of expression the rules for determining when assertions in a given form imply or suppose the truth or falsity of other assertions This includes the theory of the Import of Propositions and of their Conversion Equipollence and Opposition of those falsely called Inductions to be hereafter spoken of in which the apparent generalization is a mere abridged statement of cases known individually and finally of the syllogism while the theory of Naming and of what is inseparably connected with it Definition though belonging still more to the other and larger kind of logic than to this is a necessary preliminary to this The end aimed at by Formal Logic and attained by the observance of its precepts is not truth but consistency It has been seen that this is the only direct purpose of the rules of the syllogism the intention and effect of which is simply to keep our inferences or conclusions in complete consistency with our general formulae or directions for drawing them The Logic of Consistency is a necessary auxiliary to the logic of truth not only because what is inconsistent with itself or with other truths can not be true but also because truth can only be successfully pursued by drawing inferences from experience which if warrantable at all admit of being generalized and to test their warrantableness require to be exhibited in a generalized form after which the correctness of their application to particular cases is a question which specially concerns the Logic of Consistency This Logic not requiring any preliminary knowledge of the processes or conclusions of the various sciences may be studied with benefit in a much earlier stage of education than the Logic of Truth and the practice which has empirically obtained of teaching it apart through elementary treatises which do not attempt to include any thing else though the reasons assigned for the practice are in general very far from philosophical admits of philosophical justification In our analysis of the syllogism it appeared that the minor premise always affirms a resemblance between a new case and some cases previously known while the major premise asserts something which having been found true of those known cases we consider ourselves warranted in holding true of any other case resembling the former in certain given particulars If all ratiocinations resembled as to the minor premise the examples which were exclusively employed in the preceding chapter if the resemblance which that premise asserts were obvious to the senses as in the proposition Socrates is a man or were at once ascertainable by direct observation there would be no necessity for trains of reasoning and Deductive or Ratiocinative Sciences would not exist Trains of reasoning exist only for the sake of extending an induction founded as all inductions must be on observed cases to other cases in which we not only can not directly observe the fact which is to be proved but can not directly observe even the mark which is to prove it Suppose the syllogism to be All cows ruminate the animal which is before me is a cow therefore it ruminates The minor if true at all is obviously so the only premise the establishment of which requires any anterior process of inquiry is the major and provided the induction of which that premise is the expression was correctly performed the conclusion respecting the animal now present will be instantly drawn because as soon as she is compared with the formula she will be identified as being included in it But suppose the syllogism to be the following All arsenic is poisonous the substance which is before me is arsenic therefore it is poisonous The truth of the minor may not here be obvious at first sight it may not be intuitively evident but may itself be known only by inference It may be the conclusion of another argument which thrown into the syllogistic form would stand thus Whatever when lighted produces a dark spot on a piece of white porcelain held in the flame which spot is soluble in hypochloride of calcium is arsenic the substance before me conforms to this condition therefore it is arsenic To establish therefore the ultimate conclusion The substance before me is poisonous requires a process which in order to be syllogistically expressed stands in need of two syllogisms and we have a Train of Reasoning When however we thus add syllogism to syllogism we are really adding induction to induction Two separate inductions must have taken place to render this chain of inference possible inductions founded probably on different sets of individual instances but which converge in their results so that the instance which is the subject of inquiry comes within the range of them both The record of these inductions is contained in the majors of the two syllogisms First we or others for us have examined various objects which yielded under the given circumstances a dark spot with the given property and found that they possessed the properties connoted by the word arsenic they were metallic volatile their vapour had a smell of garlic and so forth Next we or others for us have examined various specimens which possessed this metallic and volatile character whose vapour had this smell etc and have invariably found that they were poisonous The first observation we judge that we may extend to all substances whatever which yield that particular kind of dark spot the second to all metallic and volatile substances resembling those we examined and consequently not to those only which are seen to be such but to those which are concluded to be such by the prior induction The substance before us is only seen to come within one of these inductions but by means of this one it is brought within the other We are still as before concluding from particulars to particulars but we are now concluding from particulars observed to other particulars which are not as in the simple case seen to resemble them in material points but inferred to do so because resembling them in something else which we have been led by quite a different set of instances to consider as a mark of the former resemblance This first example of a train of reasoning is still extremely simple the series consisting of only two syllogisms The following is somewhat more complicated No government which earnestly seeks the good of its subjects is likely to be overthrown some particular government earnestly seeks the good of its subjects therefore it is not likely to be overthrown The major premise in this argument we shall suppose not to be derived from considerations a priori but to be a generalization from history which whether correct or erroneous must have been founded on observation of governments concerning whose desire of the good of their subjects there was no doubt It has been found or thought to be found that these were not easily overthrown and it has been deemed that those instances warranted an extension of the same predicate to any and every government which resembles them in the attribute of desiring earnestly the good of its subjects But does the government in question thus resemble them This may be debated pro and con by many arguments and must in any case be proved by another induction for we can not directly observe the sentiments and desires of the persons who carry on the government To prove the minor therefore we require an argument in this form Every government which acts in a certain manner desires the good of its subjects the supposed government acts in that particular manner therefore it desires the good of its subjects But is it true that the government acts in the manner supposed This minor also may require proof still another induction as thus What is asserted by intelligent and disinterested witnesses may be believed to be true that the government acts in this manner is asserted by such witnesses therefore it may be believed to be true The argument hence consists of three steps Having the evidence of our senses that the case of the government under consideration resembles a number of former cases in the circumstance of having something asserted respecting it by intelligent and disinterested witnesses we infer first that as in those former instances so in this instance the assertion is true Secondly what was asserted of the government being that it acts in a particular manner and other governments or persons having been observed to act in the same manner the government in question is brought into known resemblance with those other governments or persons and since they were known to desire the good of the people it is thereupon by a second induction inferred that the particular government spoken of desires the good of the people This brings that government into known resemblance with the other governments which were thought likely to escape revolution and thence by a third induction it is concluded that this particular government is also likely to escape This is still reasoning from particulars to particulars but we now reason to the new instance from three distinct sets of former instances to one only of those sets of instances do we directly perceive the new one to be similar but from that similarity we inductively infer that it has the attribute by which it is assimilated to the next set and brought within the corresponding induction after which by a repetition of the same operation we infer it to be similar to the third set and hence a third induction conducts us to the ultimate conclusion Notwithstanding the superior complication of these examples compared with those by which in the preceding chapter we illustrated the general theory of reasoning every doctrine which we then laid down holds equally true in these more intricate cases The successive general propositions are not steps in the reasoning are not intermediate links in the chain of inference between the particulars observed and those to which we apply the observation If we had sufficiently capacious memories and a sufficient power of maintaining order among a huge mass of details the reasoning could go on without any general propositions they are mere formulae for inferring particulars from particulars The principle of general reasoning is as before explained that if from observation of certain known particulars what was seen to be true of them can be inferred to be true of any others it may be inferred of all others which are of a certain description And in order that we may never fail to draw this conclusion in a new case when it can be drawn correctly and may avoid drawing it when it can not we determine once for all what are the distinguishing marks by which such cases may be recognized The subsequent process is merely that of identifying an object and ascertaining it to have those marks whether we identify it by the very marks themselves or by others which we have ascertained through another and a similar process to be marks of those marks The real inference is always from particulars to particulars from the observed instances to an unobserved one but in drawing this inference we conform to a formula which we have adopted for our guidance in such operations and which is a record of the criteria by which we thought we had ascertained that we might distinguish when the inference could and when it could not be drawn The real premises are the individual observations even though they may have been forgotten or being the observations of others and not of ourselves may to us never have been known but we have before us proof that we or others once thought them sufficient for an induction and we have marks to show whether any new case is one of those to which if then known the induction would have been deemed to extend These marks we either recognize at once or by the aid of other marks which by another previous induction we collected to be marks of the first Even these marks of marks may only be recognized through a third set of marks and we may have a train of reasoning of any length to bring a new case within the scope of an induction grounded on particulars its similarity to which is only ascertained in this indirect manner Thus in the preceding example the ultimate inductive inference was that a certain government was not likely to be overthrown this inference was drawn according to a formula in which desire of the public good was set down as a mark of not being likely to be overthrown a mark of this mark was acting in a particular manner and a mark of acting in that manner was being asserted to do so by intelligent and disinterested witnesses this mark the government under discussion was recognized by the senses as possessing Hence that government fell within the last induction and by it was brought within all the others The perceived resemblance of the case to one set of observed particular cases brought it into known resemblance with another set and that with a third In the more complex branches of knowledge the deductions seldom consist as in the examples hitherto exhibited of a single chain a a mark of b b of c c of d therefore a a mark of d They consist to carry on the same metaphor of several chains united at the extremity as thus a a mark of d b of e c of f d e f of n therefore a b c a mark of n Suppose for example the following combination of circumstances 1st rays of light impinging on a reflecting surface 2d that surface parabolic 3d those rays parallel to each other and to the axis of the surface It is to be proved that the concourse of these three circumstances is a mark that the reflected rays will pass through the focus of the parabolic surface Now each of the three circumstances is singly a mark of something material to the case Rays of light impinging on a reflecting surface are a mark that those rays will be reflected at an angle equal to the angle of incidence The parabolic form of the surface is a mark that from any point of it a line drawn to the focus and a line parallel to the axis will make equal angles with the surface And finally the parallelism of the rays to the axis is a mark that their angle of incidence coincides with one of these equal angles The three marks taken together are therefore a mark of all these three things united But the three united are evidently a mark that the angle of reflection must coincide with the other of the two equal angles that formed by a line drawn to the focus and this again by the fundamental axiom concerning straight lines is a mark that the reflected rays pass through the focus Most chains of physical deduction are of this more complicated type and even in mathematics such are abundant as in all propositions where the hypothesis includes numerous conditions If a circle be taken and if within that circle a point be taken not the centre and if straight lines be drawn from that point to the circumference then etc The considerations now stated remove a serious difficulty from the view we have taken of reasoning which view might otherwise have seemed not easily reconcilable with the fact that there are Deductive or Ratiocinative Sciences It might seem to follow if all reasoning be induction that the difficulties of philosophical investigation must lie in the inductions exclusively and that when these were easy and susceptible of no doubt or hesitation there could be no science or at least no difficulties in science The existence for example of an extensive Science of Mathematics requiring the highest scientific genius in those who contributed to its creation and calling for a most continued and vigorous exertion of intellect in order to appropriate it when created may seem hard to be accounted for on the foregoing theory But the considerations more recently adduced remove the mystery by showing that even when the inductions themselves are obvious there may be much difficulty in finding whether the particular case which is the subject of inquiry comes within them and ample room for scientific ingenuity in so combining various inductions as by means of one within which the case evidently falls to bring it within others in which it can not be directly seen to be included When the more obvious of the inductions which can be made in any science from direct observations have been made and general formulas have been framed determining the limits within which these inductions are applicable as often as a new case can be at once seen to come within one of the formulas the induction is applied to the new case and the business is ended But new cases are continually arising which do not obviously come within any formula whereby the question we want solved in respect of them could be answered Let us take an instance from geometry and as it is taken only for illustration let the reader concede to us for the present what we shall endeavour to prove in the next chapter that the first principles of geometry are results of induction Our example shall be the fifth proposition of the first book of Euclid The inquiry is Are the angles at the base of an isosceles triangle equal or unequal The first thing to be considered is what inductions we have from which we can infer equality or inequality For inferring equality we have the following formulae Things which being applied to each other coincide are equals Things which are equal to the same thing are equals A whole and the sum of its parts are equals The sums of equal things are equals The differences of equal things are equals There are no other original formulae to prove equality For inferring inequality we have the following A whole and its parts are unequals The sums of equal things and unequal things are unequals The differences of equal things and unequal things are unequals In all eight formulae The angles at the base of an isosceles triangle do not obviously come within any of these The formulae specify certain marks of equality and of inequality but the angles can not be perceived intuitively to have any of those marks On examination it appears that they have and we ultimately succeed in bringing them within the formula The differences of equal things are equal Whence comes the difficulty of recognizing these angles as the differences of equal things Because each of them is the difference not of one pair only but of innumerable pairs of angles and out of these we had to imagine and select two which could either be intuitively perceived to be equals or possessed some of the marks of equality set down in the various formulae By an exercise of ingenuity which on the part of the first inventor deserves to be regarded as considerable two pairs of angles were hit upon which united these requisites First it could be perceived intuitively that their differences were the angles at the base and secondly they possessed one of the marks of equality namely coincidence when applied to one another This coincidence however was not perceived intuitively but inferred in conformity to another formula For greater clearness I subjoin an analysis of the demonstration Euclid it will be remembered demonstrates his fifth proposition by means of the fourth This it is not allowable for us to do because we are undertaking to trace deductive truths not to prior deductions but to their original inductive foundation We must therefore use the premises of the fourth proposition instead of its conclusion and prove the fifth directly from first principles To do so requires six formulas We presuppose an equilateral triangle whose vertices are A D E with point B on the side AD and point C on the side AE such that BC is parallel to DE We must begin as in Euclid by prolonging the equal sides AB AC to equal distances and joining the extremities BE DC FIRST FORMULA The sums of equals are equal AD and AE are sums of equals by the supposition Having that mark of equality they are concluded by this formula to be equal SECOND FORMULA Equal straight lines or angles being applied to one another coincide AC AB are within this formula by supposition AD AE have been brought within it by the preceding step The angle at A considered as an angle of the triangle ABE and the same angle considered as an angle of the triangle ACD are of course within the formula All these pairs therefore possess the property which according to the second formula is a mark that when applied to one another they will coincide Conceive them then applied to one another by turning over the triangle ABE and laying it on the triangle ACD in such a manner that AB of the one shall lie upon AC of the other Then by the equality of the angles AE will lie on AD But AB and AC AE and AD are equals therefore they will coincide altogether and of course at their extremities D E and B C THIRD FORMULA Straight lines having their extremities coincident coincide BE and CD have been brought within this formula by the preceding induction they will therefore coincide FOURTH FORMULA Angles having their sides coincident coincide The third induction having shown that BE and CD coincide and the second that AB AC coincide the angles ABE and ACD are thereby brought within the fourth formula and accordingly coincide FIFTH FORMULA Things which coincide are equal The angles ABE and ACD are brought within this formula by the induction immediately preceding This train of reasoning being also applicable mutatis mutandis to the angles EBC DCB these also are brought within the fifth formula And finally SIXTH FORMULA The differences of equals are equal The angle ABC being the difference of ABE CBE and the angle ACB being the difference of ACD DCB which have been proved to be equals ABC and ACB are brought within the last formula by the whole of the previous process The difficulty here encountered is chiefly that of figuring to ourselves the two angles at the base of the triangle ABC as remainders made by cutting one pair of angles out of another while each pair shall be corresponding angles of triangles which have two sides and the intervening angle equal It is by this happy contrivance that so many different inductions are brought to bear upon the same particular case And this not being at all an obvious thought it may be seen from an example so near the threshold of mathematics how much scope there may well be for scientific dexterity in the higher branches of that and other sciences in order so to combine a few simple inductions as to bring within each of them innumerable cases which are not obviously included in it and how long and numerous and complicated may be the processes necessary for bringing the inductions together even when each induction may itself be very easy and simple All the inductions involved in all geometry are comprised in those simple ones the formulae of which are the Axioms and a few of the socalled Definitions The remainder of the science is made up of the processes employed for bringing unforeseen cases within these inductions or in syllogistic language for proving the minors necessary to complete the syllogisms the majors being the definitions and axioms In those definitions and axioms are laid down the whole of the marks by an artful combination of which it has been found possible to discover and prove all that is proved in geometry The marks being so few and the inductions which furnish them being so obvious and familiar the connecting of several of them together which constitutes Deductions or Trains of Reasoning forms the whole difficulty of the science and with a trifling exception its whole bulk and hence Geometry is a Deductive Science It will be seen hereafter that there are weighty scientific reasons for giving to every science as much of the character of a Deductive Science as possible for endeavouring to construct the science from the fewest and the simplest possible inductions and to make these by any combinations however complicated suffice for proving even such truths relating to complex cases as could be proved if we chose by inductions from specific experience Every branch of natural philosophy was originally experimental each generalization rested on a special induction and was derived from its own distinct set of observations and experiments From being sciences of pure experiment as the phrase is or to speak more correctly sciences in which the reasonings mostly consist of no more than one step and are expressed by single syllogisms all these sciences have become to some extent and some of them in nearly the whole of their extent sciences of pure reasoning whereby multitudes of truths already known by induction from as many different sets of experiments have come to be exhibited as deductions or corollaries from inductive propositions of a simpler and more universal character Thus mechanics hydrostatics optics acoustics thermology have successively been rendered mathematical and astronomy was brought by Newton within the laws of general mechanics Why it is that the substitution of this circuitous mode of proceeding for a process apparently much easier and more natural is held and justly to be the greatest triumph of the investigation of nature we are not in this stage of our inquiry prepared to examine But it is necessary to remark that although by this progressive transformation all sciences tend to become more and more Deductive they are not therefore the less Inductive every step in the Deduction is still an Induction The opposition is not between the terms Deductive and Inductive but between Deductive and Experimental A science is experimental in proportion as every new case which presents any peculiar features stands in need of a new set of observations and experiments a fresh induction It is deductive in proportion as it can draw conclusions respecting cases of a new kind by processes which bring those cases under old inductions by ascertaining that cases which can not be observed to have the requisite marks have however marks of those marks We can now therefore perceive what is the generic distinction between sciences which can be made Deductive and those which must as yet remain Experimental The difference consists in our having been able or not yet able to discover marks of marks If by our various inductions we have been able to proceed no further than to such propositions as these a a mark of b or a and b marks of one another c a mark of d or c and d marks of one another without any thing to connect a or b with c or d we have a science of detached and mutually independent generalizations such as these that acids redden vegetable blues and that alkalies colour them green from neither of which propositions could we directly or indirectly infer the other and a science so far as it is composed of such propositions is purely experimental Chemistry in the present state of our knowledge has not yet thrown off this character There are other sciences however of which the propositions are of this kind a a mark of b b a mark of c c of d d of e etc In these sciences we can mount the ladder from a to e by a process of ratiocination we can conclude that a is a mark of e and that every object which has the mark a has the property e although perhaps we never were able to observe a and e together and although even d our only direct mark of e may not be perceptible in those objects but only inferable Or varying the first metaphor we may be said to get from a to e underground the marks b c d which indicate the route must all be possessed somewhere by the objects concerning which we are inquiring but they are below the surface a is the only mark that is visible and by it we are able to trace in succession all the rest We can now understand how an experimental may transform itself into a deductive science by the mere progress of experiment In an experimental science the inductions as we have said lie detached as a a mark of b c a mark of d e a mark of f and so on now a new set of instances and a consequent new induction may at any time bridge over the interval between two of these unconnected arches b for example may be ascertained to be a mark of c which enables us thenceforth to prove deductively that a is a mark of c Or as sometimes happens some comprehensive induction may raise an arch high in the air which bridges over hosts of them at once b d f and all the rest turning out to be marks of some one thing or of things between which a connection has already been traced As when Newton discovered that the motions whether regular or apparently anomalous of all the bodies of the solar system each of which motions had been inferred by a separate logical operation from separate marks were all marks of moving round a common centre with a centripetal force varying directly as the mass and inversely as the square of the distance from that centre This is the greatest example which has yet occurred of the transformation at one stroke of a science which was still to a great degree merely experimental into a deductive science Transformations of the same nature but on a smaller scale continually take place in the less advanced branches of physical knowledge without enabling them to throw off the character of experimental sciences Thus with regard to the two unconnected propositions before cited namely Acids redden vegetable blues Alkalies make them green it is remarked by Liebig that all blue coloring matters which are reddened by acids as well as reciprocally all red coloring matters which are rendered blue by alkalies contain nitrogen and it is quite possible that this circumstance may one day furnish a bond of connection between the two propositions in question by showing that the antagonistic action of acids and alkalies in producing or destroying the colour blue is the result of some one more general law Although this connecting of detached generalizations is so much gain it tends but little to give a deductive character to any science as a whole because the new courses of observation and experiment which thus enable us to connect together a few general truths usually make known to us a still greater number of unconnected new ones Hence chemistry though similar extensions and simplifications of its generalizations are continually taking place is still in the main an experimental science and is likely so to continue unless some comprehensive induction should be hereafter arrived at which like Newton’s shall connect a vast number of the smaller known inductions together and change the whole method of the science at once Chemistry has already one great generalization which though relating to one of the subordinate aspects of chemical phenomena possesses within its limited sphere this comprehensive character the principle of Dalton called the atomic theory or the doctrine of chemical equivalents which by enabling us to a certain extent to foresee the proportions in which two substances will combine before the experiment has been tried constitutes undoubtedly a source of new chemical truths obtainable by deduction as well as a connecting principle for all truths of the same description previously obtained by experiment The discoveries which change the method of a science from experimental to deductive mostly consist in establishing either by deduction or by direct experiment that the varieties of a particular phenomenon uniformly accompany the varieties of some other phenomenon better known Thus the science of sound which previously stood in the lowest rank of merely experimental science became deductive when it was proved by experiment that every variety of sound was consequent on and therefore a mark of a distinct and definable variety of oscillatory motion among the particles of the transmitting medium When this was ascertained it followed that every relation of succession or coexistence which obtained between phenomena of the more known class obtained also between the phenomena which correspond to them in the other class Every sound being a mark of a particular oscillatory motion became a mark of every thing which by the laws of dynamics was known to be inferable from that motion and every thing which by those same laws was a mark of any oscillatory motion among the particles of an elastic medium became a mark of the corresponding sound And thus many truths not before suspected concerning sound become deducible from the known laws of the propagation of motion through an elastic medium while facts already empirically known respecting sound become an indication of corresponding properties of vibrating bodies previously undiscovered But the grand agent for transforming experimental into deductive sciences is the science of number The properties of number alone among all known phenomena are in the most rigorous sense properties of all things whatever All things are not coloured or ponderable or even extended but all things are numerable And if we consider this science in its whole extent from common arithmetic up to the calculus of variations the truths already ascertained seem all but infinite and admit of indefinite extension These truths though affirmable of all things whatever of course apply to them only in respect of their quantity But if it comes to be discovered that variations of quality in any class of phenomena correspond regularly to variations of quantity either in those same or in some other phenomena every formula of mathematics applicable to quantities which vary in that particular manner becomes a mark of a corresponding general truth respecting the variations in quality which accompany them and the science of quantity being as far as any science can be altogether deductive the theory of that particular kind of qualities becomes to this extent deductive likewise The most striking instance in point which history affords though not an example of an experimental science rendered deductive but of an unparalleled extension given to the deductive process in a science which was deductive already is the revolution in geometry which originated with Descartes and was completed by Clairaut These great mathematicians pointed out the importance of the fact that to every variety of position in points direction in lines or form in curves or surfaces all of which are Qualities there corresponds a peculiar relation of quantity between either two or three rectilinear coordinates insomuch that if the law were known according to which those coordinates vary relatively to one another every other geometrical property of the line or surface in question whether relating to quantity or quality would be capable of being inferred Hence it followed that every geometrical question could be solved if the corresponding algebraical one could and geometry received an accession actual or potential of new truths corresponding to every property of numbers which the progress of the calculus had brought or might in future bring to light In the same general manner mechanics astronomy and in a less degree every branch of natural philosophy commonly so called have been made algebraical The varieties of physical phenomena with which those sciences are conversant have been found to answer to determinable varieties in the quantity of some circumstance or other or at least to varieties of form or position for which corresponding equations of quantity had already been or were susceptible of being discovered by geometers In these various transformations the propositions of the science of number do but fulfil the function proper to all propositions forming a train of reasoning viz that of enabling us to arrive in an indirect method by marks of marks at such of the properties of objects as we can not directly ascertain or not so conveniently by experiment We travel from a given visible or tangible fact through the truths of numbers to the facts sought The given fact is a mark that a certain relation subsists between the quantities of some of the elements concerned while the fact sought presupposes a certain relation between the quantities of some other elements now if these last quantities are dependent in some known manner upon the former or vic versa we can argue from the numerical relation between the one set of quantities to determine that which subsists between the other set the theorems of the calculus affording the intermediate links And thus one of the two physical facts becomes a mark of the other by being a mark of a mark of a mark of it If as laid down in the two preceding chapters the foundation of all sciences even deductive or demonstrative sciences is Induction if every step in the ratiocinations even of geometry is an act of induction and if a train of reasoning is but bringing many inductions to bear upon the same subject of inquiry and drawing a case within one induction by means of another wherein lies the peculiar certainty always ascribed to the sciences which are entirely or almost entirely deductive Why are they called the Exact Sciences Why are mathematical certainty and the evidence of demonstration common phrases to express the very highest degree of assurance attainable by reason Why are mathematics by almost all philosophers and by some even those branches of natural philosophy which through the medium of mathematics have been converted into deductive sciences considered to be independent of the evidence of experience and observation and characterized as systems of Necessary Truth The answer I conceive to be that this character of necessity ascribed to the truths of mathematics and even with some reservations to be hereafter made the peculiar certainty attributed to them is an illusion in order to sustain which it is necessary to suppose that those truths relate to and express the properties of purely imaginary objects It is acknowledged that the conclusions of geometry are deduced partly at least from the socalled Definitions and that those definitions are assumed to be correct representations as far as they go of the objects with which geometry is conversant Now we have pointed out that from a definition as such no proposition unless it be one concerning the meaning of a word can ever follow and that what apparently follows from a definition follows in reality from an implied assumption that there exists a real thing conformable thereto This assumption in the case of the definitions of geometry is not strictly true there exist no real things exactly conformable to the definitions There exist no points without magnitude no lines without breadth nor perfectly straight no circles with all their radii exactly equal nor squares with all their angles perfectly right It will perhaps be said that the assumption does not extend to the actual but only to the possible existence of such things I answer that according to any test we have of possibility they are not even possible Their existence so far as we can form any judgment would seem to be inconsistent with the physical constitution of our planet at least if not of the universe To get rid of this difficulty and at the same time to save the credit of the supposed system of necessary truth it is customary to say that the points lines circles and squares which are the subject of geometry exist in our conceptions merely and are part of our minds which minds by working on their own materials construct an a priori science the evidence of which is purely mental and has nothing whatever to do with outward experience By howsoever high authorities this doctrine may have been sanctioned it appears to me psychologically incorrect The points lines circles and squares which any one has in his mind are I apprehend simply copies of the points lines circles and squares which he has known in his experience Our idea of a point I apprehend to be simply our idea of the minimum visibile the smallest portion of surface which we can see A line as defined by geometers is wholly inconceivable We can reason about a line as if it had no breadth because we have a power which is the foundation of all the control we can exercise over the operations of our minds the power when a perception is present to our senses or a conception to our intellects of attending to a part only of that perception or conception instead of the whole But we can not conceive a line without breadth we can form no mental picture of such a line all the lines which we have in our minds are lines possessing breadth If any one doubts this we may refer him to his own experience I much question if any one who fancies that he can conceive what is called a mathematical line thinks so from the evidence of his consciousness I suspect it is rather because he supposes that unless such a conception were possible mathematics could not exist as a science a supposition which there will be no difficulty in showing to be entirely groundless Since then neither in nature nor in the human mind do there exist any objects exactly corresponding to the definitions of geometry while yet that science can not be supposed to be conversant about nonentities nothing remains but to consider geometry as conversant with such lines angles and figures as really exist and the definitions as they are called must be regarded as some of our first and most obvious generalizations concerning those natural objects The correctness of those generalizations as generalizations is without a flaw the equality of all the radii of a circle is true of all circles so far as it is true of any one but it is not exactly true of any circle it is only nearly true so nearly that no error of any importance in practice will be incurred by feigning it to be exactly true When we have occasion to extend these inductions or their consequences to cases in which the error would be appreciable to lines of perceptible breadth or thickness parallels which deviate sensibly from equidistance and the like we correct our conclusions by combining with them a fresh set of propositions relating to the aberration just as we also take in propositions relating to the physical or chemical properties of the material if those properties happen to introduce any modification into the result which they easily may even with respect to figure and magnitude as in the case for instance of expansion by heat So long however as there exists no practical necessity for attending to any of the properties of the object except its geometrical properties or to any of the natural irregularities in those it is convenient to neglect the consideration of the other properties and of the irregularities and to reason as if these did not exist accordingly we formally announce in the definitions that we intend to proceed on this plan But it is an error to suppose because we resolve to confine our attention to a certain number of the properties of an object that we therefore conceive or have an idea of the object denuded of its other properties We are thinking all the time of precisely such objects as we have seen and touched and with all the properties which naturally belong to them but for scientific convenience we feign them to be divested of all properties except those which are material to our purpose and in regard to which we design to consider them The peculiar accuracy supposed to be characteristic of the first principles of geometry thus appears to be fictitious The assertions on which the reasonings of the science are founded do not any more than in other sciences exactly correspond with the fact but we suppose that they do so for the sake of tracing the consequences which follow from the supposition The opinion of Dugald Stewart respecting the foundations of geometry is I conceive substantially correct that it is built on hypotheses that it owes to this alone the peculiar certainty supposed to distinguish it and that in any science whatever by reasoning from a set of hypotheses we may obtain a body of conclusions as certain as those of geometry that is as strictly in accordance with the hypotheses and as irresistibly compelling assent on condition that those hypotheses are true When therefore it is affirmed that the conclusions of geometry are necessary truths the necessity consists in reality only in this that they correctly follow from the suppositions from which they are deduced Those suppositions are so far from being necessary that they are not even true they purposely depart more or less widely from the truth The only sense in which necessity can be ascribed to the conclusions of any scientific investigation is that of legitimately following from some assumption which by the conditions of the inquiry is not to be questioned In this relation of course the derivative truths of every deductive science must stand to the inductions or assumptions on which the science is founded and which whether true or untrue certain or doubtful in themselves are always supposed certain for the purposes of the particular science And therefore the conclusions of all deductive sciences were said by the ancients to be necessary propositions We have observed already that to be predicated necessarily was characteristic of the predicable Proprium and that a proprium was any property of a thing which could be deduced from its essence that is from the properties included in its definition The important doctrine of Dugald Stewart which I have endeavoured to enforce has been contested by Dr Whewell both in the dissertation appended to his excellent Mechanical Euclid and in his elaborate work on the Philosophy of the Inductive Sciences in which last he also replies to an article in the Edinburgh Review ascribed to a writer of great scientific eminence in which Stewart’s opinion was defended against his former strictures The supposed refutation of Stewart consists in proving against him as has also been done in this work that the premises of geometry are not definitions but assumptions of the real existence of things corresponding to those definitions This however is doing little for Dr Whewell’s purpose for it is these very assumptions which are asserted to be hypotheses and which he if he denies that geometry is founded on hypotheses must show to be absolute truths All he does however is to observe that they at any rate are not arbitrary hypotheses that we should not be at liberty to substitute other hypotheses for them that not only a definition to be admissible must necessarily refer to and agree with some conception which we can distinctly frame in our thoughts but that the straight lines for instance which we define must be those by which angles are contained those by which triangles are bounded those of which parallelism may be predicated and the like And this is true but this has never been contradicted Those who say that the premises of geometry are hypotheses are not bound to maintain them to be hypotheses which have no relation whatever to fact Since an hypothesis framed for the purpose of scientific inquiry must relate to something which has real existence for there can be no science respecting nonentities it follows that any hypothesis we make respecting an object to facilitate our study of it must not involve any thing which is distinctly false and repugnant to its real nature we must not ascribe to the thing any property which it has not our liberty extends only to slightly exaggerating some of those which it has by assuming it to be completely what it really is very nearly and suppressing others under the indispensable obligation of restoring them whenever and in as far as their presence or absence would make any material difference in the truth of our conclusions Of this nature accordingly are the first principles involved in the definitions of geometry That the hypotheses should be of this particular character is however no further necessary than inasmuch as no others could enable us to deduce conclusions which with due corrections would be true of real objects and in fact when our aim is only to illustrate truths and not to investigate them we are not under any such restriction We might suppose an imaginary animal and work out by deduction from the known laws of physiology its natural history or an imaginary commonwealth and from the elements composing it might argue what would be its fate And the conclusions which we might thus draw from purely arbitrary hypotheses might form a highly useful intellectual exercise but as they could only teach us what would be the properties of objects which do not really exist they would not constitute any addition to our knowledge of nature while on the contrary if the hypothesis merely divests a real object of some portion of its properties without clothing it in false ones the conclusions will always express under known liability to correction actual truth But though Dr Whewell has not shaken Stewart’s doctrine as to the hypothetical character of that portion of the first principles of geometry which are involved in the socalled definitions he has I conceive greatly the advantage of Stewart on another important point in the theory of geometrical reasoning the necessity of admitting among those first principles axioms as well as definitions Some of the axioms of Euclid might no doubt be exhibited in the form of definitions or might be deduced by reasoning from propositions similar to what are so called Thus if instead of the axiom Magnitudes which can be made to coincide are equal we introduce a definition Equal magnitudes are those which may be so applied to one another as to coincide the three axioms which follow Magnitudes which are equal to the same are equal to one another If equals are added to equals the sums are equal If equals are taken from equals the remainders are equal may be proved by an imaginary superposition resembling that by which the fourth proposition of the first book of Euclid is demonstrated But though these and several others may be struck out of the list of first principles because though not requiring demonstration they are susceptible of it there will be found in the list of axioms two or three fundamental truths not capable of being demonstrated among which must be reckoned the proposition that two straight lines can not enclose a space or its equivalent Straight lines which coincide in two points coincide altogether and some property of parallel lines other than that which constitutes their definition one of the most suitable for the purpose being that selected by Professor Playfair Two straight lines which intersect each other can not both of them be parallel to a third straight line The axioms as well those which are indemonstrable as those which admit of being demonstrated differ from that other class of fundamental principles which are involved in the definitions in this that they are true without any mixture of hypothesis That things which are equal to the same thing are equal to one another is as true of the lines and figures in nature as it would be of the imaginary ones assumed in the definitions In this respect however mathematics are only on a par with most other sciences In almost all sciences there are some general propositions which are exactly true while the greater part are only more or less distant approximations to the truth Thus in mechanics the first law of motion the continuance of a movement once impressed until stopped or slackened by some resisting force is true without qualification or error The rotation of the earth in twentyfour hours of the same length as in our time has gone on since the first accurate observations without the increase or diminution of one second in all that period These are inductions which require no fiction to make them be received as accurately true but along with them there are others as for instance the propositions respecting the figure of the earth which are but approximations to the truth and in order to use them for the further advancement of our knowledge we must feign that they are exactly true though they really want something of being so It remains to inquire what is the ground of our belief in axioms what is the evidence on which they rest I answer they are experimental truths generalizations from observation The proposition Two straight lines can not enclose a space or, in other words, Two straight lines which have once met do not meet again but continue to diverge is an induction from the evidence of our senses This opinion runs counter to a scientific prejudice of long standing and great strength and there is probably no proposition enunciated in this work for which a more unfavourable reception is to be expected It is however no new opinion and even if it were so would be entitled to be judged not by its novelty but by the strength of the arguments by which it can be supported I consider it very fortunate that so eminent a champion of the contrary opinion as Dr Whewell has found occasion for a most elaborate treatment of the whole theory of axioms in attempting to construct the philosophy of the mathematical and physical sciences on the basis of the doctrine against which I now contend Whoever is anxious that a discussion should go to the bottom of the subject must rejoice to see the opposite side of the question worthily represented If what is said by Dr Whewell in support of an opinion which he has made the foundation of a systematic work can be shown not to be conclusive enough will have been done without going elsewhere in quest of stronger arguments and a more powerful adversary It is not necessary to show that the truths which we call axioms are originally suggested by observation and that we should never have known that two straight lines can not enclose a space if we had never seen a straight line thus much being admitted by Dr Whewell and by all in recent times who have taken his view of the subject But they contend that it is not experience which proves the axiom but that its truth is perceived a priori by the constitution of the mind itself from the first moment when the meaning of the proposition is apprehended and without any necessity for verifying it by repeated trials as is requisite in the case of truths really ascertained by observation They can not however but allow that the truth of the axiom Two straight lines can not enclose a space even if evident independently of experience is also evident from experience Whether the axiom needs confirmation or not it receives confirmation in almost every instant of our lives since we can not look at any two straight lines which intersect one another without seeing that from that point they continue to diverge more and more Experimental proof crowds in upon us in such endless profusion and without one instance in which there can be even a suspicion of an exception to the rule that we should soon have stronger ground for believing the axiom even as an experimental truth than we have for almost any of the general truths which we confessedly learn from the evidence of our senses Independently of a priori evidence we should certainly believe it with an intensity of conviction far greater than we accord to any ordinary physical truth and this too at a time of life much earlier than that from which we date almost any part of our acquired knowledge and much too early to admit of our retaining any recollection of the history of our intellectual operations at that period Where then is the necessity for assuming that our recognition of these truths has a different origin from the rest of our knowledge when its existence is perfectly accounted for by supposing its origin to be the same when the causes which produce belief in all other instances exist in this instance and in a degree of strength as much superior to what exists in other cases as the intensity of the belief itself is superior The burden of proof lies on the advocates of the contrary opinion it is for them to point out some fact inconsistent with the supposition that this part of our knowledge of nature is derived from the same sources as every other part This for instance they would be able to do if they could prove chronologically that we had the conviction at least practically so early in infancy as to be anterior to those impressions on the senses upon which on the other theory the conviction is founded This however can not be proved the point being too far back to be within the reach of memory and too obscure for external observation The advocates of the a priori theory are obliged to have recourse to other arguments These are reducible to two which I shall endeavour to state as clearly and as forcibly as possible In the first place it is said that if our assent to the proposition that two straight lines can not enclose a space were derived from the senses we could only be convinced of its truth by actual trial that is by seeing or feeling the straight lines whereas in fact it is seen to be true by merely thinking of them That a stone thrown into water goes to the bottom may be perceived by our senses but mere thinking of a stone thrown into the water would never have led us to that conclusion not so however with the axioms relating to straight lines if I could be made to conceive what a straight line is without having seen one I should at once recognize that two such lines can not enclose a space Intuition is imaginary looking but experience must be real looking if we see a property of straight lines to be true by merely fancying ourselves to be looking at them the ground of our belief can not be the senses or experience it must be something mental To this argument it might be added in the case of this particular axiom for the assertion would not be true of all axioms that the evidence of it from actual ocular inspection is not only unnecessary but unattainable What says the axiom That two straight lines can not enclose a space that after having once intersected if they are prolonged to infinity they do not meet but continue to diverge from one another How can this in any single case be proved by actual observation We may follow the lines to any distance we please but we can not follow them to infinity for aught our senses can testify they may immediately beyond the farthest point to which we have traced them begin to approach and at last meet Unless therefore we had some other proof of the impossibility than observation affords us we should have no ground for believing the axiom at all To these arguments which I trust I can not be accused of understating a satisfactory answer will I conceive be found if we advert to one of the characteristic properties of geometrical forms their capacity of being painted in the imagination with a distinctness equal to reality in other words the exact resemblance of our ideas of form to the sensations which suggest them This in the first place enables us to make at least with a little practice mental pictures of all possible combinations of lines and angles which resemble the realities quite as well as any which we could make on paper and in the next place make those pictures just as fit subjects of geometrical experimentation as the realities themselves inasmuch as pictures if sufficiently accurate exhibit of course all the properties which would be manifested by the realities at one given instant and on simple inspection and in geometry we are concerned only with such properties and not with that which pictures could not exhibit the mutual action of bodies one upon another The foundations of geometry would therefore be laid in direct experience even if the experiments which in this case consist merely in attentive contemplation were practiced solely upon what we call our ideas that is upon the diagrams in our minds and not upon outward objects For in all systems of experimentation we take some objects to serve as representatives of all which resemble them and in the present case the conditions which qualify a real object to be the representative of its class are completely fulfilled by an object existing only in our fancy Without denying therefore the possibility of satisfying ourselves that two straight lines can not enclose a space by merely thinking of straight lines without actually looking at them I contend that we do not believe this truth on the ground of the imaginary intuition simply but because we know that the imaginary lines exactly resemble real ones and that we may conclude from them to real ones with quite as much certainty as we could conclude from one real line to another The conclusion therefore is still an induction from observation And we should not be authorized to substitute observation of the image in our mind for observation of the reality if we had not learned by longcontinued experience that the properties of the reality are faithfully represented in the image just as we should be scientifically warranted in describing an animal which we have never seen from a picture made of it with a daguerreotype but not until we had learned by ample experience that observation of such a picture is precisely equivalent to observation of the original These considerations also remove the objection arising from the impossibility of ocularly following the lines in their prolongation to infinity For though in order actually to see that two given lines never meet it would be necessary to follow them to infinity yet without doing so we may know that if they ever do meet or if after diverging from one another they begin again to approach this must take place not at an infinite but at a finite distance Supposing therefore such to be the case we can transport ourselves thither in imagination and can frame a mental image of the appearance which one or both of the lines must present at that point which we may rely on as being precisely similar to the reality Now whether we fix our contemplation upon this imaginary picture or call to mind the generalizations we have had occasion to make from former ocular observation we learn by the evidence of experience that a line which after diverging from another straight line begins to approach to it produces the impression on our senses which we describe by the expression a bent line not by the expression a straight line The preceding argument which is to my mind unanswerable merges however in a still more comprehensive one which is stated most clearly and conclusively by Professor Bain The psychological reason why axioms and indeed many propositions not ordinarily classed as such may be learned from the idea only without referring to the fact is that in the process of acquiring the idea we have learned the fact The proposition is assented to as soon as the terms are understood because in learning to understand the terms we have acquired the experience which proves the proposition to be true We required says Mr Bain concrete experience in the first instance, to attain to the notion of whole and part but the notion once arrived at implies that the whole is greater In fact we could not have the notion without an experience tantamount to this conclusion When we have mastered the notion of straightness we have also mastered that aspect of it expressed by the affirmation that two straight lines can not enclose a space No intuitive or innate powers or perceptions are needed in such case We can not have the full meaning of Straightness without going through a comparison of straight objects among themselves and with their opposites bent or crooked objects The result of this comparison is inter alia that straightness in two lines is seen to be incompatible with inclosing a space the enclosure of space involves crookedness in at least one of the lines And similarly in the case of every first principle the same knowledge that makes it understood suffices to verify it The more this observation is considered the more I am convinced it will be felt to go to the very root of the controversy The first of the two arguments in support of the theory that axioms are a priori truths having I think been sufficiently answered I proceed to the second which is usually the most relied on Axioms it is asserted are conceived by us not only as true but as universally and necessarily true Now experience can not possibly give to any proposition this character I may have seen snow a hundred times and may have seen that it was white but this can not give me entire assurance even that all snow is white much less that snow must be white However many instances we may have observed of the truth of a proposition there is nothing to assure us that the next case shall not be an exception to the rule If it be strictly true that every ruminant animal yet known has cloven hoofs we still can not be sure that some creature will not hereafter be discovered which has the first of these attributes without having the other Experience must always consist of a limited number of observations and however numerous these may be they can show nothing with regard to the infinite number of cases in which the experiment has not been made Besides Axioms are not only universal they are also necessary Now experience can not offer the smallest ground for the necessity of a proposition She can observe and record what has happened but she can not find in any case or in any accumulation of cases any reason for what must happen She may see objects side by side but she can not see a reason why they must ever be side by side She finds certain events to occur in succession but the succession supplies in its occurrence no reason for its recurrence She contemplates external objects but she can not detect any internal bond which indissolubly connects the future with the past the possible with the real To learn a proposition by experience and to see it to be necessarily true are two altogether different processes of thought And Dr Whewell adds If any one does not clearly comprehend this distinction of necessary and contingent truths he will not be able to go along with us in our researches into the foundations of human knowledge nor indeed to pursue with success any speculation on the subject In the following passage we are told what the distinction is the nonrecognition of which incurs this denunciation Necessary truths are those in which we not only learn that the proposition is true but see that it must be true in which the negation of the truth is not only false but impossible in which we can not even by an effort of imagination or in a supposition conceive the reverse of that which is asserted That there are such truths can not be doubted We may take for example all relations of number Three and Two added together make Five We can not conceive it to be otherwise We can not by any freak of thought imagine Three and Two to make Seven Although Dr Whewell has naturally and properly employed a variety of phrases to bring his meaning more forcibly home he would I presume allow that they are all equivalent and that what he means by a necessary truth would be sufficiently defined a proposition the negation of which is not only false but inconceivable I am unable to find in any of his expressions turn them what way you will a meaning beyond this and I do not believe he would contend that they mean any thing more This therefore is the principle asserted that propositions the negation of which is inconceivable or in other words, which we can not figure to ourselves as being false must rest on evidence of a higher and more cogent description than any which experience can afford Now I can not but wonder that so much stress should be laid on the circumstance of inconceivableness when there is such ample experience to show that our capacity or incapacity of conceiving a thing has very little to do with the possibility of the thing in itself but is in truth very much an affair of accident and depends on the past history and habits of our own minds There is no more generally acknowledged fact in human nature than the extreme difficulty at first felt in conceiving any thing as possible which is in contradiction to long established and familiar experience or even to old familiar habits of thought And this difficulty is a necessary result of the fundamental laws of the human mind When we have often seen and thought of two things together and have never in any one instance either seen or thought of them separately there is by the primary law of association an increasing difficulty which may in the end become insuperable of conceiving the two things apart This is most of all conspicuous in uneducated persons who are in general utterly unable to separate any two ideas which have once become firmly associated in their minds and if persons of cultivated intellect have any advantage on the point it is only because having seen and heard and read more and being more accustomed to exercise their imagination they have experienced their sensations and thoughts in more varied combinations and have been prevented from forming many of these inseparable associations But this advantage has necessarily its limits The most practiced intellect is not exempt from the universal laws of our conceptive faculty If daily habit presents to any one for a long period two facts in combination and if he is not led during that period either by accident or by his voluntary mental operations to think of them apart he will probably in time become incapable of doing so even by the strongest effort and the supposition that the two facts can be separated in nature will at last present itself to his mind with all the characters of an inconceivable phenomenon There are remarkable instances of this in the history of science instances in which the most instructed men rejected as impossible because inconceivable things which their posterity by earlier practice and longer perseverance in the attempt found it quite easy to conceive and which every body now knows to be true There was a time when men of the most cultivated intellects and the most emancipated from the dominion of early prejudice could not credit the existence of antipodes were unable to conceive in opposition to old association the force of gravity acting upward instead of downward The Cartesians long rejected the Newtonian doctrine of the gravitation of all bodies toward one another on the faith of a general proposition the reverse of which seemed to them to be inconceivable the proposition that a body can not act where it is not All the cumbrous machinery of imaginary vortices assumed without the smallest particle of evidence appeared to these philosophers a more rational mode of explaining the heavenly motions than one which involved what seemed to them so great an absurdity And they no doubt found it as impossible to conceive that a body should act upon the earth from the distance of the sun or moon as we find it to conceive an end to space or time or two straight lines inclosing a space Newton himself had not been able to realize the conception or we should not have had his hypothesis of a subtle ether the occult cause of gravitation and his writings prove that though he deemed the particular nature of the intermediate agency a matter of conjecture the necessity of some such agency appeared to him indubitable If then it be so natural to the human mind even in a high state of culture to be incapable of conceiving and on that ground to believe impossible what is afterward not only found to be conceivable but proved to be true what wonder if in cases where the association is still older more confirmed and more familiar and in which nothing ever occurs to shake our conviction or even suggest to us any conception at variance with the association the acquired incapacity should continue and be mistaken for a natural incapacity It is true our experience of the varieties in nature enables us within certain limits to conceive other varieties analogous to them We can conceive the sun or moon falling for though we never saw them fall nor ever perhaps imagined them falling we have seen so many other things fall that we have innumerable familiar analogies to assist the conception which after all we should probably have some difficulty in framing were we not well accustomed to see the sun and moon move or appear to move so that we are only called upon to conceive a slight change in the direction of motion a circumstance familiar to our experience But when experience affords no model on which to shape the new conception how is it possible for us to form it How for example can we imagine an end to space or time We never saw any object without something beyond it nor experienced any feeling without something following it When therefore we attempt to conceive the last point of space we have the idea irresistibly raised of other points beyond it When we try to imagine the last instant of time we can not help conceiving another instant after it Nor is there any necessity to assume as is done by a modern school of metaphysicians a peculiar fundamental law of the mind to account for the feeling of infinity inherent in our conceptions of space and time that apparent infinity is sufficiently accounted for by simpler and universally acknowledged laws Now in the case of a geometrical axiom such for example as that two straight lines can not enclose a space a truth which is testified to us by our very earliest impressions of the external world how is it possible whether those external impressions be or be not the ground of our belief that the reverse of the proposition could be otherwise than inconceivable to us What analogy have we what similar order of facts in any other branch of our experience to facilitate to us the conception of two straight lines inclosing a space Nor is even this all I have already called attention to the peculiar property of our impressions of form that the ideas or mental images exactly resemble their prototypes and adequately represent them for the purposes of scientific observation From this and from the intuitive character of the observation which in this case reduces itself to simple inspection we can not so much as call up in our imagination two straight lines in order to attempt to conceive them inclosing a space without by that very act repeating the scientific experiment which establishes the contrary Will it really be contended that the inconceivableness of the thing in such circumstances proves any thing against the experimental origin of the conviction Is it not clear that in whichever mode our belief in the proposition may have originated the impossibility of our conceiving the negative of it must on either hypothesis be the same As then Dr Whewell exhorts those who have any difficulty in recognizing the distinction held by him between necessary and contingent truths to study geometry a condition which I can assure him I have conscientiously fulfilled I in return with equal confidence exhort those who agree with him to study the general laws of association being convinced that nothing more is requisite than a moderate familiarity with those laws to dispel the illusion which ascribes a peculiar necessity to our earliest inductions from experience and measures the possibility of things in themselves by the human capacity of conceiving them I hope to be pardoned for adding that Dr Whewell himself has both confirmed by his testimony the effect of habitual association in giving to an experimental truth the appearance of a necessary one and afforded a striking instance of that remarkable law in his own person In his Philosophy of the Inductive Sciences he continually asserts that propositions which not only are not selfevident but which we know to have been discovered gradually and by great efforts of genius and patience have when once established appeared so selfevident that but for historical proof it would have been impossible to conceive that they had not been recognized from the first by all persons in a sound state of their faculties We now despise those who in the Copernican controversy could not conceive the apparent motion of the sun on the heliocentric hypothesis or those who in opposition to Galileo thought that a uniform force might be that which generated a velocity proportional to the space or those who held there was something absurd in Newton’s doctrine of the different refrangibility of differently coloured rays or those who imagined that when elements combine their sensible qualities must be manifest in the compound or those who were reluctant to give up the distinction of vegetables into herbs shrubs and trees We can not help thinking that men must have been singularly dull of comprehension to find a difficulty in admitting what is to us so plain and simple We have a latent persuasion that we in their place should have been wiser and more clearsighted that we should have taken the right side and given our assent at once to the truth Yet in reality such a persuasion is a mere delusion The persons who in such instances as the above were on the losing side were very far in most cases from being persons more prejudiced or stupid or narrowminded than the greater part of mankind now are and the cause for which they fought was far from being a manifestly bad one till it had been so decided by the result of the war So complete has been the victory of truth in most of these instances that at present we can hardly imagine the struggle to have been necessary The very essence of these triumphs is that they lead us to regard the views we reject as not only false but inconceivable This last proposition is precisely what I contend for and I ask no more in order to overthrow the whole theory of its author on the nature of the evidence of axioms For what is that theory That the truth of axioms can not have been learned from experience because their falsity is inconceivable But Dr Whewell himself says that we are continually led by the natural progress of thought to regard as inconceivable what our forefathers not only conceived but believed nay even he might have added were unable to conceive the reverse of He can not intend to justify this mode of thought he can not mean to say that we can be right in regarding as inconceivable what others have conceived and as selfevident what to others did not appear evident at all After so complete an admission that inconceivableness is an accidental thing not inherent in the phenomenon itself but dependent on the mental history of the person who tries to conceive it how can he ever call upon us to reject a proposition as impossible on no other ground than its inconceivableness Yet he not only does so but has unintentionally afforded some of the most remarkable examples which can be cited of the very illusion which he has himself so clearly pointed out I select as specimens his remarks on the evidence of the three laws of motion and of the atomic theory With respect to the laws of motion Dr Whewell says No one can doubt that in historical fact these laws were collected from experience That such is the case is no matter of conjecture We know the time the persons the circumstances belonging to each step of each discovery After this testimony to adduce evidence of the fact would be superfluous And not only were these laws by no means intuitively evident but some of them were originally paradoxes The first law was especially so That a body once in motion would continue forever to move in the same direction with undiminished velocity unless acted upon by some new force was a proposition which mankind found for a long time the greatest difficulty in crediting It stood opposed to apparent experience of the most familiar kind which taught that it was the nature of motion to abate gradually and at last terminate of itself Yet when once the contrary doctrine was firmly established mathematicians as Dr Whewell observes speedily began to believe that laws thus contradictory to first appearances and which even after full proof had been obtained it had required generations to render familiar to the minds of the scientific world were under a demonstrable necessity compelling them to be such as they are and no other and he himself though not venturing absolutely to pronounce that all these laws can be rigorously traced to an absolute necessity in the nature of things does actually so think of the law just mentioned of which he says Though the discovery of the first law of motion was made historically speaking by means of experiment we have now attained a point of view in which we see that it might have been certainly known to be true independently of experience Can there be a more striking exemplification than is here afforded of the effect of association which we have described Philosophers for generations have the most extraordinary difficulty in putting certain ideas together they at last succeed in doing so and after a sufficient repetition of the process they first fancy a natural bond between the ideas then experience a growing difficulty which at last by the continuation of the same progress becomes an impossibility of severing them from one another If such be the progress of an experimental conviction of which the date is of yesterday and which is in opposition to first appearances how must it fare with those which are conformable to appearances familiar from the first dawn of intelligence and of the conclusiveness of which from the earliest records of human thought no sceptic has suggested even a momentary doubt The other instance which I shall quote is a truly astonishing one and may be called the reductio ad absurdum of the theory of inconceivableness Speaking of the laws of chemical composition Dr Whewell says That they could never have been clearly understood and therefore never firmly established without laborious and exact experiments is certain but yet we may venture to say that being once known they possess an evidence beyond that of mere experiment For how in fact can we conceive combinations otherwise than as definite in kind and quality If we were to suppose each element ready to combine with any other indifferently and indifferently in any quantity we should have a world in which all would be confusion and indefiniteness There would be no fixed kinds of bodies Salts and stones and ores would approach to and graduate into each other by insensible degrees Instead of this we know that the world consists of bodies distinguishable from each other by definite differences capable of being classified and named and of having general propositions asserted concerning them And as we can not conceive a world in which this should not be the case it would appear that we can not conceive a state of things in which the laws of the combination of elements should not be of that definite and measured kind which we have above asserted That a philosopher of Dr Whewell’s eminence should gravely assert that we can not conceive a world in which the simple elements should combine in other than definite proportions that by dint of meditating on a scientific truth the original discoverer of which was still living he should have rendered the association in his own mind between the idea of combination and that of constant proportions so familiar and intimate as to be unable to conceive the one fact without the other is so signal an instance of the mental law for which I am contending that one word more in illustration must be superfluous In the latest and most complete elaboration of his metaphysical system the Philosophy of Discovery as well as in the earlier discourse on the Fundamental Antithesis of Philosophy reprinted as an appendix to that work Dr Whewell while very candidly admitting that his language was open to misconception disclaims having intended to say that mankind in general can now perceive the law of definite proportions in chemical combination to be a necessary truth All he meant was that philosophical chemists in a future generation may possibly see this Some truths may be seen by intuition but yet the intuition of them may be a rare and a difficult attainment And he explains that the inconceivableness which according to his theory is the test of axioms depends entirely upon the clearness of the Ideas which the axioms involve So long as those ideas are vague and indistinct the contrary of an axiom may be assented to though it can not be distinctly conceived It may be assented to not because it is possible but because we do not see clearly what is possible To a person who is only beginning to think geometrically there may appear nothing absurd in the assertion that two straight lines may enclose a space And in the same manner to a person who is only beginning to think of mechanical truths it may not appear to be absurd that in mechanical processes Reaction should be greater or less than Action and so again to a person who has not thought steadily about Substance it may not appear inconceivable that by chemical operations we should generate new matter or destroy matter which already exists Necessary truths therefore are not those of which we can not conceive but those of which we can not distinctly conceive the contrary So long as our ideas are indistinct altogether we do not know what is or is not capable of being distinctly conceived but by the ever increasing distinctness with which scientific men apprehend the general conceptions of science they in time come to perceive that there are certain laws of nature which though historically and as a matter of fact they were learned from experience we can not now that we know them distinctly conceive to be other than they are The account which I should give of this progress of the scientific mind is somewhat different After a general law of nature has been ascertained men’s minds do not at first acquire a complete facility of familiarly representing to themselves the phenomena of nature in the character which that law assigns to them The habit which constitutes the scientific cast of mind that of conceiving facts of all descriptions conformably to the laws which regulate them phenomena of all descriptions according to the relations which have been ascertained really to exist between them this habit in the case of newlydiscovered relations comes only by degrees So long as it is not thoroughly formed no necessary character is ascribed to the new truth But in time the philosopher attains a state of mind in which his mental picture of nature spontaneously represents to him all the phenomena with which the new theory is concerned in the exact light in which the theory regards them all images or conceptions derived from any other theory or from the confused view of the facts which is anterior to any theory having entirely disappeared from his mind The mode of representing facts which results from the theory has now become to his faculties the only natural mode of conceiving them It is a known truth that a prolonged habit of arranging phenomena in certain groups and explaining them by means of certain principles makes any other arrangement or explanation of these facts be felt as unnatural and it may at last become as difficult to him to represent the facts to himself in any other mode as it often was originally to represent them in that mode But further if the theory is true as we are supposing it to be any other mode in which he tries or in which he was formerly accustomed to represent the phenomena will be seen by him to be inconsistent with the facts that suggested the new theory facts which now form a part of his mental picture of nature And since a contradiction is always inconceivable his imagination rejects these false theories and declares itself incapable of conceiving them Their inconceivableness to him does not however result from any thing in the theories themselves intrinsically and a priori repugnant to the human faculties it results from the repugnance between them and a portion of the facts which facts as long as he did not know or did not distinctly realize in his mental representations the false theory did not appear other than conceivable it becomes inconceivable merely from the fact that contradictory elements can not be combined in the same conception Although then his real reason for rejecting theories at variance with the true one is no other than that they clash with his experience he easily falls into the belief that he rejects them because they are inconceivable and that he adopts the true theory because it is selfevident and does not need the evidence of experience at all This I take to be the real and sufficient explanation of the paradoxical truth on which so much stress is laid by Dr Whewell that a scientifically cultivated mind is actually in virtue of that cultivation unable to conceive suppositions which a common man conceives without the smallest difficulty For there is nothing inconceivable in the suppositions themselves the impossibility is in combining them with facts inconsistent with them as part of the same mental picture an obstacle of course only felt by those who know the facts and are able to perceive the inconsistency As far as the suppositions themselves are concerned in the case of many of Dr Whewell’s necessary truths the negative of the axiom is and probably will be as long as the human race lasts as easily conceivable as the affirmative There is no axiom for example to which Dr Whewell ascribes a more thorough character of necessity and selfevidence than that of the indestructibility of matter That this is a true law of nature I fully admit but I imagine there is no human being to whom the opposite supposition is inconceivable who has any difficulty in imagining a portion of matter annihilated inasmuch as its apparent annihilation in no respect distinguishable from real by our unassisted senses takes place every time that water dries up or fuel is consumed Again the law that bodies combine chemically in definite proportions is undeniably true but few besides Dr Whewell have reached the point which he seems personally to have arrived at though he only dares prophesy similar success to the multitude after the lapse of generations that of being unable to conceive a world in which the elements are ready to combine with one another indifferently in any quantity nor is it likely that we shall ever rise to this sublime height of inability so long as all the mechanical mixtures in our planet whether solid liquid or a‘riform exhibit to our daily observation the very phenomenon declared to be inconceivable According to Dr Whewell these and similar laws of nature can not be drawn from experience inasmuch as they are on the contrary assumed in the interpretation of experience Our inability to add to or diminish the quantity of matter in the world is a truth which neither is nor can be derived from experience for the experiments which we make to verify it presuppose its truth When men began to use the balance in chemical analysis they did not prove by trial but took for granted as selfevident that the weight of the whole must be found in the aggregate weight of the elements True it is assumed but I apprehend no otherwise than as all experimental inquiry assumes provisionally some theory or hypothesis which is to be finally held true or not according as the experiments decide The hypothesis chosen for this purpose will naturally be one which groups together some considerable number of facts already known The proposition that the material of the world as estimated by weight is neither increased nor diminished by any of the processes of nature or art had many appearances in its favour to begin with It expressed truly a great number of familiar facts There were other facts which it had the appearance of conflicting with and which made its truth as a universal law of nature at first doubtful Because it was doubtful experiments were devised to verify it Men assumed its truth hypothetically and proceeded to try whether on more careful examination the phenomena which apparently pointed to a different conclusion would not be found to be consistent with it This turned out to be the case and from that time the doctrine took its place as a universal truth but as one proved to be such by experience That the theory itself preceded the proof of its truth that it had to be conceived before it could be proved and in order that it might be proved does not imply that it was selfevident and did not need proof Otherwise all the true theories in the sciences are necessary and selfevident for no one knows better than Dr Whewell that they all began by being assumed for the purpose of connecting them by deductions with those facts of experience on which as evidence they now confessedly rest In the examination which formed the subject of the last chapter into the nature of the evidence of those deductive sciences which are commonly represented to be systems of necessary truth we have been led to the following conclusions The results of those sciences are indeed necessary in the sense of necessarily following from certain first principles commonly called axioms and definitions that is of being certainly true if those axioms and definitions are so for the word necessity even in this acceptation of it means no more than certainty But their claim to the character of necessity in any sense beyond this as implying an evidence independent of and superior to observation and experience must depend on the previous establishment of such a claim in favour of the definitions and axioms themselves With regard to axioms we found that considered as experimental truths they rest on superabundant and obvious evidence We inquired whether since this is the case it be imperative to suppose any other evidence of those truths than experimental evidence any other origin for our belief of them than an experimental origin We decided that the burden of proof lies with those who maintain the affirmative and we examined at considerable length such arguments as they have produced The examination having led to the rejection of those arguments we have thought ourselves warranted in concluding that axioms are but a class the most universal class of inductions from experience the simplest and easiest cases of generalization from the facts furnished to us by our senses or by our internal consciousness While the axioms of demonstrative sciences thus appeared to be experimental truths the definitions as they are incorrectly called in those sciences were found by us to be generalizations from experience which are not even accurately speaking truths being propositions in which while we assert of some kind of object some property or properties which observation shows to belong to it we at the same time deny that it possesses any other properties though in truth other properties do in every individual instance accompany and in almost all instances modify the property thus exclusively predicated The denial therefore is a mere fiction or supposition made for the purpose of excluding the consideration of those modifying circumstances when their influence is of too trifling amount to be worth considering or adjourning it when important to a more convenient moment From these considerations it would appear that Deductive or Demonstrative Sciences are all without exception Inductive Sciences that their evidence is that of experience but that they are also in virtue of the peculiar character of one indispensable portion of the general formulae according to which their inductions are made Hypothetical Sciences Their conclusions are only true on certain suppositions which are or ought to be approximations to the truth but are seldom if ever exactly true and to this hypothetical character is to be ascribed the peculiar certainty which is supposed to be inherent in demonstration What we have now asserted however cannot be received as universally true of Deductive or Demonstrative Sciences until verified by being applied to the most remarkable of all those sciences that of Numbers the theory of the Calculus Arithmetic and Algebra It is harder to believe of the doctrines of this science than of any other either that they are not truths a priori but experimental truths or that their peculiar certainty is owing to their being not absolute but only conditional truths This therefore is a case which merits examination apart and the more so because on this subject we have a double set of doctrines to contend with that of the a priori philosophers on one side and on the other a theory the most opposite to theirs which was at one time very generally received and is still far from being altogether exploded among metaphysicians This theory attempts to solve the difficulty apparently inherent in the case by representing the propositions of the science of numbers as merely verbal and its processes as simple transformations of language substitutions of one expression for another The proposition Two and one is equal to three according to these writers is not a truth is not the assertion of a really existing fact but a definition of the word three a statement that mankind have agreed to use the name three as a sign exactly equivalent to two and one to call by the former name whatever is called by the other more clumsy phrase According to this doctrine the longest process in algebra is but a succession of changes in terminology by which equivalent expressions are substituted one for another a series of translations of the same fact from one into another language though how after such a series of translations the fact itself comes out changed as when we demonstrate a new geometrical theorem by algebra they have not explained and it is a difficulty which is fatal to their theory It must be acknowledged that there are peculiarities in the processes of arithmetic and algebra which render the theory in question very plausible and have not unnaturally made those sciences the stronghold of Nominalism The doctrine that we can discover facts detect the hidden processes of nature by an artful manipulation of language is so contrary to common sense that a person must have made some advances in philosophy to believe it men fly to so paradoxical a belief to avoid as they think some even greater difficulty which the vulgar do not see What has led many to believe that reasoning is a mere verbal process is that no other theory seemed reconcilable with the nature of the Science of Numbers For we do not carry any ideas along with us when we use the symbols of arithmetic or of algebra In a geometrical demonstration we have a mental diagram if not one on paper AB AC are present to our imagination as lines intersecting other lines forming an angle with one another and the like but not so a and b These may represent lines or any other magnitudes but those magnitudes are never thought of nothing is realized in our imagination but a and b The ideas which on the particular occasion they happen to represent are banished from the mind during every intermediate part of the process between the beginning when the premises are translated from things into signs and the end when the conclusion is translated back from signs into things Nothing then being in the reasoner’s mind but the symbols what can seem more inadmissible than to contend that the reasoning process has to do with any thing more We seem to have come to one of Bacon’s Prerogative Instances an experimentum crucis on the nature of reasoning itself Nevertheless it will appear on consideration that this apparently so decisive instance is no instance at all that there is in every step of an arithmetical or algebraical calculation a real induction a real inference of facts from facts and that what disguises the induction is simply its comprehensive nature and the consequent extreme generality of the language All numbers must be numbers of something there are no such things as numbers in the abstract Ten must mean ten bodies or ten sounds or ten beatings of the pulse But though numbers must be numbers of something they may be numbers of any thing Propositions therefore concerning numbers have the remarkable peculiarity that they are propositions concerning all things whatever all objects all existences of every kind known to our experience All things possess quantity consist of parts which can be numbered and in that character possess all the properties which are called properties of numbers That half of four is two must be true whatever the word four represents whether four hours four miles or four pounds weight We need only conceive a thing divided into four equal parts and all things may be conceived as so divided to be able to predicate of it every property of the number four that is every arithmetical proposition in which the number four stands on one side of the equation Algebra extends the generalization still farther every number represents that particular number of all things without distinction but every algebraical symbol does more it represents all numbers without distinction As soon as we conceive a thing divided into equal parts without knowing into what number of parts we may call it a or x and apply to it without danger of error every algebraical formula in the books The proposition 2 a b 2 a 2 b is a truth coextensive with all nature Since then algebraical truths are true of all things whatever and not like those of geometry true of lines only or of angles only it is no wonder that the symbols should not excite in our minds ideas of any things in particular When we demonstrate the fortyseventh proposition of Euclid it is not necessary that the words should raise in us an image of all rightangled triangles but only of some one rightangled triangle so in algebra we need not under the symbol a picture to ourselves all things whatever but only some one thing why not then the letter itself The mere written characters a b x y z serve as well for representatives of Things in general as any more complex and apparently more concrete conception That we are conscious of them however in their character of things and not of mere signs is evident from the fact that our whole process of reasoning is carried on by predicating of them the properties of things In resolving an algebraic equation by what rules do we proceed By applying at each step to a b and x the proposition that equals added to equals make equals that equals taken from equals leave equals and other propositions founded on these two These are not properties of language or of signs as such but of magnitudes which is as much as to say of all things The inferences therefore which are successively drawn are inferences concerning things not symbols though as any Things whatever will serve the turn there is no necessity for keeping the idea of the Thing at all distinct and consequently the process of thought may in this case be allowed without danger to do what all processes of thought when they have been performed often will do if permitted namely to become entirely mechanical Hence the general language of algebra comes to be used familiarly without exciting ideas as all other general language is prone to do from mere habit though in no other case than this can it be done with complete safety But when we look back to see from whence the probative force of the process is derived we find that at every single step unless we suppose ourselves to be thinking and talking of the things and not the mere symbols the evidence fails There is another circumstance which still more than that which we have now mentioned gives plausibility to the notion that the propositions of arithmetic and algebra are merely verbal That is that when considered as propositions respecting Things they all have the appearance of being identical propositions The assertion Two and one is equal to three considered as an assertion respecting objects as for instance Two pebbles and one pebble are equal to three pebbles does not affirm equality between two collections of pebbles but absolute identity It affirms that if we put one pebble to two pebbles those very pebbles are three The objects therefore being the very same and the mere assertion that objects are themselves being insignificant it seems but natural to consider the proposition Two and one is equal to three as asserting mere identity of signification between the two names This however though it looks so plausible will not bear examination The expression two pebbles and one pebble and the expression three pebbles stand indeed for the same aggregation of objects but they by no means stand for the same physical fact They are names of the same objects but of those objects in two different states though they denote the same things their connotation is different Three pebbles in two separate parcels and three pebbles in one parcel do not make the same impression on our senses and the assertion that the very same pebbles may by an alteration of place and arrangement be made to produce either the one set of sensations or the other though a very familiar proposition is not an identical one It is a truth known to us by early and constant experience an inductive truth and such truths are the foundation of the science of Number The fundamental truths of that science all rest on the evidence of sense they are proved by showing to our eyes and our fingers that any given number of objects ten balls for example may by separation and rearrangement exhibit to our senses all the different sets of numbers the sums of which is equal to ten All the improved methods of teaching arithmetic to children proceed on a knowledge of this fact All who wish to carry the child’s mind along with them in learning arithmetic all who wish to teach numbers and not mere ciphers now teach it through the evidence of the senses in the manner we have described We may if we please call the proposition Three is two and one a definition of the number three and assert that arithmetic as it has been asserted that geometry is a science founded on definitions But they are definitions in the geometrical sense not the logical asserting not the meaning of a term only but along with it an observed matter of fact The proposition A circle is a figure bounded by a line which has all its points equally distant from a point within it is called the definition of a circle but the proposition from which so many consequences follow and which is really a first principle in geometry is that figures answering to this description exist And thus we may call Three is two and one a definition of three but the calculations which depend on that proposition do not follow from the definition itself but from an arithmetical theorem presupposed in it namely that collections of objects exist which while they impress the senses thus Symbol three circles two above one may be separated into two parts thus Symbol two circles a space and a third circle This proposition being granted we term all such parcels Threes after which the enunciation of the abovementioned physical fact will serve also for a definition of the word Three The Science of Number is thus no exception to the conclusion we previously arrived at that the processes even of deductive sciences are altogether inductive and that their first principles are generalizations from experience It remains to be examined whether this science resembles geometry in the further circumstance that some of its inductions are not exactly true and that the peculiar certainty ascribed to it on account of which its propositions are called Necessary Truths is fictitious and hypothetical being true in no other sense than that those propositions legitimately follow from the hypothesis of the truth of premises which are avowedly mere approximations to truth The inductions of arithmetic are of two sorts first those which we have just expounded such as One and one are two Two and one are three etc which may be called the definitions of the various numbers in the improper or geometrical sense of the word Definition and secondly the two following axioms The sums of equals are equal The differences of equals are equal These two are sufficient for the corresponding propositions respecting unequals may be proved from these by a reductio ad absurdum These axioms and likewise the socalled definitions are as has already been said results of induction true of all objects whatever and as it may seem exactly true without the hypothetical assumption of unqualified truth where an approximation to it is all that exists The conclusions therefore it will naturally be inferred are exactly true and the science of number is an exception to other demonstrative sciences in this that the categorical certainty which is predicable of its demonstrations is independent of all hypothesis On more accurate investigation however it will be found that even in this case there is one hypothetical element in the ratiocination In all propositions concerning numbers a condition is implied without which none of them would be true and that condition is an assumption which may be false The condition is that 11 that all the numbers are numbers of the same or of equal units Let this be doubtful and not one of the propositions of arithmetic will hold true How can we know that one pound and one pound make two pounds if one of the pounds may be troy and the other avoirdupois They may not make two pounds of either or of any weight How can we know that a fortyhorse power is always equal to itself unless we assume that all horses are of equal strength It is certain that 1 is always equal in number to 1 and where the mere number of objects or of the parts of an object without supposing them to be equivalent in any other respect is all that is material the conclusions of arithmetic so far as they go to that alone are true without mixture of hypothesis There are such cases in statistics as for instance an inquiry into the amount of the population of any country It is indifferent to that inquiry whether they are grown people or children strong or weak tall or short the only thing we want to ascertain is their number But whenever from equality or inequality of number equality or inequality in any other respect is to be inferred arithmetic carried into such inquiries becomes as hypothetical a science as geometry All units must be assumed to be equal in that other respect and this is never accurately true for one actual pound weight is not exactly equal to another nor one measured mile’s length to another a nicer balance or more accurate measuring instruments would always detect some difference What is commonly called mathematical certainty therefore which comprises the twofold conception of unconditional truth and perfect accuracy is not an attribute of all mathematical truths but of those only which relate to pure Number as distinguished from Quantity in the more enlarged sense and only so long as we abstain from supposing that the numbers are a precise index to actual quantities The certainty usually ascribed to the conclusions of geometry and even to those of mechanics is nothing whatever but certainty of inference We can have full assurance of particular results under particular suppositions but we can not have the same assurance that these suppositions are accurately true nor that they include all the data which may exercise an influence over the result in any given instance It appears therefore that the method of all Deductive Sciences is hypothetical They proceed by tracing the consequences of certain assumptions leaving for separate consideration whether the assumptions are true or not and if not exactly true whether they are a sufficiently near approximation to the truth The reason is obvious Since it is only in questions of pure number that the assumptions are exactly true and even there only so long as no conclusions except purely numerical ones are to be founded on them it must in all other cases of deductive investigation form a part of the inquiry to determine how much the assumptions want of being exactly true in the case in hand This is generally a matter of observation to be repeated in every fresh case or if it has to be settled by argument instead of observation may require in every different case different evidence and present every degree of difficulty from the lowest to the highest But the other part of the process namely to determine what else may be concluded if we find and in proportion as we find the assumptions to be true may be performed once for all and the results held ready to be employed as the occasions turn up for use We thus do all beforehand that can be so done and leave the least possible work to be performed when cases arise and press for a decision This inquiry into the inferences which can be drawn from assumptions is what properly constitutes Demonstrative Science It is of course quite as practicable to arrive at new conclusions from facts assumed as from facts observed from fictitious as from real inductions Deduction as we have seen consists of a series of inferences in this form a is a mark of b b of c c of d therefore a is a mark of d which last may be a truth inaccessible to direct observation In like manner it is allowable to say suppose that a were a mark of b b of c and c of d a would be a mark of d which last conclusion was not thought of by those who laid down the premises A system of propositions as complicated as geometry might be deduced from assumptions which are false as was done by Ptolemy Descartes and others in their attempts to explain synthetically the phenomena of the solar system on the supposition that the apparent motions of the heavenly bodies were the real motions or were produced in some way more or less different from the true one Sometimes the same thing is knowingly done for the purpose of showing the falsity of the assumption which is called a reductio ad absurdum In such cases the reasoning is as follows a is a mark of b and b of c now if c were also a mark of d a would be a mark of d but d is known to be a mark of the absence of a consequently a would be a mark of its own absence which is a contradiction therefore c is not a mark of d It has even been held by some writers that all ratiocination rests in the last resort on a reductio ad absurdum since the way to enforce assent to it in case of obscurity would be to show that if the conclusion be denied we must deny some one at least of the premises which as they are all supposed true would be a contradiction And in accordance with this many have thought that the peculiar nature of the evidence of ratiocination consisted in the impossibility of admitting the premises and rejecting the conclusion without a contradiction in terms This theory however is inadmissible as an explanation of the grounds on which ratiocination itself rests If any one denies the conclusion notwithstanding his admission of the premises he is not involved in any direct and express contradiction until he is compelled to deny some premise and he can only be forced to do this by a reductio ad absurdum that is by another ratiocination now if he denies the validity of the reasoning process itself he can no more be forced to assent to the second syllogism than to the first In truth therefore no one is ever forced to a contradiction in terms he can only be forced to a contradiction or rather an infringement of the fundamental maxim of ratiocination namely that whatever has a mark has what it is a mark of or in the case of universal propositions that whatever is a mark of any thing is a mark of whatever else that thing is a mark of For in the case of every correct argument as soon as thrown into the syllogistic form it is evident without the aid of any other syllogism that he who admitting the premises fails to draw the conclusion does not conform to the above axiom We have now proceeded as far in the theory of Deduction as we can advance in the present stage of our inquiry Any further insight into the subject requires that the foundation shall have been laid of the philosophic theory of Induction itself in which theory that of Deduction as a mode of Induction which we have now shown it to be will assume spontaneously the place which belongs to it and will receive its share of whatever light may be thrown upon the great intellectual operation of which it forms so important a part Polemical discussion is foreign to the plan of this work But an opinion which stands in need of much illustration can often receive it most effectually and least tediously in the form of a defence against objections And on subjects concerning which speculative minds are still divided a writer does but half his duty by stating his own doctrine if he does not also examine and to the best of his ability judge those of other thinkers In the dissertation which Mr Herbert Spencer has prefixed to his in many respects highly philosophical treatise on the Mind he criticises some of the doctrines of the two preceding chapters and propounds a theory of his own on the subject of first principles Mr Spencer agrees with me in considering axioms to be simply our earliest inductions from experience But he differs from me widely as to the worth of the test of inconceivableness He thinks that it is the ultimate test of all beliefs He arrives at this conclusion by two steps First we never can have any stronger ground for believing any thing than that the belief of it invariably exists Whenever any fact or proposition is invariably believed that is if I understand Mr Spencer rightly believed by all persons and by one’s self at all times it is entitled to be received as one of the primitive truths or original premises of our knowledge Secondly the criterion by which we decide whether any thing is invariably believed to be true is our inability to conceive it as false The inconceivability of its negation is the test by which we ascertain whether a given belief invariably exists or not For our primary beliefs the fact of invariable existence tested by an abortive effort to cause their nonexistence is the only reason assignable He thinks this the sole ground of our belief in our own sensations If I believe that I feel cold I only receive this as true because I can not conceive that I am not feeling cold While the proposition remains true the negation of it remains inconceivable There are numerous other beliefs which Mr Spencer considers to rest on the same basis being chiefly those or a part of those which the metaphysicians of the Reid and Stewart school consider as truths of immediate intuition That there exists a material world that this is the very world which we directly and immediately perceive and not merely the hidden cause of our perceptions that Space Time Force Extension Figure are not modes of our consciousness but objective realities are regarded by Mr Spencer as truths known by the inconceivableness of their negatives We can not he says by any effort conceive these objects of thought as mere states of our mind as not having an existence external to us Their real existence is therefore as certain as our sensations themselves The truths which are the subject of direct knowledge being according to this doctrine known to be truths only by the inconceivability of their negation and the truths which are not the object of direct knowledge being known as inferences from those which are and those inferences being believed to follow from the premises only because we can not conceive them not to follow inconceivability is thus the ultimate ground of all assured beliefs Thus far there is no very wide difference between Mr Spencer’s doctrine and the ordinary one of philosophers of the intuitive school from Descartes to Dr Whewell but at this point Mr Spencer diverges from them For he does not like them set up the test of inconceivability as infallible On the contrary he holds that it may be fallacious not from any fault in the test itself but because men have mistaken for inconceivable things some things which were not inconceivable And he himself in this very book denies not a few propositions usually regarded as among the most marked examples of truths whose negations are inconceivable But occasional failure he says is incident to all tests If such failure vitiates the test of inconceivableness it must similarly vitiate all tests whatever We consider an inference logically drawn from established premises to be true Yet in millions of cases men have been wrong in the inferences they have thought thus drawn Do we therefore argue that it is absurd to consider an inference true on no other ground than that it is logically drawn from established premises No we say that though men may have taken for logical inferences inferences that were not logical there nevertheless are logical inferences and that we are justified in assuming the truth of what seem to us such until better instructed Similarly though men may have thought some things inconceivable which were not so there may still be inconceivable things and the inability to conceive the negation of a thing may still be our best warrant for believing it Though occasionally it may prove an imperfect test yet as our most certain beliefs are capable of no better to doubt any one belief because we have no higher guarantee for it is really to doubt all beliefs Mr Spencer’s doctrine therefore does not erect the curable but only the incurable limitations of the human conceptive faculty into laws of the outward universe The doctrine that a belief which is proved by the inconceivableness of its negation to invariably exist is true Mr Spencer enforces by two arguments one of which may be distinguished as positive and the other as negative The positive argument is that every such belief represents the aggregate of all past experience Conceding the entire truth of the position that during any phase of human progress the ability or inability to form a specific conception wholly depends on the experiences men have had and that by a widening of their experiences they may by and by be enabled to conceive things before inconceivable to them it may still be argued that as at any time the best warrant men can have for a belief is the perfect agreement of all preexisting experience in support of it it follows that at any time the inconceivableness of its negation is the deepest test any belief admits of Objective facts are ever impressing themselves upon us our experience is a register of these objective facts and the inconceivableness of a thing implies that it is wholly at variance with the register Even were this all it is not clear how if every truth is primarily inductive any better test of truth could exist But it must be remembered that while many of these facts impressing themselves upon us are occasional while others again are very general some are universal and unchanging These universal and unchanging facts are by the hypothesis certain to establish beliefs of which the negations are inconceivable while the others are not certain to do this and if they do subsequent facts will reverse their action Hence if after an immense accumulation of experiences there remain beliefs of which the negations are still inconceivable most if not all of them must correspond to universal objective facts If there be certain absolute uniformities in nature if these uniformities produce as they must absolute uniformities in our experience and if these absolute uniformities in our experience disable us from conceiving the negations of them then answering to each absolute uniformity in nature which we can cognize there must exist in us a belief of which the negation is inconceivable and which is absolutely true In this wide range of cases subjective inconceivableness must correspond to objective impossibility Further experience will produce correspondence where it may not yet exist and we may expect the correspondence to become ultimately complete In nearly all cases this test of inconceivableness must be valid now I wish I could think we were so nearly arrived at omniscience and where it is not it still expresses the net result of our experience up to the present time which is the most that any test can do To this I answer first that it is by no means true that the inconceivability by us of the negative of a proposition proves all or even any preexisting experience to be in favour of the affirmative There may have been no such preexisting experiences but only a mistaken supposition of experience How did the inconceivability of antipodes prove that experience had given any testimony against their possibility How did the incapacity men felt of conceiving sunset otherwise than as a motion of the sun represent any net result of experience in support of its being the sun and not the earth that moves It is not experience that is represented it is only a superficial semblance of experience The only thing proved with regard to real experience is the negative fact that men have not had it of the kind which would have made the inconceivable proposition conceivable Next Even if it were true that inconceivableness represents the net result of all past experience why should we stop at the representative when we can get at the thing represented If our incapacity to conceive the negation of a given supposition is proof of its truth because proving that our experience has hitherto been uniform in its favour the real evidence for the supposition is not the inconceivableness but the uniformity of experience Now this which is the substantial and only proof is directly accessible We are not obliged to presume it from an incidental consequence If all past experience is in favour of a belief let this be stated and the belief openly rested on that ground after which the question arises what that fact may be worth as evidence of its truth For uniformity of experience is evidence in very different degrees in some cases it is strong evidence in others weak in others it scarcely amounts to evidence at all That all metals sink in water was a uniform experience from the origin of the human race to the discovery of potassium in the present century by Sir Humphry Davy That all swans are white was a uniform experience down to the discovery of Australia In the few cases in which uniformity of experience does amount to the strongest possible proof as with such propositions as these Two straight lines can not enclose a space Every event has a cause it is not because their negations are inconceivable which is not always the fact but because the experience which has been thus uniform pervades all nature It will be shown in the following Book that none of the conclusions either of induction or of deduction can be considered certain except as far as their truth is shown to be inseparably bound up with truths of this class I maintain then first that uniformity of past experience is very far from being universally a criterion of truth But secondly inconceivableness is still further from being a test even of that test Uniformity of contrary experience is only one of many causes of inconceivability Tradition handed down from a period of more limited knowledge is one of the commonest The mere familiarity of one mode of production of a phenomenon often suffices to make every other mode appear inconceivable Whatever connects two ideas by a strong association may and continually does render their separation in thought impossible as Mr Spencer in other parts of his speculations frequently recognizes It was not for want of experience that the Cartesians were unable to conceive that one body could produce motion in another without contact They had as much experience of other modes of producing motion as they had of that mode The planets had revolved and heavy bodies had fallen every hour of their lives But they fancied these phenomena to be produced by a hidden machinery which they did not see because without it they were unable to conceive what they did see The inconceivableness instead of representing their experience dominated and overrode their experience Without dwelling further on what I have termed the positive argument of Mr Spencer in support of his criterion of truth I pass to his negative argument on which he lays more stress The negative argument is that whether inconceivability be good evidence or bad no stronger evidence is to be obtained That what is inconceivable can not be true is postulated in every act of thought It is the foundation of all our original premises Still more it is assumed in all conclusions from those premises The invariability of belief tested by the inconceivableness of its negation is our sole warrant for every demonstration Logic is simply a systematization of the process by which we indirectly obtain this warrant for beliefs that do not directly possess it To gain the strongest conviction possible respecting any complex fact we either analytically descend from it by successive steps each of which we unconsciously test by the inconceivableness of its negation until we reach some axiom or truth which we have similarly tested or we synthetically ascend from such axiom or truth by such steps In either case we connect some isolated belief with a belief which invariably exists by a series of intermediate beliefs which invariably exist The following passage sums up the theory When we perceive that the negation of the belief is inconceivable we have all possible warrant for asserting the invariability of its existence and in asserting this we express alike our logical justification of it and the inexorable necessity we are under of holding it We have seen that this is the assumption on which every conclusion whatever ultimately rests We have no other guarantee for the reality of consciousness of sensations of personal existence we have no other guarantee for any axiom we have no other guarantee for any step in a demonstration Hence as being taken for granted in every act of the understanding it must be regarded as the Universal Postulate But as this postulate which we are under an inexorable necessity of holding true is sometimes false as beliefs that once were shown by the inconceivableness of their negations to invariably exist have since been found untrue and as beliefs that now possess this character may some day share the same fate the canon of belief laid down by Mr Spencer is that the most certain conclusion is that which involves the postulate the fewest times Reasoning therefore never ought to prevail against one of the immediate beliefs the belief in Matter in the outward reality of Extension Space and the like because each of these involves the postulate only once while an argument besides involving it in the premises involves it again in every step of the ratiocination no one of the successive acts of inference being recognized as valid except because we can not conceive the conclusion not to follow from the premises It will be convenient to take the last part of this argument first In every reasoning according to Mr Spencer the assumption of the postulate is renewed at every step At each inference we judge that the conclusion follows from the premises our sole warrant for that judgment being that we can not conceive it not to follow Consequently if the postulate is fallible the conclusions of reasoning are more vitiated by that uncertainty than direct intuitions and the disproportion is greater the more numerous the steps of the argument To test this doctrine let us first suppose an argument consisting only of a single step which would be represented by one syllogism This argument does rest on an assumption and we have seen in the preceding chapters what the assumption is It is that whatever has a mark has what it is a mark of The evidence of this axiom I shall not consider at present let us suppose it with Mr Spencer to be the inconceivableness of its reverse Let us now add a second step to the argument we require what Another assumption No the same assumption a second time and so on to a third and a fourth I confess I do not see how on Mr Spencer’s own principles the repetition of the assumption at all weakens the force of the argument If it were necessary the second time to assume some other axiom the argument would no doubt be weakened since it would be necessary to its validity that both axioms should be true and it might happen that one was true and not the other making two chances of error instead of one But since it is the same axiom if it is true once it is true every time and if the argument being of a hundred links assumed the axiom a hundred times these hundred assumptions would make but one chance of error among them all It is satisfactory that we are not obliged to suppose the deductions of pure mathematics to be among the most uncertain of argumentative processes which on Mr Spencer’s theory they could hardly fail to be since they are the longest But the number of steps in an argument does not subtract from its reliableness if no new premises of an uncertain character are taken up by the way To speak next of the premises Our assurance of their truth whether they be generalities or individual facts is grounded in Mr Spencer’s opinion on the inconceivableness of their being false It is necessary to advert to a double meaning of the word inconceivable which Mr Spencer is aware of and would sincerely disclaim founding an argument upon but from which his case derives no little advantage notwithstanding By inconceivableness is sometimes meant inability to form or get rid of an idea sometimes inability to form or get rid of a belief The former meaning is the most conformable to the analogy of language for a conception always means an idea and never a belief The wrong meaning of inconceivable is however fully as frequent in philosophical discussion as the right meaning and the intuitive school of metaphysicians could not well do without either To illustrate the difference we will take two contrasted examples The early physical speculators considered antipodes incredible because inconceivable But antipodes were not inconceivable in the primitive sense of the word An idea of them could be formed without difficulty they could be completely pictured to the mental eye What was difficult and as it then seemed impossible was to apprehend them as believable The idea could be put together of men sticking on by their feet to the under side of the earth but the belief would follow that they must fall off Antipodes were not unimaginable but they were unbelievable On the other hand when I endeavour to conceive an end to extension the two ideas refuse to come together When I attempt to form a conception of the last point of space I can not help figuring to myself a vast space beyond that last point The combination is under the conditions of our experience unimaginable This double meaning of inconceivable it is very important to bear in mind for the argument from inconceivableness almost always turns on the alternate substitution of each of those meanings for the other In which of these two senses does Mr Spencer employ the term when he makes it a test of the truth of a proposition that its negation is inconceivable Until Mr Spencer expressly stated the contrary I inferred from the course of his argument that he meant unbelievable He has however in a paper published in the fifth number of the Fortnightly Review disclaimed this meaning and declared that by an inconceivable proposition he means now and always one of which the terms can not by any effort be brought before consciousness in that relation which the proposition asserts between them a proposition of which the subject and predicate offer an insurmountable resistance to union in thought We now therefore know positively that Mr Spencer always endeavours to use the word inconceivable in this its proper sense but it may yet be questioned whether his endeavour is always successful whether the other and popular use of the word does not sometimes creep in with its associations and prevent him from maintaining a clear separation between the two When for example he says that when I feel cold I can not conceive that I am not feeling cold this expression can not be translated into I can not conceive myself not feeling cold for it is evident that I can the word conceive therefore is here used to express the recognition of a matter of fact the perception of truth or falsehood which I apprehend to be exactly the meaning of an act of belief as distinguished from simple conception Again Mr Spencer calls the attempt to conceive something which is inconceivable an abortive effort to cause the nonexistence not of a conception or mental representation but of a belief There is need therefore to revise a considerable part of Mr Spencer’s language if it is to be kept always consistent with his definition of inconceivability But in truth the point is of little importance since inconceivability in Mr Spencer’s theory is only a test of truth inasmuch as it is a test of believability The inconceivableness of a supposition is the extreme case of its believability This is the very foundation of Mr Spencer’s doctrine The invariability of the belief is with him the real guarantee The attempt to conceive the negative is made in order to test the inevitableness of the belief It should be called an attempt to believe the negative When Mr Spencer says that while looking at the sun a man can not conceive that he is looking into darkness he should have said that a man can not believe that he is doing so For it is surely possible in broad daylight to imagine one’s self looking into darkness As Mr Spencer himself says speaking of the belief of our own existence That he might not exist he can conceive well enough but that he does not exist he finds it impossible to conceive ie to believe So that the statement resolves itself into this That I exist and that I have sensations I believe because I can not believe otherwise And in this case every one will admit that the impossibility is real Any one’s present sensations or other states of subjective consciousness that one person inevitably believes They are facts known per se it is impossible to ascend beyond them Their negative is really unbelievable and therefore there is never any question about believing it Mr Spencer’s theory is not needed for these truths But according to Mr Spencer there are other beliefs relating to other things than our own subjective feelings for which we have the same guarantee which are in a similar manner invariable and necessary With regard to these other beliefs they can not be necessary since they do not always exist There have been and are many persons who do not believe the reality of an external world still less the reality of extension and figure as the forms of that external world who do not believe that space and time have an existence independent of the mind nor any other of Mr Spencer’s objective intuitions The negations of these alleged invariable beliefs are not unbelievable for they are believed It may be maintained without obvious error that we can not imagine tangible objects as mere states of our own and other people’s consciousness that the perception of them irresistibly suggests to us the idea of something external to ourselves and I am not in a condition to say that this is not the fact though I do not think any one is entitled to affirm it of any person besides himself But many thinkers have believed whether they could conceive it or not that what we represent to ourselves as material objects are mere modifications of consciousness complex feelings of touch and of muscular action Mr Spencer may think the inference correct from the unimaginable to the unbelievable because he holds that belief itself is but the persistence of an idea and that what we can succeed in imagining we can not at the moment help apprehending as believable But of what consequence is it what we apprehend at the moment if the moment is in contradiction to the permanent state of our mind A person who has been frightened when an infant by stories of ghosts though he disbelieves them in after years and perhaps never believed them may be unable all his life to be in a dark place in circumstances stimulating to the imagination without mental discomposure The idea of ghosts with all its attendant terrors is irresistibly called up in his mind by the outward circumstances Mr Spencer may say that while he is under the influence of this terror he does not disbelieve in ghosts but has a temporary and uncontrollable belief in them Be it so but allowing it to be so which would it be truest to say of this man on the whole that he believes in ghosts or that he does not believe in them Assuredly that he does not believe in them The case is similar with those who disbelieve a material world Though they can not get rid of the idea though while looking at a solid object they can not help having the conception and therefore according to Mr Spencer’s metaphysics the momentary belief of its externality even at that moment they would sincerely deny holding that belief and it would be incorrect to call them other than disbelievers of the doctrine The belief therefore is not invariable and the test of inconceivableness fails in the only cases to which there could ever be any occasion to apply it That a thing may be perfectly believable and yet may not have become conceivable and that we may habitually believe one side of an alternative and conceive only in the other is familiarly exemplified in the state of mind of educated persons respecting sunrise and sunset All educated persons either know by investigation or believe on the authority of science that it is the earth and not the sun which moves but there are probably few who habitually conceive the phenomenon otherwise than as the ascent or descent of the sun Assuredly no one can do so without a prolonged trial and it is probably not easier now than in the first generation after Copernicus Mr Spencer does not say In looking at sunrise it is impossible not to conceive that it is the sun which moves therefore this is what every body believes and we have all the evidence for it that we can have for any truth Yet this would be an exact parallel to his doctrine about the belief in matter The existence of matter and other Noumena as distinguished from the phenomenal world remains a question of argument as it was before and the very general but neither necessary nor universal belief in them stands as a psychological phenomenon to be explained either on the hypothesis of its truth or on some other The belief is not a conclusive proof of its own truth unless there are no such things as idols but being a fact it calls on antagonists to show from what except the real existence of the thing believed so general and apparently spontaneous a belief can have originated And its opponents have never hesitated to accept this challenge The amount of their success in meeting it will probably determine the ultimate verdict of philosophers on the question In the revision or rather reconstruction of his Principles of Psychology as one of the stages or platforms in the imposing structure of his System of Philosophy Mr Spencer has resumed what he justly terms the amicable controversy that has been long pending between us expressing at the same time a regret which I cordially share that this lengthened exposition of a single point of difference unaccompanied by an exposition of the numerous points of concurrence unavoidably produces an appearance of dissent very far greater than that which exists I believe with Mr Spencer that the difference between us if measured by our conclusions is superficial rather than substantial and the value I attach to so great an amount of agreement in the field of analytic psychology with a thinker of his force and depth is such as I can hardly overstate But I also agree with him that the difference which exists in our premises is one of profound importance philosophically considered and not to be dismissed while any part of the case of either of us has not been fully examined and discussed In his present statement of the Universal Postulate Mr Spencer has exchanged his former expression beliefs which invariably exist for the following cognitions of which the predicates invariably exist along with their subjects And he says that an abortive effort to conceive the negation of a proposition shows that the cognition expressed is one of which the predicate invariably exists along with its subject and the discovery that the predicate invariably exists along with its subject is the discovery that this cognition is one we are compelled to accept Both these premises of Mr Spencer’s syllogism I am able to assent to but in different senses of the middle term If the invariable existence of the predicate along with its subject is to be understood in the most obvious meaning as an existence in actual Nature or in other words, in our objective or sensational experience I of course admit that this once ascertained compels us to accept the proposition but then I do not admit that the failure of an attempt to conceive the negative proves the predicate to be always coexistent with the subject in actual Nature If on the other hand which I believe to be Mr Spencer’s meaning the invariable existence of the predicate along with the subject is to be understood only of our conceptive faculty ie that the one is inseparable from the other in our thoughts then indeed the inability to separate the two ideas proves their inseparable conjunction here and now in the mind which has failed in the attempt but this inseparability in thought does not prove a corresponding inseparability in fact nor even in the thoughts of other people or of the same person in a possible future That some propositions have been wrongly accepted as true because their negations were supposed inconceivable when they were not does not in Mr Spencer’s opinion disprove the validity of the test not only because any test whatever is liable to yield untrue results either from incapacity or from carelessness in those who use it but because the propositions in question were complex propositions not to be established by a test applicable to propositions no further decomposable A test legitimately applicable to a simple proposition the subject and predicate of which are in direct relation can not be legitimately applied to a complex proposition the subject and predicate of which are indirectly related through the many simple propositions implied That things which are equal to the same thing are equal to one another is a fact which can be known by direct comparison of actual or ideal relations But that the square of the hypothenuse of a rightangled triangle equals the sum of the squares of the other two sides can not be known immediately by comparison of two states of consciousness here the truth can be reached only mediately through a series of simple judgments respecting the likenesses or unlikenesses of certain relations Moreover even when the proposition admits of being tested by immediate consciousness people often neglect to do it A schoolboy in adding up a column of figures will say 35 and 9 are 46 though this is contrary to the verdict which consciousness gives when 35 and 9 are really called up before it but this is not done And not only schoolboys but men and thinkers do not always distinctly translate into their equivalent states of consciousness the words they use It is but just to give Mr Spencer’s doctrine the benefit of the limitation he claims viz that it is only applicable to propositions which are assented to on simple inspection without any intervening media of proof But this limitation does not exclude some of the most marked instances of propositions now known to be false or groundless but whose negative was once found inconceivable such as that in sunrise and sunset it is the sun which moves that gravitation may exist without an intervening medium and even the case of antipodes The distinction drawn by Mr Spencer is real but in the case of the propositions classed by him as complex consciousness until the media of proof are supplied gives no verdict at all it neither declares the equality of the square of the hypothenuse with the sum of the squares of the sides to be inconceivable nor their inequality to be inconceivable But in all the three cases which I have just cited the inconceivability seems to be apprehended directly no train of argument was needed as in the case of the square of the hypothenuse to obtain the verdict of consciousness on the point Neither is any of the three a case like that of the schoolboy’s mistake in which the mind was never really brought into contact with the proposition They are cases in which one of two opposite predicates mero adspectu seemed to be incompatible with the subject and the other therefore to be proved always to exist with it As now limited by Mr Spencer the ultimate cognitions fit to be submitted to his test are only those of so universal and elementary a character as to be represented in the earliest and most unvarying experience or apparent experience of all mankind In such cases the inconceivability of the negative if real is accounted for by the experience and why I have asked should the truth be tested by the inconceivability when we can go further back for proof namely to the experience itself To this Mr Spencer answers that the experiences can not be all recalled to mind and if recalled would be of unmanageable multitude To test a proposition by experience seems to him to mean that before accepting as certain the proposition that any rectilinear figure must have as many angles as it has sides I have to think of every triangle square pentagon hexagon etc which I have ever seen and to verify the asserted relation in each case I can only say with surprise that I do not understand this to be the meaning of an appeal to experience It is enough to know that one has been seeing the fact all one’s life and has never remarked any instance to the contrary and that other people with every opportunity of observation unanimously declare the same thing It is true even this experience may be insufficient and so it might be even if I could recall to mind every instance of it but its insufficiency instead of being brought to light is disguised if instead of sifting the experience itself I appeal to a test which bears no relation to the sufficiency of the experience but at the most only to its familiarity These remarks do not lose their force even if we believe with Mr Spencer that mental tendencies originally derived from experience impress themselves permanently on the cerebral structure and are transmitted by inheritance so that modes of thinking which are acquired by the race become innate and a priori in the individual thus representing in Mr Spencer’s opinion the experience of his progenitors in addition to his own All that would follow from this is that a conviction might be really innate ie prior to individual experience and yet not be true since the inherited tendency to accept it may have been originally the result of other causes than its truth Mr Spencer would have a much stronger case if he could really show that the evidence of Reasoning rests on the Postulate or, in other words, that we believe that a conclusion follows from premises only because we can not conceive it not to follow But this statement seems to me to be of the same kind as one I have previously commented on viz that I believe I see light because I can not while the sensation remains conceive that I am looking into darkness Both these statements seem to me incompatible with the meaning as very rightly limited by Mr Spencer of the verb to conceive To say that when I apprehend that A is B and that B is C I can not conceive that A is not C is to my mind merely to say that I am compelled to believe that A is C If to conceive be taken in its proper meaning viz to form a mental representation I may be able to conceive A as not being C After assenting with full understanding to the Copernican proof that it is the earth and not the sun that moves I not only can conceive or represent to myself sunset as a motion of the sun but almost every one finds this conception of sunset easier to form than that which they nevertheless know to be the true one Sir William Hamilton holds as I do that inconceivability is no criterion of impossibility There is no ground for inferring a certain fact to be impossible merely from our inability to conceive its possibility Things there are which may nay must be true of which the understanding is wholly unable to construe to itself the possibility Sir William Hamilton is however a firm believer in the a priori character of many axioms and of the sciences deduced from them and is so far from considering those axioms to rest on the evidence of experience that he declares certain of them to be true even of Noumena of the Unconditioned of which it is one of the principal aims of his philosophy to prove that the nature of our faculties debars us from having any knowledge The axioms to which he attributes this exceptional emancipation from the limits which confine all our other possibilities of knowledge the chinks through which as he represents one ray of light finds its way to us from behind the curtain which veils from us the mysterious world of Things in themselves are the two principles which he terms after the schoolmen the Principle of Contradiction and the Principle of Excluded Middle the first that two contradictory propositions can not both be true the second that they can not both be false Armed with these logical weapons we may boldly face Things in themselves and tender to them the double alternative sure that they must absolutely elect one or the other side though we may be forever precluded from discovering which To take his favourite example we can not conceive the infinite divisibility of matter and we can not conceive a minimum or end to divisibility yet one or the other must be true As I have hitherto said nothing of the two axioms in question those of Contradiction and of Excluded Middle it is not unseasonable to consider them here The former asserts that an affirmative proposition and the corresponding negative proposition can not both be true which has generally been held to be intuitively evident Sir William Hamilton and the Germans consider it to be the statement in words of a form or law of our thinking faculty Other philosophers not less deserving of consideration deem it to be an identical proposition an assertion involved in the meaning of terms a mode of defining Negation and the word Not I am able to go one step with these last An affirmative assertion and its negative are not two independent assertions connected with each other only as mutually incompatible That if the negative be true the affirmative must be false really is a mere identical proposition for the negative proposition asserts nothing but the falsity of the affirmative and has no other sense or meaning whatever The Principium Contradictionis should therefore put off the ambitious phraseology which gives it the air of a fundamental antithesis pervading nature and should be enunciated in the simpler form that the same proposition can not at the same time be false and true But I can go no further with the Nominalists for I can not look upon this last as a merely verbal proposition I consider it to be like other axioms one of our first and most familiar generalizations from experience The original foundation of it I take to be that Belief and Disbelief are two different mental states excluding one another This we know by the simplest observation of our own minds And if we carry our observation outward we also find that light and darkness sound and silence motion and quiescence equality and inequality preceding and following succession and simultaneousness any positive phenomenon whatever and its negative are distinct phenomena pointedly contrasted and the one always absent where the other is present I consider the maxim in question to be a generalization from all these facts In like manner as the Principle of Contradiction that one of two contradictories must be false means that an assertion can not be both true and false so the Principle of Excluded Middle or that one of two contradictories must be true means that an assertion must be either true or false either the affirmative is true or otherwise the negative is true which means that the affirmative is false I can not help thinking this principle a surprising specimen of a socalled necessity of Thought since it is not even true unless with a large qualification A proposition must be either true or false provided that the predicate be one which can in any intelligible sense be attributed to the subject and as this is always assumed to be the case in treatises on logic the axiom is always laid down there as of absolute truth Abracadabra is a second intention is neither true nor false Between the true and the false there is a third possibility the Unmeaning and this alternative is fatal to Sir William Hamilton’s extension of the maxim to Noumena That Matter must either have a minimum of divisibility or be infinitely divisible is more than we can ever know For in the first place Matter in any other than the phenomenal sense of the term may not exist and it will scarcely be said that a nonentity must be either infinitely or finitely divisible In the second place though matter considered as the occult cause of our sensations do really exist yet what we call divisibility may be an attribute only of our sensations of sight and touch and not of their uncognizable cause Divisibility may not be predicable at all in any intelligible sense of Things in themselves nor therefore of Matter in itself and the assumed necessity of being either infinitely or finitely divisible may be an inapplicable alternative On this question I am happy to have the full concurrence of Mr Herbert Spencer from whose paper in the Fortnightly Review I extract the following passage The germ of an idea identical with that of Mr Spencer may be found in the present chapter on a preceding page but in Mr Spencer it is not an undeveloped thought but a philosophical theory When remembering a certain thing as in a certain place the place and the thing are mentally represented together while to think of the nonexistence of the thing in that place implies a consciousness in which the place is represented but not the thing Similarly if instead of thinking of an object as colourless we think of its having colour the change consists in the addition to the concept of an element that was before absent from it the object can not be thought of first as red and then as not red without one component of the thought being totally expelled from the mind by another The law of the Excluded Middle then is simply a generalization of the universal experience that some mental states are directly destructive of other states It formulates a certain absolutely constant law that the appearance of any positive mode of consciousness can not occur without excluding a correlative negative mode and that the negative mode can not occur without excluding the correlative positive mode the antithesis of positive and negative being indeed merely an expression of this experience Hence it follows that if consciousness is not in one of the two modes it must be in the other I must here close this supplementary chapter and with it the Second Book The theory of Induction in the most comprehensive sense of the term will form the subject of the Third According to the doctrine now stated the highest or rather the only proper object of physics is to ascertain those established conjunctions of successive events which constitute the order of the universe to record the phenomena which it exhibits to our observations or which it discloses to our experiments and to refer these phenomena to their general laws D STEWART Elements of the Philosophy of the Human Mind vol ii chap iv sect 1 In such cases the inductive and deductive methods of inquiry may be said to go hand in hand the one verifying the conclusions deduced by the other and the combination of experiment and theory which may thus be brought to bear in such cases forms an engine of discovery infinitely more powerful than either taken separately This state of any department of science is perhaps of all others the most interesting and that which promises the most to research SIR J HERSCHEL Discourse on the Study of Natural Philosophy The portion of the present inquiry upon which we are now about to enter may be considered as the principal both from its surpassing in intricacy all the other branches and because it relates to a process which has been shown in the preceding Book to be that in which the investigation of nature essentially consists We have found that all Inference consequently all Proof and all discovery of truths not selfevident consists of inductions and the interpretation of inductions that all our knowledge not intuitive comes to us exclusively from that source What Induction is therefore and what conditions render it legitimate can not but be deemed the main question of the science of logic the question which includes all others It is however one which professed writers on logic have almost entirely passed over The generalities of the subject have not been altogether neglected by metaphysicians but for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths their analysis of the inductive operation even when unexceptionable as to correctness has not been specific enough to be made the foundation of practical rules which might be for induction itself what the rules of the syllogism are for the interpretation of induction while those by whom physical science has been carried to its present state of improvement and who to arrive at a complete theory of the process needed only to generalize and adapt to all varieties of problems the methods which they themselves employed in their habitual pursuits never until very lately made any serious attempt to philosophize on the subject nor regarded the mode in which they arrived at their conclusions as deserving of study independently of the conclusions themselves For the purposes of the present inquiry Induction may be defined the operation of discovering and proving general propositions It is true that as already shown the process of indirectly ascertaining individual facts is as truly inductive as that by which we establish general truths But it is not a different kind of induction it is a form of the very same process since on the one hand generals are but collections of particulars definite in kind but indefinite in number and on the other hand whenever the evidence which we derive from observation of known cases justifies us in drawing an inference respecting even one unknown case we should on the same evidence be justified in drawing a similar inference with respect to a whole class of cases The inference either does not hold at all or it holds in all cases of a certain description in all cases which in certain definable respects resemble those we have observed If these remarks are just if the principles and rules of inference are the same whether we infer general propositions or individual facts it follows that a complete logic of the sciences would be also a complete logic of practical business and common life Since there is no case of legitimate inference from experience in which the conclusion may not legitimately be a general proposition an analysis of the process by which general truths are arrived at is virtually an analysis of all induction whatever Whether we are inquiring into a scientific principle or into an individual fact and whether we proceed by experiment or by ratiocination every step in the train of inferences is essentially inductive and the legitimacy of the induction depends in both cases on the same conditions True it is that in the case of the practical inquirer who is endeavouring to ascertain facts not for the purposes of science but for those of business such for instance as the advocate or the judge the chief difficulty is one in which the principles of induction will afford him no assistance It lies not in making his inductions but in the selection of them in choosing from among all general propositions ascertained to be true those which furnish marks by which he may trace whether the given subject possesses or not the predicate in question In arguing a doubtful question of fact before a jury the general propositions or principles to which the advocate appeals are mostly in themselves sufficiently trite and assented to as soon as stated his skill lies in bringing his case under those propositions or principles in calling to mind such of the known or received maxims of probability as admit of application to the case in hand and selecting from among them those best adapted to his object Success is here dependent on natural or acquired sagacity aided by knowledge of the particular subject and of subjects allied with it Invention though it can be cultivated can not be reduced to rule there is no science which will enable a man to bethink himself of that which will suit his purpose But when he has thought of something science can tell him whether that which he has thought of will suit his purpose or not The inquirer or arguer must be guided by his own knowledge and sagacity in the choice of the inductions out of which he will construct his argument But the validity of the argument when constructed depends on principles and must be tried by tests which are the same for all descriptions of inquiries whether the result be to give A an estate or to enrich science with a new general truth In the one case and in the other the senses or testimony must decide on the individual facts the rules of the syllogism will determine whether those facts being supposed correct the case really falls within the formulae of the different inductions under which it has been successively brought and finally the legitimacy of the inductions themselves must be decided by other rules and these it is now our purpose to investigate If this third part of the operation be in many of the questions of practical life not the most but the least arduous portion of it we have seen that this is also the case in some great departments of the field of science in all those which are principally deductive and most of all in mathematics where the inductions themselves are few in number and so obvious and elementary that they seem to stand in no need of the evidence of experience while to combine them so as to prove a given theorem or solve a problem may call for the utmost powers of invention and contrivance with which our species is gifted If the identity of the logical processes which prove particular facts and those which establish general scientific truths required any additional confirmation it would be sufficient to consider that in many branches of science single facts have to be proved as well as principles facts as completely individual as any that are debated in a court of justice but which are proved in the same manner as the other truths of the science and without disturbing in any degree the homogeneity of its method A remarkable example of this is afforded by astronomy The individual facts on which that science grounds its most important deductions such facts as the magnitudes of the bodies of the solar system their distances from one another the figure of the earth and its rotation are scarcely any of them accessible to our means of direct observation they are proved indirectly by the aid of inductions founded on other facts which we can more easily reach For example the distance of the moon from the earth was determined by a very circuitous process The share which direct observation had in the work consisted in ascertaining at one and the same instant the zenith distances of the moon as seen from two points very remote from one another on the earth’s surface The ascertainment of these angular distances ascertained their supplements and since the angle at the earth’s centre subtended by the distance between the two places of observation was deducible by spherical trigonometry from the latitude and longitude of those places the angle at the moon subtended by the same line became the fourth angle of a quadrilateral of which the other three angles were known The four angles being thus ascertained and two sides of the quadrilateral being radii of the earth the two remaining sides and the diagonal or, in other words, the moon’s distance from the two places of observation and from the centre of the earth could be ascertained at least in terms of the earth’s radius from elementary theorems of geometry At each step in this demonstration a new induction is taken in represented in the aggregate of its results by a general proposition Not only is the process by which an individual astronomical fact was thus ascertained exactly similar to those by which the same science establishes its general truths but also as we have shown to be the case in all legitimate reasoning a general proposition might have been concluded instead of a single fact In strictness indeed the result of the reasoning is a general proposition a theorem respecting the distance not of the moon in particular but of any inaccessible object showing in what relation that distance stands to certain other quantities And although the moon is almost the only heavenly body the distance of which from the earth can really be thus ascertained this is merely owing to the accidental circumstances of the other heavenly bodies which render them incapable of affording such data as the application of the theorem requires for the theorem itself is as true of them as it is of the moon We shall fall into no error then if in treating of Induction we limit our attention to the establishment of general propositions The principles and rules of Induction as directed to this end are the principles and rules of all Induction and the logic of Science is the universal Logic applicable to all inquiries in which man can engage Induction then is that operation of the mind by which we infer that what we know to be true in a particular case or cases will be true in all cases which resemble the former in certain assignable respects In other words Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class or that what is true at certain times will be true in similar circumstances at all times This definition excludes from the meaning of the term Induction various logical operations to which it is not unusual to apply that name Induction as above defined is a process of inference it proceeds from the known to the unknown and any operation involving no inference any process in which what seems the conclusion is no wider than the premises from which it is drawn does not fall within the meaning of the term Yet in the common books of Logic we find this laid down as the most perfect indeed the only quite perfect form of induction In those books every process which sets out from a less general and terminates in a more general expression which admits of being stated in the form This and that A are B therefore every A is B is called an induction whether any thing be really concluded or not and the induction is asserted not to be perfect unless every single individual of the class A is included in the antecedent or premise that is unless what we affirm of the class has already been ascertained to be true of every individual in it so that the nominal conclusion is not really a conclusion but a mere reassertion of the premises If we were to say All the planets shine by the sun’s light from observation of each separate planet or All the Apostles were Jews because this is true of Peter Paul John and every other apostle these and such as these would in the phraseology in question be called perfect and the only perfect Inductions This however is a totally different kind of induction from ours it is not an inference from facts known to facts unknown but a mere shorthand registration of facts known The two simulated arguments which we have quoted are not generalizations the propositions purporting to be conclusions from them are not really general propositions A general proposition is one in which the predicate is affirmed or denied of an unlimited number of individuals namely all whether few or many existing or capable of existing which possess the properties connoted by the subject of the proposition All men are mortal does not mean all now living but all men past present and to come When the signification of the term is limited so as to render it a name not for any and every individual falling under a certain general description but only for each of a number of individuals designated as such and as it were counted off individually the proposition though it may be general in its language is no general proposition but merely that number of singular propositions written in an abridged character The operation may be very useful as most forms of abridged notation are but it is no part of the investigation of truth though often bearing an important part in the preparation of the materials for that investigation As we may sum up a definite number of singular propositions in one proposition which will be apparently but not really general so we may sum up a definite number of general propositions in one proposition which will be apparently but not really more general If by a separate induction applied to every distinct species of animals it has been established that each possesses a nervous system and we affirm thereupon that all animals have a nervous system this looks like a generalization though as the conclusion merely affirms of all what has already been affirmed of each it seems to tell us nothing but what we knew before A distinction however must be made If in concluding that all animals have a nervous system we mean the same thing and no more as if we had said all known animals the proposition is not general and the process by which it is arrived at is not induction But if our meaning is that the observations made of the various species of animals have discovered to us a law of animal nature and that we are in a condition to say that a nervous system will be found even in animals yet undiscovered this indeed is an induction but in this case the general proposition contains more than the sum of the special propositions from which it is inferred The distinction is still more forcibly brought out when we consider that if this real generalization be legitimate at all its legitimacy probably does not require that we should have examined without exception every known species It is the number and nature of the instances and not their being the whole of those which happen to be known that makes them sufficient evidence to prove a general law while the more limited assertion which stops at all known animals can not be made unless we have rigorously verified it in every species In like manner to return to a former example we might have inferred not that all the planets but that all planets shine by reflected light the former is no induction the latter is an induction and a bad one being disproved by the case of double stars selfluminous bodies which are properly planets since they revolve round a centre There are several processes used in mathematics which require to be distinguished from Induction being not unfrequently called by that name and being so far similar to Induction properly so called that the propositions they lead to are really general propositions For example when we have proved with respect to the circle that a straight line can not meet it in more than two points and when the same thing has been successively proved of the ellipse the parabola and the hyperbola it may be laid down as a universal property of the sections of the cone The distinction drawn in the two previous examples can have no place here there being no difference between all known sections of the cone and all sections since a cone demonstrably can not be intersected by a plane except in one of these four lines It would be difficult therefore to refuse to the proposition arrived at the name of a generalization since there is no room for any generalization beyond it But there is no induction because there is no inference the conclusion is a mere summing up of what was asserted in the various propositions from which it is drawn A case somewhat though not altogether similar is the proof of a geometrical theorem by means of a diagram Whether the diagram be on paper or only in the imagination the demonstration as formerly observed does not prove directly the general theorem it proves only that the conclusion which the theorem asserts generally is true of the particular triangle or circle exhibited in the diagram but since we perceive that in the same way in which we have proved it of that circle it might also be proved of any other circle we gather up into one general expression all the singular propositions susceptible of being thus proved and embody them in a universal proposition Having shown that the three angles of the triangle ABC are together equal to two right angles we conclude that this is true of every other triangle not because it is true of ABC but for the same reason which proved it to be true of ABC If this were to be called Induction an appropriate name for it would be induction by parity of reasoning But the term can not properly belong to it the characteristic quality of Induction is wanting since the truth obtained though really general is not believed on the evidence of particular instances We do not conclude that all triangles have the property because some triangles have but from the ulterior demonstrative evidence which was the ground of our conviction in the particular instances There are nevertheless in mathematics some examples of socalled Induction in which the conclusion does bear the appearance of a generalization grounded on some of the particular cases included in it A mathematician when he has calculated a sufficient number of the terms of an algebraical or arithmetical series to have ascertained what is called the law of the series does not hesitate to fill up any number of the succeeding terms without repeating the calculations But I apprehend he only does so when it is apparent from a priori considerations which might be exhibited in the form of demonstration that the mode of formation of the subsequent terms each from that which preceded it must be similar to the formation of the terms which have been already calculated And when the attempt has been hazarded without the sanction of such general considerations there are instances on record in which it has led to false results It is said that Newton discovered the binomial theorem by induction by raising a binomial successively to a certain number of powers and comparing those powers with one another until he detected the relation in which the algebraic formula of each power stands to the exponent of that power and to the two terms of the binomial The fact is not improbable but a mathematician like Newton who seemed to arrive per saltum at principles and conclusions that ordinary mathematicians only reached by a succession of steps certainly could not have performed the comparison in question without being led by it to the a priori ground of the law since any one who understands sufficiently the nature of multiplication to venture upon multiplying several lines of symbols at one operation can not but perceive that in raising a binomial to a power the coefficients must depend on the laws of permutation and combination and as soon as this is recognized the theorem is demonstrated Indeed when once it was seen that the law prevailed in a few of the lower powers its identity with the law of permutation would at once suggest the considerations which prove it to obtain universally Even therefore such cases as these are but examples of what I have called Induction by parity of reasoning that is not really Induction because not involving inference of a general proposition from particular instances There remains a third improper use of the term Induction which it is of real importance to clear up because the theory of Induction has been in no ordinary degree confused by it and because the confusion is exemplified in the most recent and elaborate treatise on the inductive philosophy which exists in our language The error in question is that of confounding a mere description by general terms of a set of observed phenomena with an induction from them Suppose that a phenomenon consists of parts and that these parts are only capable of being observed separately and as it were piecemeal When the observations have been made there is a convenience amounting for many purposes to a necessity in obtaining a representation of the phenomenon as a whole by combining or as we may say piecing these detached fragments together A navigator sailing in the midst of the ocean discovers land he can not at first or by any one observation determine whether it is a continent or an island but he coasts along it and after a few days finds himself to have sailed completely round it he then pronounces it an island Now there was no particular time or place of observation at which he could perceive that this land was entirely surrounded by water he ascertained the fact by a succession of partial observations and then selected a general expression which summed up in two or three words the whole of what he so observed But is there any thing of the nature of an induction in this process Did he infer any thing that had not been observed from something else which had Certainly not He had observed the whole of what the proposition asserts That the land in question is an island is not an inference from the partial facts which the navigator saw in the course of his circumnavigation it is the facts themselves it is a summary of those facts the description of a complex fact to which those simpler ones are as the parts of a whole Now there is I conceive no difference in kind between this simple operation and that by which Kepler ascertained the nature of the planetary orbits and Kepler’s operation all at least that was characteristic in it was not more an inductive act than that of our supposed navigator The object of Kepler was to determine the real path described by each of the planets or let us say by the planet Mars since it was of that body that he first established the two of his three laws which did not require a comparison of planets To do this there was no other mode than that of direct observation and all which observation could do was to ascertain a great number of the successive places of the planet or rather of its apparent places That the planet occupied successively all these positions or at all events positions which produced the same impressions on the eye and that it passed from one of these to another insensibly and without any apparent breach of continuity thus much the senses with the aid of the proper instruments could ascertain What Kepler did more than this was to find what sort of a curve these different points would make supposing them to be all joined together He expressed the whole series of the observed places of Mars by what Dr Whewell calls the general conception of an ellipse This operation was far from being as easy as that of the navigator who expressed the series of his observations on successive points of the coast by the general conception of an island But it is the very same sort of operation and if the one is not an induction but a description this must also be true of the other The only real induction concerned in the case consisted in inferring that because the observed places of Mars were correctly represented by points in an imaginary ellipse therefore Mars would continue to revolve in that same ellipse and in concluding before the gap had been filled up by further observations that the positions of the planet during the time which intervened between two observations must have coincided with the intermediate points of the curve For these were facts which had not been directly observed They were inferences from the observations facts inferred as distinguished from facts seen But these inferences were so far from being a part of Kepler’s philosophical operation that they had been drawn long before he was born Astronomers had long known that the planets periodically returned to the same places When this had been ascertained there was no induction left for Kepler to make nor did he make any further induction He merely applied his new conception to the facts inferred as he did to the facts observed Knowing already that the planets continued to move in the same paths when he found that an ellipse correctly represented the past path he knew that it would represent the future path In finding a compendious expression for the one set of facts he found one for the other but he found the expression only not the inference nor did he which is the true test of a general truth add any thing to the power of prediction already possessed The descriptive operation which enables a number of details to be summed up in a single proposition Dr Whewell by an aptly chosen expression has termed the Colligation of Facts In most of his observations concerning that mental process I fully agree and would gladly transfer all that portion of his book into my own pages I only think him mistaken in setting up this kind of operation which according to the old and received meaning of the term is not induction at all as the type of induction generally and laying down throughout his work as principles of induction the principles of mere colligation Dr Whewell maintains that the general proposition which binds together the particular facts and makes them as it were one fact is not the mere sum of those facts but something more since there is introduced a conception of the mind which did not exist in the facts themselves The particular facts says he are not merely brought together but there is a new element added to the combination by the very act of thought by which they are combined When the Greeks after long observing the motions of the planets saw that these motions might be rightly considered as produced by the motion of one wheel revolving in the inside of another wheel these wheels were creations of their minds added to the facts which they perceived by sense And even if the wheels were no longer supposed to be material but were reduced to mere geometrical spheres or circles they were not the less products of the mind alone something additional to the facts observed The same is the case in all other discoveries The facts are known but they are insulated and unconnected till the discoverer supplies from his own store a principle of connection The pearls are there but they will not hang together till some one provides the string Let me first remark that Dr Whewell in this passage blends together indiscriminately examples of both the processes which I am endeavouring to distinguish from one another When the Greeks abandoned the supposition that the planetary motions were produced by the revolution of material wheels and fell back upon the idea of mere geometrical spheres or circles there was more in this change of opinion than the mere substitution of an ideal curve for a physical one There was the abandonment of a theory and the replacement of it by a mere description No one would think of calling the doctrine of material wheels a mere description That doctrine was an attempt to point out the force by which the planets were acted upon and compelled to move in their orbits But when by a great step in philosophy the materiality of the wheels was discarded and the geometrical forms alone retained the attempt to account for the motions was given up and what was left of the theory was a mere description of the orbits The assertion that the planets were carried round by wheels revolving in the inside of other wheels gave place to the proposition that they moved in the same lines which would be traced by bodies so carried which was a mere mode of representing the sum of the observed facts as Kepler’s was another and a better mode of representing the same observations It is true that for these simply descriptive operations as well as for the erroneous inductive one a conception of the mind was required The conception of an ellipse must have presented itself to Kepler’s mind before he could identify the planetary orbits with it According to Dr Whewell the conception was something added to the facts He expresses himself as if Kepler had put something into the facts by his mode of conceiving them But Kepler did no such thing The ellipse was in the facts before Kepler recognized it just as the island was an island before it had been sailed round Kepler did not put what he had conceived into the facts but saw it in them A conception implies and corresponds to something conceived and though the conception itself is not in the facts but in our mind yet if it is to convey any knowledge relating to them it must be a conception of something which really is in the facts some property which they actually possess and which they would manifest to our senses if our senses were able to take cognizance of it If for instance the planet left behind it in space a visible track and if the observer were in a fixed position at such a distance from the plane of the orbit as would enable him to see the whole of it at once he would see it to be an ellipse and if gifted with appropriate instruments and powers of locomotion he could prove it to be such by measuring its different dimensions Nay further if the track were visible and he were so placed that he could see all parts of it in succession but not all of them at once he might be able by piecing together his successive observations to discover both that it was an ellipse and that the planet moved in it The case would then exactly resemble that of the navigator who discovers the land to be an island by sailing round it If the path was visible no one I think would dispute that to identify it with an ellipse is to describe it and I can not see why any difference should be made by its not being directly an object of sense when every point in it is as exactly ascertained as if it were so Subject to the indispensable condition which has just been stated I do not conceive that the part which conceptions have in the operation of studying facts has ever been overlooked or undervalued No one ever disputed that in order to reason about any thing we must have a conception of it or that when we include a multitude of things under a general expression there is implied in the expression a conception of something common to those things But it by no means follows that the conception is necessarily preexistent or constructed by the mind out of its own materials If the facts are rightly classed under the conception it is because there is in the facts themselves something of which the conception is itself a copy and which if we can not directly perceive it is because of the limited power of our organs and not because the thing itself is not there The conception itself is often obtained by abstraction from the very facts which in Dr Whewell’s language it is afterward called in to connect This he himself admits when he observes which he does on several occasions how great a service would be rendered to the science of physiology by the philosopher who should establish a precise tenable and consistent conception of life Such a conception can only be abstracted from the phenomena of life itself from the very facts which it is put in requisition to connect In other cases no doubt instead of collecting the conception from the very phenomena which we are attempting to colligate we select it from among those which have been previously collected by abstraction from other facts In the instance of Kepler’s laws the latter was the case The facts being out of the reach of being observed in any such manner as would have enabled the senses to identify directly the path of the planet the conception requisite for framing a general description of that path could not be collected by abstraction from the observations themselves the mind had to supply hypothetically from among the conceptions it had obtained from other portions of its experience some one which would correctly represent the series of the observed facts It had to frame a supposition respecting the general course of the phenomenon and ask itself If this be the general description what will the details be and then compare these with the details actually observed If they agreed the hypothesis would serve for a description of the phenomenon if not it was necessarily abandoned and another tried It is such a case as this which gives rise to the doctrine that the mind in framing the descriptions adds something of its own which it does not find in the facts Yet it is a fact surely that the planet does describe an ellipse and a fact which we could see if we had adequate visual organs and a suitable position Not having these advantages but possessing the conception of an ellipse or to express the meaning in less technical language knowing what an ellipse was Kepler tried whether the observed places of the planet were consistent with such a path He found they were so and he consequently asserted as a fact that the planet moved in an ellipse But this fact which Kepler did not add to but found in the motions of the planet namely that it occupied in succession the various points in the circumference of a given ellipse was the very fact the separate parts of which had been separately observed it was the sum of the different observations Having stated this fundamental difference between my opinion and that of Dr Whewell I must add that his account of the manner in which a conception is selected suitable to express the facts appears to me perfectly just The experience of all thinkers will I believe testify that the process is tentative that it consists of a succession of guesses many being rejected until one at last occurs fit to be chosen We know from Kepler himself that before hitting upon the conception of an ellipse he tried nineteen other imaginary paths which finding them inconsistent with the observations he was obliged to reject But as Dr Whewell truly says the successful hypothesis though a guess ought generally to be called not a lucky but a skilful guess The guesses which serve to give mental unity and wholeness to a chaos of scattered particulars are accidents which rarely occur to any minds but those abounding in knowledge and disciplined in intellectual combinations How far this tentative method so indispensable as a means to the colligation of facts for purposes of description admits of application to Induction itself and what functions belong to it in that department will be considered in the chapter of the present Book which relates to Hypotheses On the present occasion we have chiefly to distinguish this process of Colligation from Induction properly so called and that the distinction may be made clearer it is well to advert to a curious and interesting remark which is as strikingly true of the former operation as it appears to me unequivocally false of the latter In different stages of the progress of knowledge philosophers have employed for the colligation of the same order of facts different conceptions The early rude observations of the heavenly bodies in which minute precision was neither attained nor sought presented nothing inconsistent with the representation of the path of a planet as an exact circle having the earth for its centre As observations increased in accuracy facts were disclosed which were not reconcilable with this simple supposition for the colligation of those additional facts the supposition was varied and varied again and again as facts became more numerous and precise The earth was removed from the centre to some other point within the circle the planet was supposed to revolve in a smaller circle called an epicycle round an imaginary point which revolved in a circle round the earth in proportion as observation elicited fresh facts contradictory to these representations other epicycles and other eccentrics were added producing additional complication until at last Kepler swept all these circles away and substituted the conception of an exact ellipse Even this is found not to represent with complete correctness the accurate observations of the present day which disclose many slight deviations from an orbit exactly elliptical Now Dr Whewell has remarked that these successive general expressions though apparently so conflicting were all correct they all answered the purpose of colligation they all enabled the mind to represent to itself with facility and by a simultaneous glance the whole body of facts at the time ascertained each in its turn served as a correct description of the phenomena so far as the senses had up to that time taken cognizance of them If a necessity afterward arose for discarding one of these general descriptions of the planet’s orbit and framing a different imaginary line by which to express the series of observed positions it was because a number of new facts had now been added which it was necessary to combine with the old facts into one general description But this did not affect the correctness of the former expression considered as a general statement of the only facts which it was intended to represent And so true is this that as is well remarked by M Comte these ancient generalizations even the rudest and most imperfect of them that of uniform movement in a circle are so far from being entirely false that they are even now habitually employed by astronomers when only a rough approximation to correctness is required L’astronomie moderne en dtruisant sans retour les hypothses primitives envisages comme lois relles du monde a soigneusement maintenu leur valeur positive et permanente la proprit de reprsenter commodment les phnomnes quand il s’agit d’une premire bauche Nos ressources ˆ cet gard sont mme bien plus tendues prcisment ˆ cause que nous ne nous faisons aucune illusion sur la ralit des hypothses ce qui nous permet d’employer sans scrupule en chaque cas celle que nous jugeons la plus avantageuse Dr Whewell’s remark therefore is philosophically correct Successive expressions for the colligation of observed facts or, in other words, successive descriptions of a phenomenon as a whole which has been observed only in parts may though conflicting be all correct as far as they go But it would surely be absurd to assert this of conflicting inductions The scientific study of facts may be undertaken for three different purposes the simple description of the facts their explanation or their prediction meaning by prediction the determination of the conditions under which similar facts may be expected again to occur To the first of these three operations the name of Induction does not properly belong to the other two it does Now Dr Whewell’s observation is true of the first alone Considered as a mere description the circular theory of the heavenly motions represents perfectly well their general features and by adding epicycles without limit those motions even as now known to us might be expressed with any degree of accuracy that might be required The elliptical theory as a mere description would have a great advantage in point of simplicity and in the consequent facility of conceiving it and reasoning about it but it would not really be more true than the other Different descriptions therefore may be all true but not surely different explanations The doctrine that the heavenly bodies moved by a virtue inherent in their celestial nature the doctrine that they were moved by impact which led to the hypothesis of vortices as the only impelling force capable of whirling bodies in circles and the Newtonian doctrine that they are moved by the composition of a centripetal with an original projectile force all these are explanations collected by real induction from supposed parallel cases and they were all successively received by philosophers as scientific truths on the subject of the heavenly bodies Can it be said of these as was said of the different descriptions that they are all true as far as they go Is it not clear that only one can be true in any degree and the other two must be altogether false So much for explanations let us now compare different predictions the first that eclipses will occur when one planet or satellite is so situated as to cast its shadow upon another the second that they will occur when some great calamity is impending over mankind Do these two doctrines only differ in the degree of their truth as expressing real facts with unequal degrees of accuracy Assuredly the one is true and the other absolutely false In every way therefore it is evident that to explain induction as the colligation of facts by means of appropriate conceptions that is conceptions which will really express them is to confound mere description of the observed facts with inference from those facts and ascribe to the latter what is a characteristic property of the former There is however between Colligation and Induction a real correlation which it is important to conceive correctly Colligation is not always induction but induction is always colligation The assertion that the planets move in ellipses was but a mode of representing observed facts it was but a colligation while the assertion that they are drawn or tend toward the sun was the statement of a new fact inferred by induction But the induction once made accomplishes the purposes of colligation likewise It brings the same facts which Kepler had connected by his conception of an ellipse under the additional conception of bodies acted upon by a central force and serves therefore as a new bond of connection for those facts a new principle for their classification Further the descriptions which are improperly confounded with induction are nevertheless a necessary preparation for induction no less necessary than correct observation of the facts themselves Without the previous colligation of detached observations by means of one general conception we could never have obtained any basis for an induction except in the case of phenomena of very limited compass We should not be able to affirm any predicates at all of a subject incapable of being observed otherwise than piecemeal much less could we extend those predicates by induction to other similar subjects Induction therefore always presupposes not only that the necessary observations are made with the necessary accuracy but also that the results of these observations are so far as practicable connected together by general descriptions enabling the mind to represent to itself as wholes whatever phenomena are capable of being so represented Dr Whewell has replied at some length to the preceding observations restating his opinions but without as far as I can perceive adding any thing material to his former arguments Since however mine have not had the good fortune to make any impression upon him I will subjoin a few remarks tending to show more clearly in what our difference of opinion consists as well as in some measure to account for it Nearly all the definitions of induction by writers of authority make it consist in drawing inferences from known cases to unknown affirming of a class a predicate which has been found true of some cases belonging to the class concluding because some things have a certain property that other things which resemble them have the same property or because a thing has manifested a property at a certain time that it has and will have that property at other times It will scarcely be contended that Kepler’s operation was an Induction in this sense of the term The statement that Mars moves in an elliptical orbit was no generalization from individual cases to a class of cases Neither was it an extension to all time of what had been found true at some particular time The whole amount of generalization which the case admitted of was already completed or might have been so Long before the elliptic theory was thought of it had been ascertained that the planets returned periodically to the same apparent places the series of these places was or might have been completely determined and the apparent course of each planet marked out on the celestial globe in an uninterrupted line Kepler did not extend an observed truth to other cases than those in which it had been observed he did not widen the subject of the proposition which expressed the observed facts The alteration he made was in the predicate Instead of saying the successive places of Mars are so and so he summed them up in the statement that the successive places of Mars are points in an ellipse It is true this statement as Dr Whewell says was not the sum of the observations merely it was the sum of the observations seen under a new point of view But it was not the sum of more than the observations as a real induction is It took in no cases but those which had been actually observed or which could have been inferred from the observations before the new point of view presented itself There was not that transition from known cases to unknown which constitutes Induction in the original and acknowledged meaning of the term Old definitions it is true can not prevail against new knowledge and if the Keplerian operation as a logical process be really identical with what takes place in acknowledged induction the definition of induction ought to be so widened as to take it in since scientific language ought to adapt itself to the true relations which subsist between the things it is employed to designate Here then it is that I am at issue with Dr Whewell He does think the operations identical He allows of no logical process in any case of induction other than what there was in Kepler’s case namely guessing until a guess is found which tallies with the facts and accordingly as we shall see hereafter he rejects all canons of induction because it is not by means of them that we guess Dr Whewell’s theory of the logic of science would be very perfect if it did not pass over altogether the question of Proof But in my apprehension there is such a thing as proof and inductions differ altogether from descriptions in their relation to that element Induction is proof it is inferring something unobserved from something observed it requires therefore an appropriate test of proof and to provide that test is the special purpose of inductive logic When on the contrary we merely collate known observations and in Dr Whewell’s phraseology connect them by means of a new conception if the conception does serve to connect the observations we have all we want As the proposition in which it is embodied pretends to no other truth than what it may share with many other modes of representing the same facts to be consistent with the facts is all it requires it neither needs nor admits of proof though it may serve to prove other things inasmuch as by placing the facts in mental connection with other facts not previously seen to resemble them it assimilates the case to another class of phenomena concerning which real Inductions have already been made Thus Kepler’s socalled law brought the orbit of Mars into the class ellipse and by doing so proved all the properties of an ellipse to be true of the orbit but in this proof Kepler’s law supplied the minor premise and not as is the case with real Inductions the major Dr Whewell calls nothing Induction where there is not a new mental conception introduced and every thing induction where there is But this is to confound two very different things Invention and Proof The introduction of a new conception belongs to Invention and invention may be required in any operation but is the essence of none A new conception may be introduced for descriptive purposes and so it may for inductive purposes But it is so far from constituting induction that induction does not necessarily stand in need of it Most inductions require no conception but what was present in every one of the particular instances on which the induction is grounded That all men are mortal is surely an inductive conclusion yet no new conception is introduced by it Whoever knows that any man has died has all the conceptions involved in the inductive generalization But Dr Whewell considers the process of invention which consists in framing a new conception consistent with the facts to be not merely a necessary part of all induction but the whole of it The mental operation which extracts from a number of detached observations certain general characters in which the observed phenomena resemble one another or resemble other known facts is what Bacon Locke and most subsequent metaphysicians have understood by the word Abstraction A general expression obtained by abstraction connecting known facts by means of common characters but without concluding from them to unknown may I think with strict logical correctness be termed a Description nor do I know in what other way things can ever be described My position however does not depend on the employment of that particular word I am quite content to use Dr Whewell’s term Colligation or the more general phrases mode of representing or of expressing phenomena provided it be clearly seen that the process is not Induction but something radically different What more may usefully be said on the subject of Colligation or of the correlative expression invented by Dr Whewell the Explication of Conceptions and generally on the subject of ideas and mental representations as connected with the study of facts will find a more appropriate place in the Fourth Book on the Operations Subsidiary to Induction to which I must refer the reader for the removal of any difficulty which the present discussion may have left Induction properly so called as distinguished from those mental operations sometimes though improperly designated by the name which I have attempted in the preceding chapter to characterize may then be summarily defined as Generalization from Experience It consists in inferring from some individual instances in which a phenomenon is observed to occur that it occurs in all instances of a certain class namely in all which resemble the former in what are regarded as the material circumstances In what way the material circumstances are to be distinguished from those which are immaterial or why some of the circumstances are material and others not so we are not yet ready to point out We must first observe that there is a principle implied in the very statement of what Induction is an assumption with regard to the course of nature and the order of the universe namely that there are such things in nature as parallel cases that what happens once will under a sufficient degree of similarity of circumstances happen again and not only again but as often as the same circumstances recur This I say is an assumption involved in every case of induction And if we consult the actual course of nature we find that the assumption is warranted The universe so far as known to us is so constituted that whatever is true in any one case is true in all cases of a certain description the only difficulty is to find what description This universal fact which is our warrant for all inferences from experience has been described by different philosophers in different forms of language that the course of nature is uniform that the universe is governed by general laws and the like One of the most usual of these modes of expression but also one of the most inadequate is that which has been brought into familiar use by the metaphysicians of the school of Reid and Stewart The disposition of the human mind to generalize from experience a propensity considered by these philosophers as an instinct of our nature they usually describe under some such name as our intuitive conviction that the future will resemble the past Now it has been well pointed out by Mr Bailey that whether the tendency be or not an original and ultimate element of our nature Time in its modifications of past present and future has no concern either with the belief itself or with the grounds of it We believe that fire will burn tomorrow because it burned today and yesterday but we believe on precisely the same grounds that it burned before we were born and that it burns this very day in CochinChina It is not from the past to the future as past and future that we infer but from the known to the unknown from facts observed to facts unobserved from what we have perceived or been directly conscious of to what has not come within our experience In this last predicament is the whole region of the future but also the vastly greater portion of the present and of the past Whatever be the most proper mode of expressing it the proposition that the course of nature is uniform is the fundamental principle or general axiom of Induction It would yet be a great error to offer this large generalization as any explanation of the inductive process On the contrary I hold it to be itself an instance of induction and induction by no means of the most obvious kind Far from being the first induction we make it is one of the last or at all events one of those which are latest in attaining strict philosophical accuracy As a general maxim indeed it has scarcely entered into the minds of any but philosophers nor even by them as we shall have many opportunities of remarking have its extent and limits been always very justly conceived The truth is that this great generalization is itself founded on prior generalizations The obscurer laws of nature were discovered by means of it but the more obvious ones must have been understood and assented to as general truths before it was ever heard of We should never have thought of affirming that all phenomena take place according to general laws if we had not first arrived in the case of a great multitude of phenomena at some knowledge of the laws themselves which could be done no otherwise than by induction In what sense then can a principle which is so far from being our earliest induction be regarded as our warrant for all the others In the only sense in which as we have already seen the general propositions which we place at the head of our reasonings when we throw them into syllogisms ever really contribute to their validity As Archbishop Whately remarks every induction is a syllogism with the major premise suppressed or as I prefer expressing it every induction may be thrown into the form of a syllogism by supplying a major premise If this be actually done the principle which we are now considering that of the uniformity of the course of nature will appear as the ultimate major premise of all inductions and will therefore stand to all inductions in the relation in which as has been shown at so much length the major proposition of a syllogism always stands to the conclusion not contributing at all to prove it but being a necessary condition of its being proved since no conclusion is proved for which there can not be found a true major premise The statement that the uniformity of the course of nature is the ultimate major premise in all cases of induction may be thought to require some explanation The immediate major premise in every inductive argument it certainly is not Of that Archbishop Whately’s must be held to be the correct account The induction John Peter etc are mortal therefore all mankind are mortal may as he justly says be thrown into a syllogism by prefixing as a major premise what is at any rate a necessary condition of the validity of the argument namely that what is true of John Peter etc is true of all mankind But how came we by this major premise It is not selfevident nay in all cases of unwarranted generalization it is not true How then is it arrived at Necessarily either by induction or ratiocination and if by induction the process like all other inductive arguments may be thrown into the form of a syllogism This previous syllogism it is therefore necessary to construct There is in the long run only one possible construction The real proof that what is true of John Peter etc is true of all mankind can only be that a different supposition would be inconsistent with the uniformity which we know to exist in the course of nature Whether there would be this inconsistency or not may be a matter of long and delicate inquiry but unless there would we have no sufficient ground for the major of the inductive syllogism It hence appears that if we throw the whole course of any inductive argument into a series of syllogisms we shall arrive by more or fewer steps at an ultimate syllogism which will have for its major premise the principle or axiom of the uniformity of the course of nature It was not to be expected that in the case of this axiom any more than of other axioms there should be unanimity among thinkers with respect to the grounds on which it is to be received as true I have already stated that I regard it as itself a generalization from experience Others hold it to be a principle which antecedently to any verification by experience we are compelled by the constitution of our thinking faculty to assume as true Having so recently and at so much length combated a similar doctrine as applied to the axioms of mathematics by arguments which are in a great measure applicable to the present case I shall defer the more particular discussion of this controverted point in regard to the fundamental axiom of induction until a more advanced period of our inquiry At present it is of more importance to understand thoroughly the import of the axiom itself For the proposition that the course of nature is uniform possesses rather the brevity suitable to popular than the precision requisite in philosophical language its terms require to be explained and a stricter than their ordinary signification given to them before the truth of the assertion can be admitted Every person’s consciousness assures him that he does not always expect uniformity in the course of events he does not always believe that the unknown will be similar to the known that the future will resemble the past Nobody believes that the succession of rain and fine weather will be the same in every future year as in the present Nobody expects to have the same dreams repeated every night On the contrary every body mentions it as something extraordinary if the course of nature is constant and resembles itself in these particulars To look for constancy where constancy is not to be expected as for instance that a day which has once brought good fortune will always be a fortunate day is justly accounted superstition The course of nature in truth is not only uniform it is also infinitely various Some phenomena are always seen to recur in the very same combinations in which we met with them at first others seem altogether capricious while some which we had been accustomed to regard as bound down exclusively to a particular set of combinations we unexpectedly find detached from some of the elements with which we had hitherto found them conjoined and united to others of quite a contrary description To an inhabitant of Central Africa fifty years ago no fact probably appeared to rest on more uniform experience than this that all human beings are black To Europeans not many years ago the proposition All swans are white appeared an equally unequivocal instance of uniformity in the course of nature Further experience has proved to both that they were mistaken but they had to wait fifty centuries for this experience During that long time mankind believed in a uniformity of the course of nature where no such uniformity really existed According to the notion which the ancients entertained of induction the foregoing were cases of as legitimate inference as any inductions whatever In these two instances in which the conclusion being false the ground of inference must have been insufficient there was nevertheless as much ground for it as this conception of induction admitted of The induction of the ancients has been well described by Bacon under the name of Inductio per enumerationem simplicem ubi non reperitur instantia contradictoria It consists in ascribing the character of general truths to all propositions which are true in every instance that we happen to know of This is the kind of induction which is natural to the mind when unaccustomed to scientific methods The tendency which some call an instinct and which others account for by association to infer the future from the past the known from the unknown is simply a habit of expecting that what has been found true once or several times and never yet found false will be found true again Whether the instances are few or many conclusive or inconclusive does not much affect the matter these are considerations which occur only on reflection the unprompted tendency of the mind is to generalize its experience provided this points all in one direction provided no other experience of a conflicting character comes unsought The notion of seeking it of experimenting for it of interrogating nature to use Bacon’s expression is of much later growth The observation of nature by uncultivated intellects is purely passive they accept the facts which present themselves without taking the trouble of searching for more it is a superior mind only which asks itself what facts are needed to enable it to come to a safe conclusion and then looks out for these But though we have always a propensity to generalize from unvarying experience we are not always warranted in doing so Before we can be at liberty to conclude that something is universally true because we have never known an instance to the contrary we must have reason to believe that if there were in nature any instances to the contrary we should have known of them This assurance in the great majority of cases we can not have or can have only in a very moderate degree The possibility of having it is the foundation on which we shall see hereafter that induction by simple enumeration may in some remarkable cases amount practically to proof No such assurance however can be had on any of the ordinary subjects of scientific inquiry Popular notions are usually founded on induction by simple enumeration in science it carries us but a little way We are forced to begin with it we must often rely on it provisionally in the absence of means of more searching investigation But for the accurate study of nature we require a surer and a more potent instrument It was above all by pointing out the insufficiency of this rude and loose conception of Induction that Bacon merited the title so generally awarded to him of Founder of the Inductive Philosophy The value of his own contributions to a more philosophical theory of the subject has certainly been exaggerated Although along with some fundamental errors his writings contain more or less fully developed several of the most important principles of the Inductive Method physical investigation has now far outgrown the Baconian conception of Induction Moral and political inquiry indeed are as yet far behind that conception The current and approved modes of reasoning on these subjects are still of the same vicious description against which Bacon protested the method almost exclusively employed by those professing to treat such matters inductively is the very inductio per enumerationem simplicem which he condemns and the experience which we hear so confidently appealed to by all sects parties and interests is still in his own emphatic words mera palpatio In order to a better understanding of the problem which the logician must solve if he would establish a scientific theory of Induction let us compare a few cases of incorrect inductions with others which are acknowledged to be legitimate Some we know which were believed for centuries to be correct were nevertheless incorrect That all swans are white can not have been a good induction since the conclusion has turned out erroneous The experience however on which the conclusion rested was genuine From the earliest records the testimony of the inhabitants of the known world was unanimous on the point The uniform experience therefore of the inhabitants of the known world agreeing in a common result without one known instance of deviation from that result is not always sufficient to establish a general conclusion But let us now turn to an instance apparently not very dissimilar to this Mankind were wrong it seems in concluding that all swans were white are we also wrong when we conclude that all men’s heads grow above their shoulders and never below in spite of the conflicting testimony of the naturalist Pliny As there were black swans though civilized people had existed for three thousand years on the earth without meeting with them may there not also be men whose heads do grow beneath their shoulders notwithstanding a rather less perfect unanimity of negative testimony from observers Most persons would answer No it was more credible that a bird should vary in its colour than that men should vary in the relative position of their principal organs And there is no doubt that in so saying they would be right but to say why they are right would be impossible without entering more deeply than is usually done into the true theory of Induction Again there are cases in which we reckon with the most unfailing confidence upon uniformity and other cases in which we do not count upon it at all In some we feel complete assurance that the future will resemble the past the unknown be precisely similar to the known In others however invariable may be the result obtained from the instances which have been observed we draw from them no more than a very feeble presumption that the like result will hold in all other cases That a straight line is the shortest distance between two points we do not doubt to be true even in the region of the fixed stars When a chemist announces the existence and properties of a newlydiscovered substance if we confide in his accuracy we feel assured that the conclusions he has arrived at will hold universally though the induction be founded but on a single instance We do not withhold our assent waiting for a repetition of the experiment or if we do it is from a doubt whether the one experiment was properly made not whether if properly made it would be conclusive Here then is a general law of nature inferred without hesitation from a single instance a universal proposition from a singular one Now mark another case and contrast it with this Not all the instances which have been observed since the beginning of the world in support of the general proposition that all crows are black would be deemed a sufficient presumption of the truth of the proposition to outweigh the testimony of one unexceptionable witness who should affirm that in some region of the earth not fully explored he had caught and examined a crow and had found it to be gray Why is a single instance in some cases sufficient for a complete induction while in others myriads of concurring instances without a single exception known or presumed go such a very little way toward establishing a universal proposition Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients and has solved the problem of induction In the contemplation of that uniformity in the course of nature which is assumed in every inference from experience one of the first observations that present themselves is that the uniformity in question is not properly uniformity but uniformities The general regularity results from the coexistence of partial regularities The course of nature in general is constant because the course of each of the various phenomena that compose it is so A certain fact invariably occurs whenever certain circumstances are present and does not occur when they are absent the like is true of another fact and so on From these separate threads of connection between parts of the great whole which we term nature a general tissue of connection unavoidably weaves itself by which the whole is held together If A is always accompanied by D B by E and C by F it follows that A B is accompanied by D E A C by D F B C by E F and finally A B C by D E F and thus the general character of regularity is produced which along with and in the midst of infinite diversity pervades all nature The first point therefore to be noted in regard to what is called the uniformity of the course of nature is that it is itself a complex fact compounded of all the separate uniformities which exist in respect to single phenomena These various uniformities when ascertained by what is regarded as a sufficient induction we call in common parlance Laws of Nature Scientifically speaking that title is employed in a more restricted sense to designate the uniformities when reduced to their most simple expression Thus in the illustration already employed there were seven uniformities all of which if considered sufficiently certain would in the more lax application of the term be called laws of nature But of the seven three alone are properly distinct and independent these being presupposed the others follow of course The first three therefore according to the stricter acceptation are called laws of nature the remainder not because they are in truth mere cases of the first three virtually included in them said therefore to result from them whoever affirms those three has already affirmed all the rest To substitute real examples for symbolical ones the following are three uniformities or call them laws of nature the law that air has weight the law that pressure on a fluid is propagated equally in all directions and the law that pressure in one direction not opposed by equal pressure in the contrary direction produces motion which does not cease until equilibrium is restored From these three uniformities we should be able to predict another uniformity namely the rise of the mercury in the Torricellian tube This in the stricter use of the phrase is not a law of nature It is the result of laws of nature It is a case of each and every one of the three laws and is the only occurrence by which they could all be fulfilled If the mercury were not sustained in the barometer and sustained at such a height that the column of mercury were equal in weight to a column of the atmosphere of the same diameter here would be a case either of the air not pressing upon the surface of the mercury with the force which is called its weight or of the downward pressure on the mercury not being propagated equally in an upward direction or of a body pressed in one direction and not in the direction opposite either not moving in the direction in which it is pressed or stopping before it had attained equilibrium If we knew therefore the three simple laws but had never tried the Torricellian experiment we might deduce its result from those laws The known weight of the air combined with the position of the apparatus would bring the mercury within the first of the three inductions the first induction would bring it within the second and the second within the third in the manner which we characterized in treating of Ratiocination We should thus come to know the more complex uniformity independently of specific experience through our knowledge of the simpler ones from which it results though for reasons which will appear hereafter verification by specific experience would still be desirable and might possibly be indispensable Complex uniformities which like this are mere cases of simpler ones and have therefore been virtually affirmed in affirming those may with propriety be called laws but can scarcely in the strictness of scientific speech be termed Laws of Nature It is the custom in science wherever regularity of any kind can be traced to call the general proposition which expresses the nature of that regularity a law as when in mathematics we speak of the law of decrease of the successive terms of a converging series But the expression law of nature has generally been employed with a sort of tacit reference to the original sense of the word law namely the expression of the will of a superior When therefore it appeared that any of the uniformities which were observed in nature would result spontaneously from certain other uniformities no separate act of creative will being supposed necessary for the production of the derivative uniformities these have not usually been spoken of as laws of nature According to one mode of expression the question What are the laws of nature may be stated thus What are the fewest and simplest assumptions which being granted the whole existing order of nature would result Another mode of stating it would be thus What are the fewest general propositions from which all the uniformities which exist in the universe might be deductively inferred Every great advance which marks an epoch in the progress of science has consisted in a step made toward the solution of this problem Even a simple colligation of inductions already made without any fresh extension of the inductive inference is already an advance in that direction When Kepler expressed the regularity which exists in the observed motions of the heavenly bodies by the three general propositions called his laws he in so doing pointed out three simple suppositions which instead of a much greater number would suffice to construct the whole scheme of the heavenly motions so far as it was known up to that time A similar and still greater step was made when these laws which at first did not seem to be included in any more general truths were discovered to be cases of the three laws of motion as obtaining among bodies which mutually tend toward one another with a certain force and have had a certain instantaneous impulse originally impressed upon them After this great discovery Kepler’s three propositions though still called laws would hardly by any person accustomed to use language with precision be termed laws of nature that phrase would be reserved for the simpler and more general laws into which Newton is said to have resolved them According to this language every wellgrounded inductive generalization is either a law of nature or a result of laws of nature capable if those laws are known of being predicted from them And the problem of Inductive Logic may be summed up in two questions how to ascertain the laws of nature and how after having ascertained them to follow them into their results On the other hand we must not suffer ourselves to imagine that this mode of statement amounts to a real analysis or to any thing but a mere verbal transformation of the problem for the expression Laws of Nature means nothing but the uniformities which exist among natural phenomena or, in other words, the results of induction when reduced to their simplest expression It is however something to have advanced so far as to see that the study of nature is the study of laws not a law of uniformities in the plural number that the different natural phenomena have their separate rules or modes of taking place which though much intermixed and entangled with one another may to a certain extent be studied apart that to resume our former metaphor the regularity which exists in nature is a web composed of distinct threads and only to be understood by tracing each of the threads separately for which purpose it is often necessary to unravel some portion of the web and exhibit the fibres apart The rules of experimental inquiry are the contrivances for unravelling the web In thus attempting to ascertain the general order of nature by ascertaining the particular order of the occurrence of each one of the phenomena of nature the most scientific proceeding can be no more than an improved form of that which was primitively pursued by the human understanding while undirected by science When mankind first formed the idea of studying phenomena according to a stricter and surer method than that which they had in the first instance spontaneously adopted they did not conformably to the wellmeant but impracticable precept of Descartes set out from the supposition that nothing had been already ascertained Many of the uniformities existing among phenomena are so constant and so open to observation as to force themselves upon involuntary recognition Some facts are so perpetually and familiarly accompanied by certain others that mankind learned as children learn to expect the one where they found the other long before they knew how to put their expectation into words by asserting in a proposition the existence of a connection between those phenomena No science was needed to teach that food nourishes that water drowns or quenches thirst that the sun gives light and heat that bodies fall to the ground The first scientific inquirers assumed these and the like as known truths and set out from them to discover others which were unknown nor were they wrong in so doing subject however as they afterward began to see to an ulterior revision of these spontaneous generalizations themselves when the progress of knowledge pointed out limits to them or showed their truth to be contingent on some circumstance not originally attended to It will appear I think from the subsequent part of our inquiry that there is no logical fallacy in this mode of proceeding but we may see already that any other mode is rigorously impracticable since it is impossible to frame any scientific method of induction or test of the correctness of inductions unless on the hypothesis that some inductions deserving of reliance have been already made Let us revert for instance to one of our former illustrations and consider why it is that with exactly the same amount of evidence both negative and positive we did not reject the assertion that there are black swans while we should refuse credence to any testimony which asserted that there were men wearing their heads underneath their shoulders The first assertion was more credible than the latter But why more credible So long as neither phenomenon had been actually witnessed what reason was there for finding the one harder to be believed than the other Apparently because there is less constancy in the colours of animals than in the general structure of their anatomy But how do we know this Doubtless from experience It appears then that we need experience to inform us in what degree and in what cases or sorts of cases experience is to be relied on Experience must be consulted in order to learn from it under what circumstances arguments from it will be valid We have no ulterior test to which we subject experience in general but we make experience its own test Experience testifies that among the uniformities which it exhibits or seems to exhibit some are more to be relied on than others and uniformity therefore may be presumed from any given number of instances with a greater degree of assurance in proportion as the case belongs to a class in which the uniformities have hitherto been found more uniform This mode of correcting one generalization by means of another a narrower generalization by a wider which common sense suggests and adopts in practice is the real type of scientific Induction All that art can do is but to give accuracy and precision to this process and adapt it to all varieties of cases without any essential alteration in its principle There are of course no means of applying such a test as that above described unless we already possess a general knowledge of the prevalent character of the uniformities existing throughout nature The indispensable foundation therefore of a scientific formula of induction must be a survey of the inductions to which mankind have been conducted in unscientific practice with the special purpose of ascertaining what kinds of uniformities have been found perfectly invariable pervading all nature and what are those which have been found to vary with difference of time place or other changeable circumstances The necessity of such a survey is confirmed by the consideration that the stronger inductions are the touchstone to which we always endeavour to bring the weaker If we find any means of deducing one of the less strong inductions from stronger ones it acquires at once all the strength of those from which it is deduced and even adds to that strength since the independent experience on which the weaker induction previously rested becomes additional evidence of the truth of the better established law in which it is now found to be included We may have inferred from historical evidence that the uncontrolled power of a monarch of an aristocracy or of the majority will often be abused but we are entitled to rely on this generalization with much greater assurance when it is shown to be a corollary from still better established facts the very low degree of elevation of character ever yet attained by the average of mankind and the little efficacy for the most part of the modes of education hitherto practiced in maintaining the predominance of reason and conscience over the selfish propensities It is at the same time obvious that even these more general facts derive an accession of evidence from the testimony which history bears to the effects of despotism The strong induction becomes still stronger when a weaker one has been bound up with it On the other hand if an induction conflicts with stronger inductions or with conclusions capable of being correctly deduced from them then unless on reconsideration it should appear that some of the stronger inductions have been expressed with greater universality than their evidence warrants the weaker one must give way The opinion so long prevalent that a comet or any other unusual appearance in the heavenly regions was the precursor of calamities to mankind or to those at least who witnessed it the belief in the veracity of the oracles of Delphi or Dodona the reliance on astrology or on the weatherprophecies in almanacs were doubtless inductions supposed to be grounded on experience and faith in such delusions seems quite capable of holding out against a great multitude of failures provided it be nourished by a reasonable number of casual coincidences between the prediction and the event What has really put an end to these insufficient inductions is their inconsistency with the stronger inductions subsequently obtained by scientific inquiry respecting the causes on which terrestrial events really depend and where those scientific truths have not yet penetrated the same or similar delusions still prevail It may be affirmed as a general principle that all inductions whether strong or weak which can be connected by ratiocination are confirmatory of one another while any which lead deductively to consequences that are incompatible become mutually each other’s test showing that one or other must be given up or at least more guardedly expressed In the case of inductions which confirm each other the one which becomes a conclusion from ratiocination rises to at least the level of certainty of the weakest of those from which it is deduced while in general all are more or less increased in certainty Thus the Torricellian experiment though a mere case of three more general laws not only strengthened greatly the evidence on which those laws rested but converted one of them the weight of the atmosphere from a still doubtful generalization into a completely established doctrine If then a survey of the uniformities which have been ascertained to exist in nature should point out some which as far as any human purpose requires certainty may be considered quite certain and quite universal then by means of these uniformities we may be able to raise multitudes of other inductions to the same point in the scale For if we can show with respect to any inductive inference that either it must be true or one of these certain and universal inductions must admit of an exception the former generalization will attain the same certainty and indefeasibleness within the bounds assigned to it which are the attributes of the latter It will be proved to be a law and if not a result of other and simpler laws it will be a law of nature There are such certain and universal inductions and it is because there are such that a Logic of Induction is possible The phenomena of nature exist in two distinct relations to one another that of simultaneity and that of succession Every phenomenon is related in a uniform manner to some phenomena that coexist with it and to some that have preceded and will follow it Of the uniformities which exist among synchronous phenomena the most important on every account are the laws of number and next to them those of space or, in other words, of extension and figure The laws of number are common to synchronous and successive phenomena That two and two make four is equally true whether the second two follow the first two or accompany them It is as true of days and years as of feet and inches The laws of extension and figure in other words the theorems of geometry from its lowest to its highest branches are on the contrary laws of simultaneous phenomena only The various parts of space and of the objects which are said to fill space coexist and the unvarying laws which are the subject of the science of geometry are an expression of the mode of their coexistence This is a class of laws or in other words, of uniformities for the comprehension and proof of which it is not necessary to suppose any lapse of time any variety of facts or events succeeding one another The propositions of geometry are independent of the succession of events All things which possess extension or, in other words, which fill space are subject to geometrical laws Possessing extension they possess figure possessing figure they must possess some figure in particular and have all the properties which geometry assigns to that figure If one body be a sphere and another a cylinder of equal height and diameter the one will be exactly twothirds of the other let the nature and quality of the material be what it will Again each body and each point of a body must occupy some place or position among other bodies and the position of two bodies relatively to each other of whatever nature the bodies be may be unerringly inferred from the position of each of them relatively to any third body In the laws of number then and in those of space we recognize in the most unqualified manner the rigorous universality of which we are in quest Those laws have been in all ages the type of certainty the standard of comparison for all inferior degrees of evidence Their invariability is so perfect that it renders us unable even to conceive any exception to them and philosophers have been led though as I have endeavoured to show erroneously to consider their evidence as lying not in experience but in the original constitution of the intellect If therefore from the laws of space and number we were able to deduce uniformities of any other description this would be conclusive evidence to us that those other uniformities possessed the same rigorous certainty But this we can not do From laws of space and number alone nothing can be deduced but laws of space and number Of all truths relating to phenomena the most valuable to us are those which relate to the order of their succession On a knowledge of these is founded every reasonable anticipation of future facts and whatever power we possess of influencing those facts to our advantage Even the laws of geometry are chiefly of practical importance to us as being a portion of the premises from which the order of the succession of phenomena may be inferred Inasmuch as the motion of bodies the action of forces and the propagation of influences of all sorts take place in certain lines and over definite spaces the properties of those lines and spaces are an important part of the laws to which those phenomena are themselves subject Again motions forces or other influences and times are numerable quantities and the properties of number are applicable to them as to all other things But though the laws of number and space are important elements in the ascertainment of uniformities of succession they can do nothing toward it when taken by themselves They can only be made instrumental to that purpose when we combine with them additional premises expressive of uniformities of succession already known By taking for instance as premises these propositions that bodies acted upon by an instantaneous force move with uniform velocity in straight lines that bodies acted upon by a continuous force move with accelerated velocity in straight lines and that bodies acted upon by two forces in different directions move in the diagonal of a parallelogram whose sides represent the direction and quantity of those forces we may by combining these truths with propositions relating to the properties of straight lines and of parallelograms as that a triangle is half a parallelogram of the same base and altitude deduce another important uniformity of succession viz that a body moving round a centre of force describes areas proportional to the times But unless there had been laws of succession in our premises there could have been no truths of succession in our conclusions A similar remark might be extended to every other class of phenomena really peculiar and had it been attended to would have prevented many chimerical attempts at demonstrations of the indemonstrable and explanations which do not explain It is not therefore enough for us that the laws of space which are only laws of simultaneous phenomenon and the laws of number which though true of successive phenomena do not relate to their succession possess the rigorous certainty and universality of which we are in search We must endeavour to find some law of succession which has those same attributes and is therefore fit to be made the foundation of processes for discovering and of a test for verifying all other uniformities of succession This fundamental law must resemble the truths of geometry in their most remarkable peculiarity that of never being in any instance whatever defeated or suspended by any change of circumstances Now among all those uniformities in the succession of phenomena which common observation is sufficient to bring to light there are very few which have any even apparent pretension to this rigorous indefeasibility and of those few one only has been found capable of completely sustaining it In that one however we recognize a law which is universal also in another sense it is coextensive with the entire field of successive phenomena all instances whatever of succession being examples of it This law is the Law of Causation The truth that every fact which has a beginning has a cause is coextensive with human experience This generalization may appear to some minds not to amount to much since after all it asserts only this it is a law that every event depends on some law it is a law that there is a law for every thing We must not however conclude that the generality of the principle is merely verbal it will be found on inspection to be no vague or unmeaning assertion but a most important and really fundamental truth The notion of Cause being the root of the whole theory of Induction it is indispensable that this idea should at the very outset of our inquiry be with the utmost practicable degree of precision fixed and determined If indeed it were necessary for the purpose of inductive logic that the strife should be quelled which has so long raged among the different schools of metaphysicians respecting the origin and analysis of our idea of causation the promulgation or at least the general reception of a true theory of induction might be considered desperate for a long time to come But the science of the Investigation of Truth by means of Evidence is happily independent of many of the controversies which perplex the science of the ultimate constitution of the human mind and is under no necessity of pushing the analysis of mental phenomenon to that extreme limit which alone ought to satisfy a metaphysician I premise then that when in the course of this inquiry I speak of the cause of any phenomenon I do not mean a cause which is not itself a phenomenon I make no research into the ultimate or ontological cause of any thing To adopt a distinction familiar in the writings of the Scotch metaphysicians and especially of Reid the causes with which I concern myself are not efficient but physical causes They are causes in that sense alone in which one physical fact is said to be the cause of another Of the efficient causes of phenomena or whether any such causes exist at all I am not called upon to give an opinion The notion of causation is deemed by the schools of metaphysics most in vogue at the present moment to imply a mysterious and most powerful tie such as can not or at least does not exist between any physical fact and that other physical fact on which it is invariably consequent and which is popularly termed its cause and thence is deduced the supposed necessity of ascending higher into the essences and inherent constitution of things to find the true cause the cause which is not only followed by but actually produces the effect No such necessity exists for the purposes of the present inquiry nor will any such doctrine be found in the following pages The only notion of a cause which the theory of induction requires is such a notion as can be gained from experience The Law of Causation the recognition of which is the main pillar of inductive science is but the familiar truth that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it independently of all considerations respecting the ultimate mode of production of phenomena and of every other question regarding the nature of Things in themselves Between the phenomena then which exist at any instant and the phenomena which exist at the succeeding instant there is an invariable order of succession and as we said in speaking of the general uniformity of the course of nature this web is composed of separate fibres this collective order is made up of particular sequences obtaining invariably among the separate parts To certain facts certain facts always do and as we believe will continue to succeed The invariable antecedent is termed the cause the invariable consequent the effect And the universality of the law of causation consists in this that every consequent is connected in this manner with some particular antecedent or set of antecedents Let the fact be what it may if it has begun to exist it was preceded by some fact or facts with which it is invariably connected For every event there exists some combination of objects or events some given concurrence of circumstances positive and negative the occurrence of which is always followed by that phenomenon We may not have found out what this concurrence of circumstances may be but we never doubt that there is such a one and that it never occurs without having the phenomenon in question as its effect or consequence On the universality of this truth depends the possibility of reducing the inductive process to rules The undoubted assurance we have that there is a law to be found if we only knew how to find it will be seen presently to be the source from which the canons of the Inductive Logic derive their validity It is seldom if ever between a consequent and a single antecedent that this invariable sequence subsists It is usually between a consequent and the sum of several antecedents the concurrence of all of them being requisite to produce that is to be certain of being followed by the consequent In such cases it is very common to single out one only of the antecedents under the denomination of Cause calling the others merely Conditions Thus if a person eats of a particular dish and dies in consequence that is would not have died if he had not eaten of it people would be apt to say that eating of that dish was the cause of his death There needs not however be any invariable connection between eating of the dish and death but there certainly is among the circumstances which took place some combination or other on which death is invariably consequent as for instance the act of eating of the dish combined with a particular bodily constitution a particular state of present health and perhaps even a certain state of the atmosphere the whole of which circumstances perhaps constituted in this particular case the conditions of the phenomenon or, in other words, the set of antecedents which determined it and but for which it would not have happened The real Cause is the whole of these antecedents and we have philosophically speaking no right to give the name of cause to one of them exclusively of the others What in the case we have supposed disguises the incorrectness of the expression is this that the various conditions except the single one of eating the food were not events that is instantaneous changes or successions of instantaneous changes but states possessing more or less of permanency and might therefore have preceded the effect by an indefinite length of duration for want of the event which was requisite to complete the required concurrence of conditions while as soon as that event eating the food occurs no other cause is waited for but the effect begins immediately to take place and hence the appearance is presented of a more immediate and close connection between the effect and that one antecedent than between the effect and the remaining conditions But though we may think proper to give the name of cause to that one condition the fulfilment of which completes the tale and brings about the effect without further delay this condition has really no closer relation to the effect than any of the other conditions has All the conditions were equally indispensable to the production of the consequent and the statement of the cause is incomplete unless in some shape or other we introduce them all A man takes mercury goes outofdoors and catches cold We say perhaps that the cause of his taking cold was exposure to the air It is clear however that his having taken mercury may have been a necessary condition of his catching cold and though it might consist with usage to say that the cause of his attack was exposure to the air to be accurate we ought to say that the cause was exposure to the air while under the effect of mercury If we do not when aiming at accuracy enumerate all the conditions it is only because some of them will in most cases be understood without being expressed or because for the purpose in view they may without detriment be overlooked For example when we say the cause of a man’s death was that his foot slipped in climbing a ladder we omit as a thing unnecessary to be stated the circumstance of his weight though quite as indispensable a condition of the effect which took place When we say that the assent of the crown to a bill makes it law we mean that the assent being never given until all the other conditions are fulfilled makes up the sum of the conditions though no one now regards it as the principal one When the decision of a legislative assembly has been determined by the casting vote of the chairman we sometimes say that this one person was the cause of all the effects which resulted from the enactment Yet we do not really suppose that his single vote contributed more to the result than that of any other person who voted in the affirmative but for the purpose we have in view which is to insist on his individual responsibility the part which any other person had in the transaction is not material In all these instances the fact which was dignified with the name of cause was the one condition which came last into existence But it must not be supposed that in the employment of the term this or any other rule is always adhered to Nothing can better show the absence of any scientific ground for the distinction between the cause of a phenomenon and its conditions than the capricious manner in which we select from among the conditions that which we choose to denominate the cause However numerous the conditions may be there is hardly any of them which may not according to the purpose of our immediate discourse obtain that nominal preeminence This will be seen by analysing the conditions of some one familiar phenomenon For example a stone thrown into water falls to the bottom What are the conditions of this event In the first place there must be a stone and water and the stone must be thrown into the water but these suppositions forming part of the enunciation of the phenomenon itself to include them also among the conditions would be a vicious tautology and this class of conditions therefore have never received the name of cause from any but the Aristotelians by whom they were called the material cause causa materialis The next condition is there must be an earth and accordingly it is often said that the fall of a stone is caused by the earth or by a power or property of the earth or a force exerted by the earth all of which are merely roundabout ways of saying that it is caused by the earth or lastly the earth’s attraction which also is only a technical mode of saying that the earth causes the motion with the additional particularity that the motion is toward the earth which is not a character of the cause but of the effect Let us now pass to another condition It is not enough that the earth should exist the body must be within that distance from it in which the earth’s attraction preponderates over that of any other body Accordingly we may say and the expression would be confessedly correct that the cause of the stone’s falling is its being within the sphere of the earth’s attraction We proceed to a further condition The stone is immersed in water it is therefore a condition of its reaching the ground that its specific gravity exceed that of the surrounding fluid or in other words that it surpass in weight an equal volume of water Accordingly any one would be acknowledged to speak correctly who said that the cause of the stone’s going to the bottom is its exceeding in specific gravity the fluid in which it is immersed Thus we see that each and every condition of the phenomenon may be taken in its turn and with equal propriety in common parlance but with equal impropriety in scientific discourse may be spoken of as if it were the entire cause And in practice that particular condition is usually styled the cause whose share in the matter is superficially the most conspicuous or whose requisiteness to the production of the effect we happen to be insisting on at the moment So great is the force of this last consideration that it sometimes induces us to give the name of cause even to one of the negative conditions We say for example The army was surprised because the sentinel was off his post But since the sentinel’s absence was not what created the enemy or put the soldiers asleep how did it cause them to be surprised All that is really meant is that the event would not have happened if he had been at his duty His being off his post was no producing cause but the mere absence of a preventing cause it was simply equivalent to his nonexistence From nothing from a mere negation no consequences can proceed All effects are connected by the law of causation with some set of positive conditions negative ones it is true being almost always required in addition In other words every fact or phenomenon which has a beginning invariably arises when some certain combination of positive facts exists provided certain other positive facts do not exist There is no doubt a tendency which our first example that of death from taking a particular food sufficiently illustrates to associate the idea of causation with the proximate antecedent event rather than with any of the antecedent states or permanent facts which may happen also to be conditions of the phenomenon the reason being that the event not only exists but begins to exist immediately previous while the other conditions may have preexisted for an indefinite time And this tendency shows itself very visibly in the different logical fictions which are resorted to even by men of science to avoid the necessity of giving the name of cause to any thing which had existed for an indeterminate length of time before the effect Thus rather than say that the earth causes the fall of bodies they ascribe it to a force exerted by the earth or an attraction by the earth abstractions which they can represent to themselves as exhausted by each effort and therefore constituting at each successive instant a fresh fact simultaneous with or only immediately preceding the effect Inasmuch as the coming of the circumstance which completes the assemblage of conditions is a change or event it thence happens that an event is always the antecedent in closest apparent proximity to the consequent and this may account for the illusion which disposes us to look upon the proximate event as standing more peculiarly in the position of a cause than any of the antecedent states But even this peculiarity of being in closer proximity to the effect than any other of its conditions is as we have already seen far from being necessary to the common notion of a cause with which notion on the contrary any one of the conditions either positive or negative is found on occasion completely to accord The cause then philosophically speaking is the sum total of the conditions positive and negative taken together the whole of the contingencies of every description which being realized the consequent invariably follows The negative conditions however of any phenomenon a special enumeration of which would generally be very prolix may be all summed up under one head namely the absence of preventing or counteracting causes The convenience of this mode of expression is mainly grounded on the fact that the effects of any cause in counteracting another cause may in most cases be with strict scientific exactness regarded as a mere extension of its own proper and separate effects If gravity retards the upward motion of a projectile and deflects it into a parabolic trajectory it produces in so doing the very same kind of effect and even as mathematicians know the same quantity of effect as it does in its ordinary operation of causing the fall of bodies when simply deprived of their support If an alkaline solution mixed with an acid destroys its sourness and prevents it from reddening vegetable blues it is because the specific effect of the alkali is to combine with the acid and form a compound with totally different qualities This property which causes of all descriptions possess of preventing the effects of other causes by virtue for the most part of the same laws according to which they produce their own enables us by establishing the general axiom that all causes are liable to be counteracted in their effects by one another to dispense with the consideration of negative conditions entirely and limit the notion of cause to the assemblage of the positive conditions of the phenomenon one negative condition invariably understood and the same in all instances namely the absence of counteracting causes being sufficient along with the sum of the positive conditions to make up the whole set of circumstances on which the phenomenon is dependent Among the positive conditions as we have seen that there are some to which in common parlance the term cause is more readily and frequently awarded so there are others to which it is in ordinary circumstances refused In most cases of causation a distinction is commonly drawn between something which acts and some other thing which is acted upon between an agent and a patient Both of these it would be universally allowed are conditions of the phenomenon but it would be thought absurd to call the latter the cause that title being reserved for the former The distinction however vanishes on examination or rather is found to be only verbal arising from an incident of mere expression namely that the object said to be acted upon and which is considered as the scene in which the effect takes place is commonly included in the phrase by which the effect is spoken of so that if it were also reckoned as part of the cause the seeming incongruity would arise of its being supposed to cause itself In the instance which we have already had of falling bodies the question was thus put What is the cause which makes a stone fall and if the answer had been the stone itself the expression would have been in apparent contradiction to the meaning of the word cause The stone therefore is conceived as the patient and the earth or according to the common and most unphilosophical practice an occult quality of the earth is represented as the agent or cause But that there is nothing fundamental in the distinction may be seen from this that it is quite possible to conceive the stone as causing its own fall provided the language employed be such as to save the mere verbal incongruity We might say that the stone moves toward the earth by the properties of the matter composing it and according to this mode of presenting the phenomenon the stone itself might without impropriety be called the agent though to save the established doctrine of the inactivity of matter men usually prefer here also to ascribe the effect to an occult quality and say that the cause is not the stone itself but the weight or gravitation of the stone Those who have contended for a radical distinction between agent and patient have generally conceived the agent as that which causes some state of or some change in the state of another object which is called the patient But a little reflection will show that the license we assume of speaking of phenomena as states of the various objects which take part in them an artifice of which so much use has been made by some philosophers Brown in particular for the apparent explanation of phenomena is simply a sort of logical fiction useful sometimes as one among several modes of expression but which should never be supposed to be the enunciation of a scientific truth Even those attributes of an object which might seem with greatest propriety to be called states of the object itself its sensible qualities its colour hardness shape and the like are in reality as no one has pointed out more clearly than Brown himself phenomena of causation in which the substance is distinctly the agent or producing cause the patient being our own organs and those of other sentient beings What we call states of objects are always sequences into which the objects enter generally as antecedents or causes and things are never more active than in the production of those phenomena in which they are said to be acted upon Thus in the example of a stone falling to the earth according to the theory of gravitation the stone is as much an agent as the earth which not only attracts but is itself attracted by the stone In the case of a sensation produced in our organs the laws of our organization and even those of our minds are as directly operative in determining the effect produced as the laws of the outward object Though we call prussic acid the agent of a person’s death the whole of the vital and organic properties of the patient are as actively instrumental as the poison in the chain of effects which so rapidly terminates his sentient existence In the process of education we may call the teacher the agent and the scholar only the material acted upon yet in truth all the facts which preexisted in the scholar’s mind exert either cooperating or counteracting agencies in relation to the teacher’s efforts It is not light alone which is the agent in vision but light coupled with the active properties of the eye and brain and with those of the visible object The distinction between agent and patient is merely verbal patients are always agents in a great proportion indeed of all natural phenomena they are so to such a degree as to react forcibly on the causes which acted upon them and even when this is not the case they contribute in the same manner as any of the other conditions to the production of the effect of which they are vulgarly treated as the mere theatre All the positive conditions of a phenomenon are alike agents alike active and in any expression of the cause which professes to be complete none of them can with reason be excluded except such as have already been implied in the words used for describing the effect nor by including even these would there be incurred any but a merely verbal impropriety There is a case of causation which calls for separate notice as it possesses a peculiar feature and presents a greater degree of complexity than the common case It often happens that the effect or one of the effects of a cause is not to produce of itself a certain phenomenon but to fit something else for producing it In other words there is a case of causation in which the effect is to invest an object with a certain property When sulphur charcoal and nitre are put together in certain proportions and in a certain manner the effect is not an explosion but that the mixture acquires a property by which in given circumstances it will explode The various causes natural and artificial which educate the human body or the human mind have for their principal effect not to make the body or mind immediately do any thing but to endow it with certain properties in other words to give assurance that in given circumstances certain results will take place in it or as consequences of it Physiological agencies often have for the chief part of their operation to predispose the constitution to some mode of action To take a simpler instance than all these putting a coat of white paint upon a wall does not merely produce in those who see it done the sensation of white it confers on the wall the permanent property of giving that kind of sensation Regarded in reference to the sensation the putting on of the paint is a condition of a condition it is a condition of the wall’s causing that particular fact The wall may have been painted years ago but it has acquired a property which has lasted till now and will last longer the antecedent condition necessary to enable the wall to become in its turn a condition has been fulfilled once for all In a case like this where the immediate consequent in the sequence is a property produced in an object no one now supposes the property to be a substantive entity inherent in the object What has been produced is what in other language may be called a state of preparation in an object for producing an effect The ingredients of the gunpowder have been brought into a state of preparation for exploding as soon as the other conditions of an explosion shall have occurred In the case of the gunpowder this state of preparation consists in a certain collocation of its particles relatively to one another In the example of the wall it consists in a new collocation of two things relatively to each other the wall and the paint In the example of the moulding influences on the human mind its being a collocation at all is only conjectural for even on the materialistic hypothesis it would remain to be proved that the increased facility with which the brain sums up a column of figures when it has been long trained to calculation is the result of a permanent new arrangement of some of its material particles We must therefore content ourselves with what we know and must include among the effects of causes the capacities given to objects of being causes of other effects This capacity is not a real thing existing in the objects it is but a name for our conviction that they will act in a particular manner when certain new circumstances arise We may invest this assurance of future events with a fictitious objective existence by calling it a state of the object But unless the state consists as in the case of the gunpowder it does in a collocation of particles it expresses no present fact it is but the contingent future fact brought back under another name It may be thought that this form of causation requires us to admit an exception to the doctrine that the conditions of a phenomenon the antecedents required for calling it into existence must all be found among the facts immediately not remotely preceding its commencement But what we have arrived at is not a correction it is only an explanation of that doctrine In the enumeration of the conditions required for the occurrence of any phenomenon it always has to be included that objects must be present possessed of given properties It is a condition of the phenomenon explosion that an object should be present of one or other of certain kinds which for that reason are called explosive The presence of one of these objects is a condition immediately precedent to the explosion The condition which is not immediately precedent is the cause which produced not the explosion but the explosive property The conditions of the explosion itself were all present immediately before it took place and the general law therefore remains intact It now remains to advert to a distinction which is of firstrate importance both for clearing up the notion of cause and for obviating a very specious objection often made against the view which we have taken of the subject When we define the cause of any thing in the only sense in which the present inquiry has any concern with causes to be the antecedent which it invariably follows we do not use this phrase as exactly synonymous with the antecedent which it invariably has followed in our past experience Such a mode of conceiving causation would be liable to the objection very plausibly urged by Dr Reid namely that according to this doctrine night must be the cause of day and day the cause of night since these phenomena have invariably succeeded one another from the beginning of the world But it is necessary to our using the word cause that we should believe not only that the antecedent always has been followed by the consequent but that as long as the present constitution of things endures it always will be so And this would not be true of day and night We do not believe that night will be followed by day under all imaginable circumstances but only that it will be so provided the sun rises above the horizon If the sun ceased to rise which for aught we know may be perfectly compatible with the general laws of matter night would be or might be eternal On the other hand if the sun is above the horizon his light not extinct and no opaque body between us and him we believe firmly that unless a change takes place in the properties of matter this combination of antecedents will be followed by the consequent day that if the combination of antecedents could be indefinitely prolonged it would be always day and that if the same combination had always existed it would always have been day quite independently of night as a previous condition Therefore is it that we do not call night the cause nor even a condition of day The existence of the sun or some such luminous body and there being no opaque medium in a straight line between that body and the part of the earth where we are situated are the sole conditions and the union of these without the addition of any superfluous circumstance constitutes the cause This is what writers mean when they say that the notion of cause involves the idea of necessity If there be any meaning which confessedly belongs to the term necessity it is unconditionalness That which is necessary that which must be means that which will be whatever supposition we may make in regard to all other things The succession of day and night evidently is not necessary in this sense It is conditional on the occurrence of other antecedents That which will be followed by a given consequent when and only when some third circumstance also exists is not the cause even though no case should ever have occurred in which the phenomenon took place without it Invariable sequence therefore is not synonymous with causation unless the sequence besides being invariable is unconditional There are sequences as uniform in past experience as any others whatever which yet we do not regard as cases of causation but as conjunctions in some sort accidental Such to an accurate thinker is that of day and night The one might have existed for any length of time and the other not have followed the sooner for its existence it follows only if certain other antecedents exist and where those antecedents existed it would follow in any case No one probably ever called night the cause of day mankind must so soon have arrived at the very obvious generalization that the state of general illumination which we call day would follow from the presence of a sufficiently luminous body whether darkness had preceded or not We may define therefore the cause of a phenomenon to be the antecedent or the concurrence of antecedents on which it is invariably and unconditionally consequent Or if we adopt the convenient modification of the meaning of the word cause which confines it to the assemblage of positive conditions without the negative then instead of unconditionally we must say subject to no other than negative conditions To some it may appear that the sequence between night and day being invariable in our experience we have as much ground in this case as experience can give in any case for recognizing the two phenomena as cause and effect and that to say that more is necessary to require a belief that the succession is unconditional or, in other words, that it would be invariable under all changes of circumstances is to acknowledge in causation an element of belief not derived from experience The answer to this is that it is experience itself which teaches us that one uniformity of sequence is conditional and another unconditional When we judge that the succession of night and day is a derivative sequence depending on something else we proceed on grounds of experience It is the evidence of experience which convinces us that day could equally exist without being followed by night and that night could equally exist without being followed by day To say that these beliefs are not generated by our mere observation of sequence is to forget that twice in every twentyfour hours when the sky is clear we have an experimentum crucis that the cause of day is the sun We have an experimental knowledge of the sun which justifies us on experimental grounds in concluding that if the sun were always above the horizon there would be day though there had been no night and that if the sun were always below the horizon there would be night though there had been no day We thus know from experience that the succession of night and day is not unconditional Let me add that the antecedent which is only conditionally invariable is not the invariable antecedent Though a fact may in experience have always been followed by another fact yet if the remainder of our experience teaches us that it might not always be so followed or if the experience itself is such as leaves room for a possibility that the known cases may not correctly represent all possible cases the hitherto invariable antecedent is not accounted the cause but why Because we are not sure that it is the invariable antecedent Such cases of sequence as that of day and night not only do not contradict the doctrine which resolves causation into invariable sequence but are necessarily implied in that doctrine It is evident, that from a limited number of unconditional sequences there will result a much greater number of conditional ones Certain causes being given that is certain antecedents which are unconditionally followed by certain consequents the mere coexistence of these causes will give rise to an unlimited number of additional uniformities If two causes exist together the effects of both will exist together and if many causes coexist these causes by what we shall term hereafter the intermixture of their laws will give rise to new effects accompanying or succeeding one another in some particular order which order will be invariable while the causes continue to coexist but no longer The motion of the earth in a given orbit round the sun is a series of changes which follow one another as antecedents and consequents and will continue to do so while the sun’s attraction and the force with which the earth tends to advance in a direct line through space continue to coexist in the same quantities as at present But vary either of these causes and this particular succession of motions would cease to take place The series of the earth’s motions therefore though a case of sequence invariable within the limits of human experience is not a case of causation It is not unconditional This distinction between the relations of succession which so far as we know are unconditional and those relations whether of succession or of coexistence which like the earth’s motions or the succession of day and night depend on the existence or on the coexistence of other antecedent facts corresponds to the great division which Dr Whewell and other writers have made of the field of science into the investigation of what they term the Laws of Phenomena and the investigation of causes a phraseology as I conceive not philosophically sustainable inasmuch as the ascertainment of causes such causes as the human faculties can ascertain namely causes which are themselves phenomena is therefore merely the ascertainment of other and more universal Laws of Phenomena And let me here observe that Dr Whewell and in some degree even Sir John Herschel seem to have misunderstood the meaning of those writers who like M Comt limit the sphere of scientific investigation to Laws of Phenomena and speak of the inquiry into causes as vain and futile The causes which M Comt designates as inaccessible are efficient causes The investigation of physical as opposed to efficient causes including the study of all the active forces in Nature considered as facts of observation is as important a part of M Comt’s conception of science as of Dr Whewell’s His objection to the word cause is a mere matter of nomenclature in which as a matter of nomenclature I consider him to be entirely wrong Those it is justly remarked by Mr Bailey who like M Comt object to designate events as causes are objecting without any real ground to a mere but extremely convenient generalization to a very useful common name the employment of which involves or needs involve no particular theory To which it may be added that by rejecting this form of expression M Comt leaves himself without any term for marking a distinction which however incorrectly expressed is not only real but is one of the fundamental distinctions in science indeed it is on this alone as we shall hereafter find that the possibility rests of framing a rigorous Canon of Induction And as things left without a name are apt to be forgotten a Canon of that description is not one of the many benefits which the philosophy of Induction has received from M Comt’s great powers Does a cause always stand with its effect in the relation of antecedent and consequent Do we not often say of two simultaneous facts that they are cause and effect as when we say that fire is the cause of warmth the sun and moisture the cause of vegetation and the like Since a cause does not necessarily perish because its effect has been produced the two things do very generally coexist and there are some appearances and some common expressions seeming to imply not only that causes may but that they must be contemporaneous with their effects Cessante causae cessat et effectus has been a dogma of the schools the necessity for the continued existence of the cause in order to the continuance of the effect seems to have been once a generally received doctrine Kepler’s numerous attempts to account for the motions of the heavenly bodies on mechanical principles were rendered abortive by his always supposing that the agency which set those bodies in motion must continue to operate in order to keep up the motion which it at first produced Yet there were at all times many familiar instances of the continuance of effects long after their causes had ceased A coup de soleil gives a person brainfever will the fever go off as soon as he is moved out of the sunshine A sword is run through his body must the sword remain in his body in order that he may continue dead A ploughshare once made remains a ploughshare without any continuance of heating and hammering and even after the man who heated and hammered it has been gathered to his fathers On the other hand the pressure which forces up the mercury in an exhausted tube must be continued in order to sustain it in the tube This it may be replied is because another force is acting without intermission the force of gravity which would restore it to its level unless counterpoised by a force equally constant But again a tight bandage causes pain which pain will sometimes go off as soon as the bandage is removed The illumination which the sun diffuses over the earth ceases when the sun goes down There is therefore a distinction to be drawn The conditions which are necessary for the first production of a phenomenon are occasionally also necessary for its continuance though more commonly its continuance requires no condition except negative ones Most things once produced continue as they are until something changes or destroys them but some require the permanent presence of the agencies which produced them at first These may if we please be considered as instantaneous phenomena requiring to be renewed at each instant by the cause by which they were at first generated Accordingly the illumination of any given point of space has always been looked upon as an instantaneous fact which perishes and is perpetually renewed as long as the necessary conditions subsist If we adopt this language we avoid the necessity of admitting that the continuance of the cause is ever required to maintain the effect We may say it is not required to maintain but to reproduce the effect or else to counteract some force tending to destroy it And this may be a convenient phraseology But it is only a phraseology The fact remains that in some cases though those are a minority the continuance of the conditions which produced an effect is necessary to the continuance of the effect As to the ulterior question whether it is strictly necessary that the cause or assemblage of conditions should precede by ever so short an instant the production of the effect a question raised and argued with much ingenuity by Sir John Herschel in an Essay already quoted the inquiry is of no consequence for our present purpose There certainly are cases in which the effect follows without any interval perceptible by our faculties and when there is an interval we can not tell by how many intermediate links imperceptible to us that interval may really be filled up But even granting that an effect may commence simultaneously with its cause the view I have taken of causation is in no way practically affected Whether the cause and its effect be necessarily successive or not the beginning of a phenomenon is what implies a cause and causation is the law of the succession of phenomena If these axioms be granted we can afford though I see no necessity for doing so to drop the words antecedent and consequent as applied to cause and effect I have no objection to define a cause the assemblage of phenomena which occurring some other phenomenon invariably commences or has its origin Whether the effect coincides in point of time with or immediately follows the hindmost of its conditions is immaterial At all events it does not precede it and when we are in doubt between two coexistent phenomena which is cause and which effect we rightly deem the question solved if we can ascertain which of them preceded the other It continually happens that several different phenomena which are not in the slightest degree dependent or conditional on one another are found all to depend as the phrase is on one and the same agent in other words one and the same phenomenon is seen to be followed by several sorts of effects quite heterogeneous but which go on simultaneously one with another provided of course that all other conditions requisite for each of them also exist Thus the sun produces the celestial motions it produces daylight and it produces heat The earth causes the fall of heavy bodies and it also in its capacity of a great magnet causes the phenomena of the magnetic needle A crystal of galena causes the sensations of hardness of weight of cubical form of gray colour and many others between which we can trace no interdependence The purpose to which the phraseology of Properties and Powers is specially adapted is the expression of this sort of cases When the same phenomenon is followed either subject or not to the presence of other conditions by effects of different and dissimilar orders it is usual to say that each different sort of effect is produced by a different property of the cause Thus we distinguish the attractive or gravitative property of the earth and its magnetic property the gravitative luminiferous and calorific properties of the sun the colour shape weight and hardness of a crystal These are mere phrases which explain nothing and add nothing to our knowledge of the subject but considered as abstract names denoting the connection between the different effects produced and the object which produces them they are a very powerful instrument of abridgment and of that acceleration of the process of thought which abridgment accomplishes This class of considerations leads to a conception which we shall find to be of great importance that of a Permanent Cause or original natural agent There exist in nature a number of permanent causes which have subsisted ever since the human race has been in existence and for an indefinite and probably an enormous length of time previous The sun the earth and planets with their various constituents air water and other distinguishable substances whether simple or compound of which nature is made up are such Permanent Causes These have existed and the effects or consequences which they were fitted to produce have taken place as often as the other conditions of the production met from the very beginning of our experience But we can give no account of the origin of the Permanent Causes themselves Why these particular natural agents existed originally and no others or why they are commingled in such and such proportions and distributed in such and such a manner throughout space is a question we can not answer More than this we can discover nothing regular in the distribution itself we can reduce it to no uniformity to no law There are no means by which from the distribution of these causes or agents in one part of space we could conjecture whether a similar distribution prevails in another The coexistence therefore of Primeval Causes ranks to us among merely casual concurrences and all those sequences or coexistences among the effects of several such causes which though invariable while those causes coexist would if the coexistence terminated terminate along with it we do not class as cases of causation or laws of nature we can only calculate on finding these sequences or coexistences where we know by direct evidence that the natural agents on the properties of which they ultimately depend are distributed in the requisite manner These Permanent Causes are not always objects they are sometimes events that is to say periodical cycles of events that being the only mode in which events can possess the property of permanence Not only for instance is the earth itself a permanent cause or primitive natural agent but the earth’s rotation is so too it is a cause which has produced from the earliest period by the aid of other necessary conditions the succession of day and night the ebb and flow of the sea and many other effects while as we can assign no cause except conjecturally for the rotation itself it is entitled to be ranked as a primeval cause It is however only the origin of the rotation which is mysterious to us once begun its continuance is accounted for by the first law of motion that of the permanence of rectilinear motion once impressed combined with the gravitation of the parts of the earth toward one another All phenomena without exception which begin to exist that is all except the primeval causes are effects either immediate or remote of those primitive facts or of some combination of them There is no Thing produced no event happening in the known universe which is not connected by a uniformity or invariable sequence with some one or more of the phenomena which preceded it insomuch that it will happen again as often as those phenomena occur again and as no other phenomenon having the character of a counteracting cause shall coexist These antecedent phenomena again were connected in a similar manner with some that preceded them and so on until we reach as the ultimate step attainable by us either the properties of some one primeval cause or the conjunction of several The whole of the phenomena of nature were therefore the necessary or, in other words, the unconditional consequences of some former collocation of the Permanent Causes The state of the whole universe at any instant we believe to be the consequence of its state at the previous instant insomuch that one who knew all the agents which exist at the present moment their collocation in space and all their properties in other words the laws of their agency could predict the whole subsequent history of the universe at least unless some new volition of a power capable of controlling the universe should supervene And if any particular state of the entire universe could ever recur a second time all subsequent states would return too and history would like a circulating decimal of many figures periodically repeat itself Jam redit et virgo redeunt Saturnia regna Alter erit tum Tiphys et altera quae vehat Argo Delectos heroas erunt quoque altera bella Atque iterum ad Trojam magnus mittetur Achilles And though things do not really revolve in this eternal round the whole series of events in the history of the universe past and future is not the less capable in its own nature of being constructed a priori by any one whom we can suppose acquainted with the original distribution of all natural agents and with the whole of their properties that is the laws of succession existing between them and their effects saving the far more than human powers of combination and calculation which would be required even in one possessing the data for the actual performance of the task Since every thing which occurs is determined by laws of causation and collocations of the original causes it follows that the coexistences which are observable among effects can not be themselves the subject of any similar set of laws distinct from laws of causation Uniformities there are as well of coexistence as of succession among effects but these must in all cases be a mere result either of the identity or of the coexistence of their causes if the causes did not coexist neither could the effects And these causes being also effects of prior causes and these of others until we reach the primeval causes it follows that except in the case of effects which can be traced immediately or remotely to one and the same cause the coexistences of phenomena can in no case be universal unless the coexistences of the primeval causes to which the effects are ultimately traceable can be reduced to a universal law but we have seen that they can not There are accordingly no original and independent in other words no unconditional uniformities of coexistence between effects of different causes if they coexist it is only because the causes have casually coexisted The only independent and unconditional coexistences which are sufficiently invariable to have any claim to the character of laws are between different and mutually independent effects of the same cause in other words between different properties of the same natural agent This portion of the Laws of Nature will be treated of in the latter part of the present Book under the name of the Specific Properties of Kinds Since the first publication of the present treatise the sciences of physical nature have made a great advance in generalization through the doctrine known as the Conservation or Persistence of Force This imposing edifice of theory the building and laying out of which has for some time been the principal occupation of the most systematic minds among physical inquirers consists of two stages one of ascertained fact the other containing a large element of hypothesis To begin with the first It is proved by numerous facts both natural and of artificial production that agencies which had been regarded as distinct and independent sources of force heat electricity chemical action nervous and muscular action momentum of moving bodies are interchangeable in definite and fixed quantities with one another It had long been known that these dissimilar phenomena had the power under certain conditions of producing one another what is new in the theory is a more accurate estimation of what this production consists in What happens is that the whole or part of the one kind of phenomena disappears and is replaced by phenomena of one of the other descriptions and that there is an equivalence in quantity between the phenomena that have disappeared and those which have been produced insomuch that if the process be reversed the very same quantity which had disappeared will reappear without increase or diminution Thus the amount of heat which will raise the temperature of a pound of water one degree of the thermometer will if expended say in the expansion of steam lift a weight of 772 pounds one foot or a weight of one pound 772 feet and the same exact quantity of heat can by certain means be recovered through the expenditure of exactly that amount of mechanical motion The establishment of this comprehensive law has led to a change in the language in which the scientific world had been accustomed to speak of what are called the Forces of nature Before this correlation between phenomena most unlike one another had been ascertained their unlikeness had caused them to be referred to so many distinct forces Now that they are known to be convertible into one another without loss they are spoken of as all of them results of one and the same force manifesting itself in different modes This force it is said can only produce a limited and definite quantity of effect but always does produce that definite quantity and produces it according to circumstances in one or another of the forms or divides it among several but so as according to a scale of numerical equivalents established by experiment always to make up the same sum and no one of the manifestations can be produced save by the disappearance of the equivalent quantity of another which in its turn in appropriate circumstances will reappear undiminished This mutual interchangeability of the forces of nature according to fixed numerical equivalents is the part of the new doctrine which rests on irrefragable fact To make the statement true however it is necessary to add that an indefinite and perhaps immense interval of time may elapse between the disappearance of the force in one form and its reappearance in another A stone thrown up into the air with a given force and falling back immediately will by the time it reaches the earth recover the exact amount of mechanical momentum which was expended in throwing it up deduction being made of a small portion of motion which has been communicated to the air But if the stone has lodged on a height it may not fall back for years or perhaps ages and until it does the force expended in raising it is temporarily lost being represented only by what in the language of the new theory is called potential energy The coal imbedded in the earth is considered by the theory as a vast reservoir of force which has remained dormant for many geological periods and will so remain until by being burned it gives out the storedup force in the form of heat Yet it is not supposed that this force is a material thing which can be confined by bounds as used to be thought of latent heat when that important phenomenon was first discovered What is meant is that when the coal does at last by combustion generate a quantity of heat transformable like all other heat into mechanical momentum and the other forms of force this extrication of heat is the reappearance of a force derived from the sun’s rays expended myriads of ages ago in the vegetation of the organic substances which were the material of the coal Let us now pass to the higher stage of the theory of Conservation of Force the part which is no longer a generalization of proved fact but a combination of fact and hypothesis Stated in few words it is as follows That the Conservation of Force is really the Conservation of Motion that in the various interchanges between the forms of force it is always motion that is transformed into motion To establish this it is necessary to assume motions which are hypothetical The supposition is that there are motions which manifest themselves to our senses only as heat electricity etc being molecular motions oscillations invisible to us among the minute particles of bodies and that these molecular motions are transmutable into molar motions motions of masses and molar motions into molecular Now there is a real basis of fact for this supposition we have positive evidence of the existence of molecular motion in these manifestations of force In the case of chemical action for instance the particles separate and form new combinations often with a great visible disturbance of the mass In the case of heat the evidence is equally conclusive since heat expands bodies that is causes their particles to move from one another and if of sufficient amount changes their mode of aggregation from solid to liquid or from liquid to gaseous Again the mechanical actions which produce heat friction and the collision of bodies must from the nature of the case produce a shock that is an internal motion of particles which indeed we find is often so violent as to break them permanently asunder Such facts are thought to warrant the inference that it is not as was supposed heat that causes the motion of particles but the motion of particles that causes heat the original cause of both being the previous motion whether molar or molecular collision of bodies or combustion of fuel which formed the heating agency This inference already contains hypothesis but at least the supposed cause the intestine motion of molecules is a vera causa But in order to reduce the Conservation of Force to Conservation of Motion it was necessary to attribute to motion the heat propagated through apparently empty space from the sun This required the supposition already made for the explanation of the laws of light of a subtle ether pervading space which though impalpable to us must have the property which constitutes matter that of resistance since waves are propagated through it by an impulse from a given point The ether must be supposed a supposition not required by the theory of light to penetrate into the minute interstices of all bodies The vibratory motion supposed to be taking place in the heated mass of the sun is considered as imparted from that mass to the particles of the surrounding ether and through them to the particles of the same ether in the interstices of terrestrial bodies and this too with a sufficient mechanical force to throw the particles of those bodies into a state of similar vibration producing the expansion of their mass and the sensation of heat in sentient creatures All this is hypothesis though of its legitimacy as hypothesis I do not mean to express any doubt It would seem to follow as a consequence from this theory that Force may and should be defined matter in motion This definition however will not stand for as has already been seen the matter needs not be in actual motion It is not necessary to suppose that the motion afterward manifested is actually taking place among the molecules of the coal during its sojourn in the earth certainly not in the stone which is at rest on the eminence to which it has been raised The true definition of Force must be not motion but Potentiality of Motion and what the doctrine if established amounts to is not that there is at all times the same quantity of actual motion in the universe but that the possibilities of motion are limited to a definite quantity which can not be added to but which can not be exhausted and that all actual motion which takes place in Nature is a draft upon this limited stock It needs not all of it have ever existed as actual motion There is a vast amount of potential motion in the universe in the form of gravitation which it would be a great abuse of hypothesis to suppose to have been stored up by the expenditure of an equal amount of actual motion in some former state of the universe Nor does the motion produced by gravity take place so far as we know at the expense of any other motion either molar or molecular It is proper to consider whether the adoption of this theory as a scientific truth involving as it does a change in the conception hitherto entertained of the most general physical agencies requires any modification in the view I have taken of Causation as a law of nature As it appears to me none whatever The manifestations which the theory regards as modes of motion are as much distinct and separate phenomena when referred to a single force as when attributed to several Whether the phenomenon is called a transformation of force or the generation of one it has its own set or sets of antecedents with which it is connected by invariable and unconditional sequence and that set or those sets of antecedents are its cause The relation of the Conservation theory to the principle of Causation is discussed in much detail and very instructively by Professor Bain in the second volume of his Logic The chief practical conclusion drawn by him bearing on Causation is that we must distinguish in the assemblage of conditions which constitutes the Cause of a phenomenon two elements one the presence of a force the other the collocation or position of objects which is required in order that the force may undergo the particular transmutation which constitutes the phenomenon Now it might always have been said with acknowledged correctness that a force and a collocation were both of them necessary to produce any phenomenon The law of causation is that change can only be produced by change Along with any number of stationary antecedents which are collocations there must be at least one changing antecedent which is a force To produce a bonfire there must not only be fuel and air and a spark which are collocations but chemical action between the air and the materials which is a force To grind corn there must be a certain collocation of the parts composing a mill relatively to one another and to the corn but there must also be the gravitation of water or the motion of wind to supply a force But as the force in these cases was regarded as a property of the objects in which it is embodied it seemed tautology to say that there must be the collocation and the force As the collocation must be a collocation of objects possessing the forcegiving property the collocation so understood included the force How then shall we have to express these facts if the theory be finally substantiated that all Force is reducible to a previous Motion We shall have to say that one of the conditions of every phenomenon is an antecedent Motion But it will have to be explained that this needs not be actual motion The coal which supplies the force exerted in combustion is not shown to have been exerting that force in the form of molecular motion in the pit it was not even exerting pressure The stone on the eminence is exerting a pressure but only equivalent to its weight not to the additional momentum it would acquire by falling The antecedent therefore is not a force in action and we can still only call it a property of the objects by which they would exert a force on the occurrence of a fresh collocation The collocation therefore still includes the force The force said to be stored up is simply a particular property which the object has acquired The cause we are in search of is a collocation of objects possessing that particular property When indeed we inquire further into the cause from which they derive that property the new conception introduced by the Conservation theory comes in the property is itself an effect and its cause according to the theory is a former motion of exactly equivalent amount which has been impressed on the particles of the body perhaps at some very distant period But the case is simply one of those we have already considered in which the efficacy of a cause consists in its investing an object with a property The force said to be laid up and merely potential is no more a really existing thing than any other properties of objects are really existing things The expression is a mere artifice of language convenient for describing the phenomena it is unnecessary to suppose that any thing has been in continuous existence except an abstract potentiality A force suspended in its operation neither manifesting itself by motion nor by pressure is not an existing fact but a name for our conviction that in appropriate circumstances a fact would take place We know that a pound weight were it to fall from the earth into the sun would acquire in falling a momentum equal to millions of pounds but we do not credit the pound weight with more of actually existing force than is equal to the pressure it is now exerting on the earth and that is exactly a pound We might as well say that a force of millions of pounds exists in a pound as that the force which will manifest itself when the coal is burned is a real thing existing in the coal What is fixed in the coal is only a certain property it has become fit to be the antecedent of an effect called combustion which partly consists in giving out under certain conditions a given definite quantity of heat We thus see that no new general conception of Causation is introduced by the Conservation theory The indestructibility of Force no more interferes with the theory of Causation than the indestructibility of Matter meaning by matter the element of resistance in the sensible world It only enables us to understand better than before the nature and laws of some of the sequences This better understanding however enables us with Mr Bain to admit as one of the tests for distinguishing causation from mere concomitance the expenditure or transfer of energy If the effect or any part of the effect to be accounted for consists in putting matter in motion then any of the objects present which has lost motion has contributed to the effect and this is the true meaning of the proposition that the cause is that one of the antecedents which exerts active force It is proper in this place to advert to a rather ancient doctrine respecting causation which has been revived during the last few years in many quarters and at present gives more signs of life than any other theory of causation at variance with that set forth in the preceding pages According to the theory in question Mind or to speak move precisely Will is the only cause of phenomena The type of Causation as well as the exclusive source from which we derive the idea is our own voluntary agency Here and here only it is said we have direct evidence of causation We know that we can move our bodies Respecting the phenomena of inanimate nature we have no other direct knowledge than that of antecedence and sequence But in the case of our voluntary actions it is affirmed that we are conscious of power before we have experience of results An act of volition whether followed by an effect or not is accompanied by a consciousness of effort of force exerted of power in action which is necessarily causal or causative This feeling of energy or force inherent in an act of will is knowledge a priori assurance prior to experience that we have the power of causing effects Volition therefore it is asserted is something more than an unconditional antecedent it is a cause in a different sense from that in which physical phenomena are said to cause one another it is an Efficient Cause From this the transition is easy to the further doctrine that Volition is the sole Efficient Cause of all phenomena It is inconceivable that dead force could continue unsupported for a moment beyond its creation We can not even conceive of change or phenomena without the energy of a mind The word action itself says another writer of the same school has no real significance except when applied to the doings of an intelligent agent Let any one conceive if he can of any power energy or force inherent in a lump of matter Phenomena may have the semblance of being produced by physical causes but they are in reality produced say these writers by the immediate agency of mind All things which do not proceed from a human or I suppose an animal will proceed they say directly from divine will The earth is not moved by the combination of a centripetal and a projectile force this is but a mode of speaking which serves to facilitate our conceptions It is moved by the direct volition of an omnipotent Being in a path coinciding with that which we deduce from the hypothesis of these two forces As I have so often observed the general question of the existence of Efficient Causes does not fall within the limits of our subject but a theory which represents them as capable of being subjects of human knowledge and which passes off as efficient causes what are only physical or phenomenal causes belongs as much to Logic as to metaphysics and is a fit subject for discussion here To my apprehension a volition is not an efficient but simply a physical cause Our will causes our bodily actions in the same sense and in no other in which cold causes ice or a spark causes an explosion of gunpowder The volition a state of our mind is the antecedent the motion of our limbs in conformity to the volition is the consequent This sequence I conceive to be not a subject of direct consciousness in the sense intended by the theory The antecedent indeed and the consequent are subjects of consciousness But the connection between them is a subject of experience I can not admit that our consciousness of the volition contains in itself any a priori knowledge that the muscular motion will follow If our nerves of motion were paralyzed or our muscles stiff and inflexible and had been so all our lives I do not see the slightest ground for supposing that we should ever unless by information from other people have known any thing of volition as a physical power or been conscious of any tendency in feelings of our mind to produce motions of our body or of other bodies I will not undertake to say whether we should in that case have had the physical feeling which I suppose is meant when these writers speak of consciousness of effort I see no reason why we should not since that physical feeling is probably a state of nervous sensation beginning and ending in the brain without involving the motor apparatus but we certainly should not have designated it by any term equivalent to effort since effort implies consciously aiming at an end which we should not only in that case have had no reason to do but could not even have had the idea of doing If conscious at all of this peculiar sensation we should have been conscious of it I conceive only as a kind of uneasiness accompanying our feelings of desire It is well argued by Sir William Hamilton against the theory in question that it is refuted by the consideration that between the overt fact of corporeal movement of which we are cognizant and the internal act of mental determination of which we are also cognizant there intervenes a numerous series of intermediate agencies of which we have no knowledge and consequently that we can have no consciousness of any causal connection between the extreme links of this chain the volition to move and the limb moving as this hypothesis asserts No one is immediately conscious for example of moving his arm through his volition Previously to this ultimate movement muscles nerves a multitude of solid and fluid parts must be set in motion by the will but of this motion we know from consciousness absolutely nothing A person struck with paralysis is conscious of no inability in his limb to fulfil the determinations of his will and it is only after having willed and finding that his limbs do not obey his volition that he learns by this experience that the external movement does not follow the internal act But as the paralytic learns after the volition that his limbs do not obey his mind so it is only after volition that the man in health learns that his limbs do obey the mandates of his will Those against whom I am contending have never produced and do not pretend to produce any positive evidence that the power of our will to move our bodies would be known to us independently of experience What they have to say on the subject is that the production of physical events by a will seems to carry its own explanation with it while the action of matter upon matter seems to require something else to explain it and is even according to them inconceivable on any other supposition than that some will intervenes between the apparent cause and its apparent effect They thus rest their case on an appeal to the inherent laws of our conceptive faculty mistaking as I apprehend for the laws of that faculty its acquired habits grounded on the spontaneous tendencies of its uncultured state The succession between the will to move a limb and the actual motion is one of the most direct and instantaneous of all sequences which come under our observation and is familiar to every moment’s experience from our earliest infancy more familiar than any succession of events exterior to our bodies and especially more so than any other case of the apparent origination as distinguished from the mere communication of motion Now it is the natural tendency of the mind to be always attempting to facilitate its conception of unfamiliar facts by assimilating them to others which are familiar Accordingly our voluntary acts being the most familiar to us of all cases of causation are in the infancy and early youth of the human race spontaneously taken as the type of causation in general and all phenomena are supposed to be directly produced by the will of some sentient being This original Fetishism I shall not characterize in the words of Hume or of any follower of Hume but in those of a religious metaphysician Dr Reid in order more effectually to show the unanimity which exists on the subject among all competent thinkers When we turn our attention to external objects and begin to exercise our rational faculties about them we find that there are some motions and changes in them which we have power to produce and that there are many which must have some other cause Either the objects must have life and active power as we have or they must be moved or changed by something that has life and active power as external objects are moved by us Our first thoughts seem to be that the objects in which we perceive such motion have understanding and active power as we have Savages’ says the Abbe Raynal wherever they see motion which they can not account for there they suppose a soul’ All men may be considered as savages in this respect until they are capable of instruction and of using their faculties in a more perfect manner than savages do The Abbe Raynal’s observation is sufficiently confirmed both from fact and from the structure of all languages Rude nations do really believe sun moon and stars earth sea and air fountains and lakes to have understanding and active power To pay homage to them and implore their favour is a kind of idolatry natural to savages All languages carry in their structure the marks of their being formed when this belief prevailed The distinction of verbs and participles into active and passive which is found in all languages must have been originally intended to distinguish what is really active from what is merely passive and in all languages we find active verbs applied to those objects in which according to the Abbe Raynal’s observation savages suppose a soul Thus we say the sun rises and sets and comes to the meridian the moon changes the sea ebbs and flows the winds blow Languages were formed by men who believed these objects to have life and active power in themselves It was therefore proper and natural to express their motions and changes by active verbs There is no surer way of tracing the sentiments of nations before they have records than by the structure of their language which notwithstanding the changes produced in it by time will always retain some signatures of the thoughts of those by whom it was invented When we find the same sentiments indicated in the structure of all languages those sentiments must have been common to the human species when languages were invented When a few of superior intellectual abilities find leisure for speculation they begin to philosophize and soon discover that many of those objects which at first they believed to be intelligent and active are really lifeless and passive This is a very important discovery It elevates the mind emancipates from many vulgar superstitions and invites to further discoveries of the same kind As philosophy advances life and activity in natural objects retires and leaves them dead and inactive Instead of moving voluntarily we find them to be moved necessarily instead of acting we find them to be acted upon and Nature appears as one great machine where one wheel is turned by another that by a third and how far this necessary succession may reach the philosopher does not know There is then a spontaneous tendency of the intellect to account to itself for all cases of causation by assimilating them to the intentional acts of voluntary agents like itself This is the instinctive philosophy of the human mind in its earliest stage before it has become familiar with any other invariable sequences than those between its own volitions or those of other human beings and their voluntary acts As the notion of fixed laws of succession among external phenomena gradually establishes itself the propensity to refer all phenomena to voluntary agency slowly gives way before it The suggestions however of daily life continuing to be more powerful than those of scientific thought the original instinctive philosophy maintains its ground in the mind underneath the growths obtained by cultivation and keeps up a constant resistance to their throwing their roots deep into the soil The theory against which I am contending derives its nourishment from that substratum Its strength does not lie in argument but in its affinity to an obstinate tendency of the infancy of the human mind That this tendency however is not the result of an inherent mental law is proved by superabundant evidence The history of science from its earliest dawn shows that mankind have not been unanimous in thinking either that the action of matter upon matter was not conceivable or that the action of mind upon matter was To some thinkers and some schools of thinkers both in ancient and in modern times this last has appeared much more inconceivable than the former Sequences entirely physical and material as soon as they had become sufficiently familiar to the human mind came to be thought perfectly natural and were regarded not only as needing no explanation themselves but as being capable of affording it to others and even of serving as the ultimate explanation of things in general One of the ablest recent supporters of the Volitional theory has furnished an explanation at once historically true and philosophically acute of the failure of the Greek philosophers in physical inquiry in which as I conceive he unconsciously depicts his own state of mind Their stumblingblock was one as to the nature of the evidence they had to expect for their conviction They had not seized the idea that they must not expect to understand the processes of outward causes but only their results and consequently the whole physical philosophy of the Greeks was an attempt to identify mentally the effect with its cause to feel after some not only necessary but natural connection where they meant by natural that which would per se carry some presumption to their own mind They wanted to see some reason why the physical antecedent should produce this particular consequent and their only attempts were in directions where they could find such reasons In other words they were not content merely to know that one phenomenon was always followed by another they thought that they had not attained the true aim of science unless they could perceive something in the nature of the one phenomenon from which it might have been known or presumed previous to trial that it would be followed by the other just what the writer who has so clearly pointed out their error thinks that he perceives in the nature of the phenomenon Volition And to complete the statement of the case he should have added that these early speculators not only made this their aim but were quite satisfied with their success in it not only sought for causes which should carry in their mere statement evidence of their efficiency but fully believed that they had found such causes The reviewer can see plainly that this was an error because he does not believe that there exist any relations between material phenomena which can account for their producing one another but the very fact of the persistency of the Greeks in this error shows that their minds were in a very different state they were able to derive from the assimilation of physical facts to other physical facts the kind of mental satisfaction which we connect with the word explanation and which the reviewer would have us think can only be found in referring phenomena to a will When Thales and Hippo held that moisture was the universal cause and external element of which all other things were but the infinitely various sensible manifestations when Anaximenes predicated the same thing of air Pythagoras of numbers and the like they all thought that they had found a real explanation and were content to rest in this explanation as ultimate The ordinary sequences of the external universe appeared to them no less than to their critic to be inconceivable without the supposition of some universal agency to connect the antecedents with the consequents but they did not think that Volition exerted by minds was the only agency which fulfilled this requirement Moisture or air or numbers carried to their minds a precisely similar impression of making intelligible what was otherwise inconceivable and gave the same full satisfaction to the demands of their conceptive faculty It was not the Greeks alone who wanted to see some reason why the physical antecedent should produce this particular consequent some connection which would per se carry some presumption to their own mind Among modern philosophers Leibnitz laid it down as a selfevident principle that all physical causes without exception must contain in their own nature something which makes it intelligible that they should be able to produce the effects which they do produce Far from admitting Volition as the only kind of cause which carried internal evidence of its own power and as the real bond of connection between physical antecedents and their consequents he demanded some naturally and per se efficient physical antecedent as the bond of connection between Volition itself and its effects He distinctly refused to admit the will of God as a sufficient explanation of any thing except miracles and insisted upon finding something that would account better for the phenomena of nature than a mere reference to divine volition Again and conversely the action of mind upon matter which we are now told not only needs no explanation itself but is the explanation of all other effects has appeared to some thinkers to be itself the grand inconceivability It was to get over this very difficulty that the Cartesians invented the system of Occasional Causes They could not conceive that thoughts in a mind could produce movements in a body or that bodily movements could produce thoughts They could see no necessary connection no relation a priori between a motion and a thought And as the Cartesians more than any other school of philosophical speculation before or since made their own minds the measure of all things and refused on principle to believe that Nature had done what they were unable to see any reason why she must do they affirmed it to be impossible that a material and a mental fact could be causes one of another They regarded them as mere Occasions on which the real agent God thought fit to exert his power as a Cause When a man wills to move his foot it is not his will that moves it but God they said moves it on the occasion of his will God according to this system is the only efficient cause not qua mind or qua endowed with volition but qua omnipotent This hypothesis was as I said originally suggested by the supposed inconceivability of any real mutual action between Mind and Matter but it was afterward extended to the action of Matter upon Matter for on a nicer examination they found this inconceivable too and therefore according to their logic impossible The deus ex machina was ultimately called in to produce a spark on the occasion of a flint and steel coming together or to break an egg on the occasion of its falling on the ground All this undoubtedly shows that it is the disposition of mankind in general not to be satisfied with knowing that one fact is invariably antecedent and another consequent but to look out for something which may seem to explain their being so But we also see that this demand may be completely satisfied by an agency purely physical provided it be much more familiar than that which it is invoked to explain To Thales and Anaximenes it appeared inconceivable that the antecedents which we see in nature should produce the consequents but perfectly natural that water or air should produce them The writers whom I oppose declare this inconceivable but can conceive that mind or volition is per se an efficient cause while the Cartesians could not conceive even that but peremptorily declared that no mode of production of any fact whatever was conceivable except the direct agency of an omnipotent being thus giving additional proof of what finds new confirmation in every stage of the history of science that both what persons can and what they can not conceive is very much an affair of accident and depends altogether on their experience and their habits of thought that by cultivating the requisite associations of ideas people may make themselves unable to conceive any given thing and may make themselves able to conceive most things however inconceivable these may at first appear and the same facts in each person’s mental history which determine what is or is not conceivable to him determine also which among the various sequences in nature will appear to him so natural and plausible as to need no other proof of their existence to be evident by their own light independent equally of experience and of explanation By what rule is any one to decide between one theory of this description and another The theorists do not direct us to any external evidence they appeal each to his own subjective feelings One says the succession C B appears to me more natural conceivable and credible per se than the succession A B you are therefore mistaken in thinking that B depends upon A I am certain though I can give no other evidence of it that C comes in between A and B and is the real and only cause of B The other answers the successions C B and A B appear to me equally natural and conceivable or the latter more so than the former A is quite capable of producing B without any other intervention A third agrees with the first in being unable to conceive that A can produce B but finds the sequence D B still more natural than C B or of nearer kin to the subjectmatter and prefers his D theory to the C theory It is plain that there is no universal law operating here except the law that each person’s conceptions are governed and limited by his individual experiences and habits of thought We are warranted in saying of all three what each of them already believes of the other two namely that they exalt into an original law of the human intellect and of outward nature one particular sequence of phenomena which appears to them more natural and more conceivable than other sequences only because it is more familiar And from this judgment I am unable to except the theory that Volition is an Efficient Cause I am unwilling to leave the subject without adverting to the additional fallacy contained in the corollary from this theory in the inference that because Volition is an efficient cause therefore it is the only cause and the direct agent in producing even what is apparently produced by something else Volitions are not known to produce any thing directly except nervous action for the will influences even the muscles only through the nerves Though it were granted then that every phenomenon has an efficient and not merely a phenomenal cause and that volition in the case of the peculiar phenomena which are known to be produced by it is that efficient cause are we therefore to say with these writers that since we know of no other efficient cause and ought not to assume one without evidence there is no other and volition is the direct cause of all phenomena A more outrageous stretch of inference could hardly be made Because among the infinite variety of the phenomena of nature there is one namely a particular mode of action of certain nerves which has for its cause and as we are now supposing for its efficient cause a state of our mind and because this is the only efficient cause of which we are conscious being the only one of which in the nature of the case we can be conscious since it is the only one which exists within ourselves does this justify us in concluding that all other phenomena must have the same kind of efficient cause with that one eminently special narrow and peculiarly human or animal phenomenon The nearest parallel to this specimen of generalization is suggested by the recently revived controversy on the old subject of Plurality of Worlds in which the contending parties have been so conspicuously successful in overthrowing one another Here also we have experience only of a single case that of the world in which we live but that this is inhabited we know absolutely and without possibility of doubt Now if on this evidence any one were to infer that every heavenly body without exception sun planet satellite comet fixed star or nebula is inhabited and must be so from the inherent constitution of things his inference would exactly resemble that of the writers who conclude that because volition is the efficient cause of our own bodily motions it must be the efficient cause of every thing else in the universe It is true there are cases in which with acknowledged propriety we generalize from a single instance to a multitude of instances But they must be instances which resemble the one known instance and not such as have no circumstance in common with it except that of being instances I have for example no direct evidence that any creature is alive except myself yet I attribute with full assurance life and sensation to other human beings and animals But I do not conclude that all other things are alive merely because I am I ascribe to certain other creatures a life like my own because they manifest it by the same sort of indications by which mine is manifested I find that their phenomena and mine conform to the same laws and it is for this reason that I believe both to arise from a similar cause Accordingly I do not extend the conclusion beyond the grounds for it Earth fire mountains trees are remarkable agencies but their phenomena do not conform to the same laws as my actions do and I therefore do not believe earth or fire mountains or trees to possess animal life But the supporters of the Volition Theory ask us to infer that volition causes every thing for no reason except that it causes one particular thing although that one phenomenon far from being a type of all natural phenomena is eminently peculiar its laws bearing scarcely any resemblance to those of any other phenomenon whether of inorganic or of organic nature NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER The author of the Second Burnett Prize Essay Dr Tulloch who has employed a considerable number of pages in controverting the doctrines of the preceding chapter has somewhat surprised me by denying a fact which I imagined too well known to require proof that there have been philosophers who found in physical explanations of phenomena the same complete mental satisfaction which we are told is only given by volitional explanation and others who denied the Volitional Theory on the same ground of inconceivability on which it is defended The assertion of the Essayist is countersigned still more positively by an able reviewer of the Essay Two illustrations says the reviewer are advanced by Mr Mill the case of Thales and Anaximenes stated by him to have maintained the one Moisture and the other Air to be the origin of all things and that of Descartes and Leibnitz whom he asserts to have found the action of Mind upon Matter the grand inconceivability In counterstatement as to the first of these cases the author shows what we believe now hardly admits of doubt that the Greek philosophers distinctly recognized as beyond and above their primal material source the or Divine Intelligence as the efficient and originating Source of all and as to the second by proof that it was the mode not the fact of that action on matter which was represented as inconceivable A greater quantity of historical error has seldom been comprised in a single sentence With regard to Thales the assertion that he considered water as a mere material in the hands of rests on a passage of Cicero de Natura Deorum and whoever will refer to any of the accurate historians of philosophy will find that they treat this as a mere fancy of Cicero resting on no authority opposed to all the evidence and make surmises as to the manner in which Cicero may have been led into the error See Rutter vol i p 211 2d ed Brandis vol i pp 1189 1st ed Preller Historia Philosophiae GraecoRomanae p 10 Schiefe Ansicht durchaus zu verwerfen augenscheinlich folgernd statt zu berichten quibus vera sententia Thaletis plane detorquetur are the expressions of these writers As for Anaximenes he even according to Cicero maintained not that air was the material out of which God made the world but that the air was a god Anaximenes a‘ra deum statuit or according to St Augustine that it was the material out of which the gods were made non tamen ab ipsis Diis a‘rem factum sed ipsos ex a‘re ortos credidit Those who are not familiar with the metaphysical terminology of antiquity must not be misled by finding it stated that Anaximenes attributed translated soul or life to his universal element the air The Greek philosophers acknowledged several kinds of the nutritive the sensitive and the intellective Even the moderns with admitted correctness attribute life to plants As far as we can make out the meaning of Anaximenes he made choice of Air as the universal agent on the ground that it is perpetually in motion without any apparent cause external to itself so that he conceived it as exercising spontaneous force and as the principle of life and activity in all things men and gods inclusive If this be not representing it as the Efficient Cause the dispute altogether has no meaning If either Anaximenes or Thales or any of their contemporaries had held the doctrine that was the Efficient Cause that doctrine could not have been reputed as it was throughout antiquity to have originated with Anaxagoras The testimony of Aristotle in the first book of his Metaphysics is perfectly decisive with respect to these early speculations After enumerating four kinds of causes or rather four different meanings of the word Cause viz the Essence of a thing the Matter of it the Origin of Motion Efficient Cause and the End or Final Cause he proceeds to say that most of the early philosophers recognized only the second kind of Cause the Matter of a thing As his first example he specifies Thales whom he describes as taking the lead in this view of the subject and goes on to Hippon Anaximenes Diogenes of Apollonia Hippasus of Metapontum Heraclitus and Empedocles Anaxagoras however he proceeds to say taught a different doctrine as we know and it is alleged that Hermotimus of Clazomenae taught it before him Anaxagoras represented that even if these various theories of the universal material were true there would be need of some other cause to account for the transformations of the materials since the material can not originate its own changes viz the other kind of cause an Efficient Cause Aristotle expresses great approbation of this doctrine which he says made its author appear the only sober man among persons raving but while describing the influence which it exercised over subsequent speculation he remarks that the philosophers against whom this as he thinks insuperable difficulty was urged had not felt it to be any difficulty It is surely unnecessary to say more in proof of the matter of fact which Dr Tulloch and his reviewer disbelieve Having pointed out what he thinks the error of these early speculators in not recognizing the need of an efficient cause Aristotle goes on to mention two other efficient causes to which they might have had recourse instead of intelligence chance and spontaneity He indeed puts these aside as not sufficiently worthy causes for the order in the universe but he does not reject them as incapable of producing any effect but only as incapable of producing that effect He himself recognizes and as coordinate agents with Mind in producing the phenomena of the universe the department allotted to them being composed of all the classes of phenomena which are not supposed to follow any uniform law By thus including Chance among efficient causes Aristotle fell into an error which philosophy has now outgrown but which is by no means so alien to the spirit even of modern speculation as it may at first sight appear Up to quite a recent period philosophers went on ascribing and many of them have not yet ceased to ascribe a real existence to the results of abstraction Chance could make out as good a title to that dignity as many other of the mind’s abstract creations it had had a name given to it and why should it not be a reality As for it is recognized even yet as one of the modes of origination of phenomena by all those thinkers who maintain what is called the Freedom of the Will The same selfdetermining power which that doctrine attributes to volitions was supposed by the ancients to be possessed also by some other natural phenomena a circumstance which throws considerable light on more than one of the supposed invincible necessities of belief I have introduced it here because this belief of Aristotle or rather of the Greek philosophers generally is as fatal as the doctrines of Thales and the Ionic school to the theory that the human mind is compelled by its constitution to conceive volition as the origin of all force and the efficient cause of all phenomena With regard to the modern philosophers Leibnitz and the Cartesians whom I had cited as having maintained that the action of mind upon matter so far from being the only conceivable origin of material phenomena is itself inconceivable the attempt to rebut this argument by asserting that the mode not the fact of the action of mind on matter was represented as inconceivable is an abuse of the privilege of writing confidently about authors without reading them for any knowledge whatever of Leibnitz would have taught those who thus speak of him that the inconceivability of the mode and the impossibility of the thing were in his mind convertible expressions What was his famous Principle of the Sufficient Reason the very cornerstone of his Philosophy
from which the Preestablished Harmony the doctrine of Monads and all the opinions most characteristic of Leibnitz were corollaries It was that nothing exists the existence of which is not capable of being proved and explained a priori the proof and explanation in the case of contingent facts being derived from the nature of their causes which could not be the causes unless there was something in their nature showing them to be capable of producing those particular effects And this something which accounts for the
production of physical effects he was able to find in many physical causes but could not find it in any finite minds which therefore he unhesitatingly asserted to be incapable of producing any physical effects whatever On ne saurait concevoir he says une action rciproque de la matire et de l’intelligence l’une sur l’autre and there is therefore he contends no choice but between the Occasional Causes of the Cartesians and his own Preestablished Harmony according to which there is no more connection between our volitions and our muscular actions than there is between two clocks which are wound up to strike at the same instant But he felt no similar difficulty as to physical causes and throughout his speculations as in the passage I have already cited respecting gravitation he distinctly refuses to consider as part of the order of nature any fact which is not explicable from the nature of its physical cause With regard to the Cartesians not Descartes I did not make that mistake though the reviewer of Dr Tulloch’s Essay attributes it to me I take a passage almost at random from Malebranche who is the best known of the Cartesians and though not the inventor of the system of Occasional Causes is its principal expositor In Part II chap iii of his Sixth Book having first said that matter can not have the power of moving itself he proceeds to argue that neither can mind have the power of moving it Quand on examine l’ide que l’on a de tous les esprits finis on ne voit point de liaison ncessaire entre leur volont et le mouvement de quelque corps que ce soit on voit au contraire qu’il n’y en a point et qu’il n’y en peut avoir there is nothing in the idea of finite mind which can account for its causing the motion of a body on doit aussi conclure si on vent raisonner selon ses lumires qu’il n’y a aucun esprit cr qui puisse remuer quelque corps que ce soit comme cause vritable on principale de mme que l’on a dit qu’aucun corps ne se pouvait remuer soimme thus the idea of Mind is according to him as incompatible as the idea of Matter with the exercise of active force But when he continues we consider not a created but a Divine Mind the case is altered for the idea of a Divine Mind includes omnipotence and the idea of omnipotence does contain the idea of being able to move bodies Thus it is the nature of omnipotence which renders the motion of bodies even by the Divine Mind credible or conceivable while so far as depended on the mere nature of mind it would have been inconceivable and incredible If Malebranche had not believed in an omnipotent Being he would have held all action of mind on body to be a demonstrated impossibility A doctrine more precisely the reverse of the Volitional theory of causation can not well be imagined The Volitional theory is that we know by intuition or by direct experience the action of our own mental volitions on matter that we may hence infer all other action upon matter to be that of volition and might thus know without any other evidence that matter is under the government of a Divine Mind Leibnitz and the Cartesians on the contrary maintain that our volitions do not and can not act upon matter and that it is only the existence of an allgoverning Being and that Being omnipotent which can account for the sequence between our volitions and our bodily actions When we consider that each of these two theories which as theories of causation stand at the opposite extremes of possible divergence from one another invokes not only as its evidence but as its sole evidence the absolute inconceivability of any theory but itself we are enabled to measure the worth of this kind of evidence and when we find the Volitional theory entirely built upon the assertion that by our mental constitution we are compelled to recognize our volitions as efficient causes and then find other thinkers maintaining that we know that they are not and can not be such causes and can not conceive them to be so I think we have a right to say that this supposed law of our mental constitution does not exist Dr Tulloch pp 4547 thinks it a sufficient answer to this that Leibnitz and the Cartesians were Theists and believed the will of God to be an efficient cause Doubtless they did and the Cartesians even believed though Leibnitz did not that it is the only such cause Dr Tulloch mistakes the nature of the question I was not writing on Theism as Dr Tulloch is but against a particular theory of causation which if it be unfounded can give no effective support to Theism or to any thing else I found it asserted that volition is the only efficient cause on the ground that no other efficient cause is conceivable To this assertion I oppose the instances of Leibnitz and of the Cartesians who affirmed with equal positiveness that volition as an efficient cause is itself not conceivable and that omnipotence which renders all things conceivable can alone take away the impossibility This I thought and think a conclusive answer to the argument on which this theory of causation avowedly depends But I certainly did not imagine that Theism was bound up with that theory nor expected to be charged with denying Leibnitz and the Cartesians to be Theists because I denied that they held the theory
To complete the general notion of causation on which the rules of experimental inquiry into the laws of nature must be founded one distinction still remains to be pointed out a distinction so radical and of so much importance as to require a chapter to itself The preceding discussions have rendered us familiar with the case in which several agents or causes concur as conditions to the production of an effect a case in truth almost universal there being very few effects to the production of which no more than one agent contributes Suppose then that two different agents operating jointly are followed under a certain set of collateral conditions by a given effect If either of these agents instead of being joined with the other had operated alone under the same set of conditions in all other respects some effect would probably have followed which would have been different from the joint effect of the two and more or less dissimilar to it Now if we happen to know what would be the effect of each cause when acting separately from the other we are often able to arrive deductively or a priori at a correct prediction of what will arise from their conjunct agency To render this possible it is only necessary that the same law which expresses the effect of each cause acting by itself shall also correctly express the part due to that cause of the effect which follows from the two together This condition is realized in the extensive and important class of phenomena commonly called mechanical namely the phenomena of the communication of motion or of pressure which is tendency to motion from one body to another In this important class of cases of causation one cause never properly speaking defeats or frustrates another both have their full effect If a body is propelled in two directions by two forces one tending to drive it to the north and the other to the east it is caused to move in a given time exactly as far in both directions as the two forces would separately have carried it and is left precisely where it would have arrived if it had been acted upon first by one of the two forces and afterward by the other This law of nature is called in dynamics the principle of the Composition of Forces and in imitation of that wellchosen expression I shall give the name of the Composition of Causes to the principle which is exemplified in all cases in which the joint effect of several causes is identical with the sum of their separate effects This principle however by no means prevails in all departments of the field of nature The chemical combination of two substances produces as is well known a third substance with properties different from those of either of the two substances separately or of both of them taken together Not a trace of the properties of hydrogen or of oxygen is observable in those of their compound water The taste of sugar of lead is not the sum of the tastes of its component elements acetic acid and lead or its oxide nor is the colour of blue vitriol a mixture of the colours of sulphuric acid and copper This explains why mechanics is a deductive or demonstrative science and chemistry not In the one we can compute the effects of combinations of causes whether real or hypothetical from the laws which we know to govern those causes when acting separately because they continue to observe the same laws when in combination which they observe when separate whatever would have happened in consequence of each cause taken by itself happens when they are together and we have only to cast up the results Not so in the phenomena which are the peculiar subject of the science of chemistry There most of the uniformities to which the causes conform when separate cease altogether when they are conjoined and we are not at least in the present state of our knowledge able to foresee what result will follow from any new combination until we have tried the specific experiment If this be true of chemical combinations it is still more true of those far more complex combinations of elements which constitute organized bodies and in which those extraordinary new uniformities arise which are called the laws of life All organized bodies are composed of parts similar to those composing inorganic nature and which have even themselves existed in an inorganic state but the phenomena of life which result from the juxtaposition of those parts in a certain manner bear no analogy to any of the effects which would be produced by the action of the component substances considered as mere physical agents To whatever degree we might imagine our knowledge of the properties of the several ingredients of a living body to be extended and perfected it is certain that no mere summing up of the separate actions of those elements will ever amount to the action of the living body itself The tongue for instance is like all other parts of the animal frame composed of gelatine fibrine and other products of the chemistry of digestion but from no knowledge of the properties of those substances could we ever predict that it could taste unless gelatine or fibrine could themselves taste for no elementary fact can be in the conclusion which was not in the premises There are thus two different modes of the conjunct action of causes from which arise two modes of conflict or mutual interference between laws of nature Suppose at a given point of time and space two or more causes which if they acted separately would produce effects contrary or at least conflicting with each other one of them tending to undo wholly or partially what the other tends to do Thus the expansive force of the gases generated by the ignition of gunpowder tends to project a bullet toward the sky while its gravity tends to make it fall to the ground A stream running into a reservoir at one end tends to fill it higher and higher while a drain at the other extremity tends to empty it Now in such cases as these even if the two causes which are in joint action exactly annul one another still the laws of both are fulfilled the effect is the same as if the drain had been open for half an hour first and the stream had flowed in for as long afterward Each agent produces the same amount of effect as if it had acted separately though the contrary effect which was taking place during the same time obliterated it as fast as it was produced Here then are two causes producing by their joint operations an effect which at first seems quite dissimilar to those which they produce separately but which on examination proves to be really the sum of those separate effects It will be noticed that we here enlarge the idea of the sum of two effects so as to include what is commonly called their difference but which is in reality the result of the addition of opposites a conception to which mankind are indebted for that admirable extension of the algebraical calculus which has so vastly increased its powers as an instrument of discovery by introducing into its reasonings with the sign of subtraction prefixed and under the name of Negative Quantities every description whatever of positive phenomena provided they are of such a quality in reference to those previously introduced that to add the one is equivalent to subtracting an equal quantity of the other There is then one mode of the mutual interference of laws of nature in which even when the concurrent causes annihilate each other’s effects each exerts its full efficacy according to its own law its law as a separate agent But in the other description of cases the agencies which are brought together cease entirely and a totally different set of phenomena arise as in the experiment of two liquids which when mixed in certain proportions instantly become not a larger amount of liquid but a solid mass This difference between the case in which the joint effect of causes is the sum of their separate effects and the case in which it is heterogeneous to them between laws which work together without alteration and laws which when called upon to work together cease and give place to others is one of the fundamental distinctions in nature The former case that of the Composition of Causes is the general one the other is always special and exceptional There are no objects which do not as to some of their phenomena obey the principle of the Composition of Causes none that have not some laws which are rigidly fulfilled in every combination into which the objects enter The weight of a body for instance is a property which it retains in all the combinations in which it is placed The weight of a chemical compound or of an organized body is equal to the sum of the weights of the elements which compose it The weight either of the elements or of the compound will vary if they be carried farther from their centre of attraction or brought nearer to it but whatever effects the one effects the other They always remain precisely equal So again the component parts of a vegetable or animal substance do not lose their mechanical and chemical properties as separate agents when by a peculiar mode of juxtaposition they as an aggregate whole acquire physiological or vital properties in addition Those bodies continue as before to obey mechanical and chemical laws in so far as the operation of those laws is not counteracted by the new laws which govern them as organized beings when in short a concurrence of causes takes place which calls into action new laws bearing no analogy to any that we can trace in the separate operation of the causes the new laws while they supersede one portion of the previous laws may coexist with another portion and may even compound the effect of those previous laws with their own Again laws which were themselves generated in the second mode may generate others in the first Though there are laws which like those of chemistry and physiology owe their existence to a breach of the principle of Composition of Causes it does not follow that these peculiar or as they might be termed heteropathic laws are not capable of composition with one another The causes which by one combination have had their laws altered may carry their new laws with them unaltered into their ulterior combinations And hence there is no reason to despair of ultimately raising chemistry and physiology to the condition of deductive sciences for though it is impossible to deduce all chemical and physiological truths from the laws or properties of simple substances or elementary agents they may possibly be deducible from laws which commence when these elementary agents are brought together into some moderate number of not very complex combinations The Laws of Life will never be deducible from the mere laws of the ingredients but the prodigiously complex Facts of Life may all be deducible from comparatively simple laws of life which laws depending indeed on combinations but on comparatively simple combinations of antecedents may in more complex circumstances be strictly compounded with one another and with the physical and chemical laws of the ingredients The details of the vital phenomena even now afford innumerable exemplifications of the Composition of Causes and in proportion as these phenomena are more accurately studied there appears more reason to believe that the same laws which operate in the simpler combinations of circumstances do in fact continue to be observed in the more complex This will be found equally true in the phenomena of mind and even in social and political phenomena the results of the laws of mind It is in the case of chemical phenomena that the least progress has yet been made in bringing the special laws under general ones from which they may be deduced but there are even in chemistry many circumstances to encourage the hope that such general laws will hereafter be discovered The different actions of a chemical compound will never undoubtedly be found to be the sums of the actions of its separate elements but there may exist between the properties of the compound and those of its elements some constant relation which if discoverable by a sufficient induction would enable us to foresee the sort of compound which will result from a new combination before we have actually tried it and to judge of what sort of elements some new substance is compounded before we have analysed it The law of definite proportions first discovered in its full generality by Dalton is a complete solution of this problem in one though but a secondary aspect that of quantity and in respect to quality we have already some partial generalizations sufficient to indicate the possibility of ultimately proceeding farther We can predicate some common properties of the kind of compounds which result from the combination in each of the small number of possible proportions of any acid whatever with any base We have also the curious law discovered by Berthollet that two soluble salts mutually decompose one another whenever the new combinations which result produce an insoluble compound or one less soluble than the two former Another uniformity is that called the law of isomorphism the identity of the crystalline forms of substances which possess in common certain peculiarities of chemical composition Thus it appears that even heteropathic laws such laws of combined agency as are not compounded of the laws of the separate agencies are yet at least in some cases derived from them according to a fixed principle There may therefore be laws of the generation of laws from others dissimilar to them and in chemistry these undiscovered laws of the dependence of the properties of the compound on the properties of its elements may together with the laws of the elements themselves furnish the premises by which the science is perhaps destined one day to be rendered deductive It would seem therefore that there is no class of phenomena in which the Composition of Causes does not obtain that as a general rule causes in combination produce exactly the same effects as when acting singly but that this rule though general is not universal that in some instances at some particular points in the transition from separate to united action the laws change and an entirely new set of effects are either added to or take the place of those which arise from the separate agency of the same causes the laws of these new effects being again susceptible of composition to an indefinite extent like the laws which they superseded That effects are proportional to their causes is laid down by some writers as an axiom in the theory of causation and great use is sometimes made of this principle in reasonings respecting the laws of nature though it is encumbered with many difficulties and apparent exceptions which much ingenuity has been expended in showing not to be real ones This proposition in so far as it is true enters as a particular case into the general principle of the Composition of Causes the causes compounded being in this instance homogeneous in which case if in any their joint effect might be expected to be identical with the sum of their separate effects If a force equal to one hundred weight will raise a certain body along an inclined plane a force equal to two hundred weight will raise two bodies exactly similar and thus the effect is proportional to the cause But does not a force equal to two hundred weight actually contain in itself two forces each equal to one hundred weight which if employed apart would separately raise the two bodies in question The fact therefore that when exerted jointly they raise both bodies at once results from the Composition of Causes and is a mere instance of the general fact that mechanical forces are subject to the law of Composition And so in every other case which can be supposed For the doctrine of the proportionality of effects to their causes can not of course be applicable to cases in which the augmentation of the cause alters the kind of effect that is in which the surplus quantity superadded to the cause does not become compounded with it but the two together generate an altogether new phenomenon Suppose that the application of a certain quantity of heat to a body merely increases its bulk that a double quantity melts it and a triple quantity decomposes it these three effects being heterogeneous no ratio whether corresponding or not to that of the quantities of heat applied can be established between them Thus the supposed axiom of the proportionality of effects to their causes fails at the precise point where the principle of the Composition of Causes also fails viz where the concurrence of causes is such as to determine a change in the properties of the body generally and render it subject to new laws more or less dissimilar to those to which it conformed in its previous state The recognition therefore of any such law of proportionality is superseded by the more comprehensive principle in which as much of it as is true is implicitly asserted The general remarks on causation which seemed necessary as an introduction to the theory of the inductive process may here terminate That process is essentially an inquiry into cases of causation All the uniformities which exist in the succession of phenomena and most of the uniformities in their coexistence are either as we have seen themselves laws of causation or consequences resulting from and corollaries capable of being deduced from such laws If we could determine what causes are correctly assigned to what effects and what effects to what causes we should be virtually acquainted with the whole course of nature All those uniformities which are mere results of causation might then be explained and accounted for and every individual fact or event might be predicted provided we had the requisite data that is the requisite knowledge of the circumstances which in the particular instance preceded it To ascertain therefore what are the laws of causation which exist in nature to determine the effect of every cause and the causes of all effects is the main business of Induction and to point out how this is done is the chief object of Inductive Logic It results from the preceding exposition that the process of ascertaining what consequents in nature are invariably connected with what antecedents or in other words what phenomena are related to each other as causes and effects is in some sort a process of analysis That every fact which begins to exist has a cause and that this cause must be found in some fact or concourse of facts which immediately preceded the occurrence may be taken for certain The whole of the present facts are the infallible result of all past facts and more immediately of all the facts which existed at the moment previous Here then is a great sequence which we know to be uniform If the whole prior state of the entire universe could again recur it would again be followed by the present state The question is how to resolve this complex uniformity into the simpler uniformities which compose it and assign to each portion of the vast antecedent the portion of the consequent which is attendant on it This operation which we have called analytical inasmuch as it is the resolution of a complex whole into the component elements is more than a merely mental analysis No mere contemplation of the phenomena and partition of them by the intellect alone will of itself accomplish the end we have now in view Nevertheless such a mental partition is an indispensable first step The order of nature as perceived at a first glance presents at every instant a chaos followed by another chaos We must decompose each chaos into single facts We must learn to see in the chaotic antecedent a multitude of distinct antecedents in the chaotic consequent a multitude of distinct consequents This supposing it done will not of itself tell us on which of the antecedents each consequent is invariably attendant To determine that point we must endeavour to effect a separation of the facts from one another not in our minds only but in nature The mental analysis however must take place first And every one knows that in the mode of performing it one intellect differs immensely from another It is the essence of the act of observing for the observer is not he who merely sees the thing which is before his eyes but he who sees what parts that thing is composed of To do this well is a rare talent One person from inattention or attending only in the wrong place overlooks half of what he sees another sets down much more than he sees confounding it with what he imagines or with what he infers another takes note of the kind of all the circumstances but being inexpert in estimating their degree leaves the quantity of each vague and uncertain another sees indeed the whole but makes such an awkward division of it into parts throwing things into one mass which require to be separated and separating others which might more conveniently be considered as one that the result is much the same sometimes even worse than if no analysis had been attempted at all It would be possible to point out what qualities of mind and modes of mental culture fit a person for being a good observer that however is a question not of Logic but of the Theory of Education in the most enlarged sense of the term There is not properly an Art of Observing There may be rules for observing But these like rules for inventing are properly instructions for the preparation of one’s own mind for putting it into the state in which it will be most fitted to observe or most likely to invent They are therefore essentially rules of selfeducation which is a different thing from Logic They do not teach how to do the thing but how to make ourselves capable of doing it They are an art of strengthening the limbs not an art of using them The extent and minuteness of observation which may be requisite and the degree of decomposition to which it may be necessary to carry the mental analysis depend on the particular purpose in view To ascertain the state of the whole universe at any particular moment is impossible but would also be useless In making chemical experiments we do not think it necessary to note the position of the planets because experience has shown as a very superficial experience is sufficient to show that in such cases that circumstance is not material to the result and accordingly in the ages when men believed in the occult influences of the heavenly bodies it might have been unphilosophical to omit ascertaining the precise condition of those bodies at the moment of the experiment As to the degree of minuteness of the mental subdivision if we were obliged to break down what we observe into its very simplest elements that is literally into single facts it would be difficult to say where we should find them we can hardly ever affirm that our divisions of any kind have reached the ultimate unit But this too is fortunately unnecessary The only object of the mental separation is to suggest the requisite physical separation so that we may either accomplish it ourselves or seek for it in nature and we have done enough when we have carried the subdivision as far as the point at which we are able to see what observations or experiments we require It is only essential at whatever point our mental decomposition of facts may for the present have stopped that we should hold ourselves ready and able to carry it further as occasion requires and should not allow the freedom of our discriminating faculty to be imprisoned by the swathes and bands of ordinary classification as was the case with all early speculative inquirers not excepting the Greeks to whom it seldom occurred that what was called by one abstract name might in reality be several phenomena or that there was a possibility of decomposing the facts of the universe into any elements but those which ordinary language already recognized The different antecedents and consequents being then supposed to be so far as the case requires ascertained and discriminated from one another we are to inquire which is connected with which In every instance which comes under our observation there are many antecedents and many consequents If those antecedents could not be severed from one another except in thought or if those consequents never were found apart it would be impossible for us to distinguish a posteriori at least the real laws or to assign to any cause its effect or to any effect its cause To do so we must be able to meet with some of the antecedents apart from the rest and observe what follows from them or some of the consequents and observe by what they are preceded We must in short follow the Baconian rule of varying the circumstances This is indeed only the first rule of physical inquiry and not as some have thought the sole rule but it is the foundation of all the rest For the purpose of varying the circumstances we may have recourse according to a distinction commonly made either to observation or to experiment we may either find an instance in nature suited to our purposes or by an artificial arrangement of circumstances make one The value of the instance depends on what it is in itself not on the mode in which it is obtained its employment for the purposes of induction depends on the same principles in the one case and in the other as the uses of money are the same whether it is inherited or acquired There is in short no difference in kind no real logical distinction between the two processes of investigation There are however practical distinctions to which it is of considerable importance to advert The first and most obvious distinction between Observation and Experiment is that the latter is an immense extension of the former It not only enables us to produce a much greater number of variations in the circumstances than nature spontaneously offers but also in thousands of cases to produce the precise sort of variation which we are in want of for discovering the law of the phenomenon a service which nature being constructed on a quite different scheme from that of facilitating our studies is seldom so friendly as to bestow upon us For example in order to ascertain what principle in the atmosphere enables it to sustain life the variation we require is that a living animal should be immersed in each component element of the atmosphere separately But nature does not supply either oxygen or azote in a separate state We are indebted to artificial experiment for our knowledge that it is the former and not the latter which supports respiration and for our knowledge of the very existence of the two ingredients Thus far the advantage of experimentation over simple observation is universally recognized all are aware that it enables us to obtain innumerable combinations of circumstances which are not to be found in nature and so add to nature’s experiments a multitude of experiments of our own But there is another superiority or as Bacon would have expressed it another prerogative of instances artificially obtained over spontaneous instances of our own experiments over even the same experiments when made by nature which is not of less importance and which is far from being felt and acknowledged in the same degree When we can produce a phenomenon artificially we can take it as it were home with us and observe it in the midst of circumstances with which in all other respects we are accurately acquainted If we desire to know what are the effects of the cause A and are able to produce A by means at our disposal we can generally determine at our own discretion so far as is compatible with the nature of the phenomenon A the whole of the circumstances which shall be present along with it and thus knowing exactly the simultaneous state of every thing else which is within the reach of A’s influence we have only to observe what alteration is made in that state by the presence of A For example by the electric machine we can produce in the midst of known circumstances the phenomena which nature exhibits on a grander scale in the form of lightning and thunder Now let any one consider what amount of knowledge of the effects and laws of electric agency mankind could have obtained from the mere observation of thunderstorms and compare it with that which they have gained and may expect to gain from electrical and galvanic experiments This example is the more striking now that we have reason to believe that electric action is of all natural phenomena except heat the most pervading and universal which therefore it might antecedently have been supposed could stand least in need of artificial means of production to enable it to be studied while the fact is so much the contrary that without the electric machine the Leyden jar and the voltaic battery we probably should never have suspected the existence of electricity as one of the great agents in nature the few electric phenomena we should have known of would have continued to be regarded either as supernatural or as a sort of anomalies and eccentricities in the order of the universe When we have succeeded in insulating the phenomenon which is the subject of inquiry by placing it among known circumstances we may produce further variations of circumstances to any extent and of such kinds as we think best calculated to bring the laws of the phenomenon into a clear light By introducing one welldefined circumstance after another into the experiment we obtain assurance of the manner in which the phenomenon behaves under an indefinite variety of possible circumstances Thus chemists after having obtained some newlydiscovered substance in a pure state that is having made sure that there is nothing present which can interfere with and modify its agency introduce various other substances one by one to ascertain whether it will combine with them or decompose them and with what result and also apply heat or electricity or pressure to discover what will happen to the substance under each of these circumstances But if on the other hand it is out of our power to produce the phenomenon and we have to seek for instances in which nature produces it the task before us is very different Instead of being able to choose what the concomitant circumstances shall be we now have to discover what they are which when we go beyond the simplest and most accessible cases it is next to impossible to do with any precision and completeness Let us take as an exemplification of a phenomenon which we have no means of fabricating artificially a human mind Nature produces many but the consequence of our not being able to produce them by art is that in every instance in which we see a human mind developing itself or acting upon other things we see it surrounded and obscured by an indefinite multitude of unascertainable circumstances rendering the use of the common experimental methods almost delusive We may conceive to what extent this is true if we consider among other things that whenever Nature produces a human mind she produces in close connection with it a body that is a vast complication of physical facts in no two cases perhaps exactly similar and most of which except the mere structure which we can examine in a sort of coarse way after it has ceased to act are radically out of the reach of our means of exploration If instead of a human mind we suppose the subject of investigation to be a human society or State all the same difficulties recur in a greatly augmented degree We have thus already come within sight of a conclusion which the progress of the inquiry will I think bring before us with the clearest evidence namely that in the sciences which deal with phenomena in which artificial experiments are impossible as in the case of astronomy or in which they have a very limited range as in mental philosophy social science and even physiology induction from direct experience is practiced at a disadvantage in most cases equivalent to impracticability from which it follows that the methods of those sciences in order to accomplish any thing worthy of attainment must be to a great extent if not principally deductive This is already known to be the case with the first of the sciences we have mentioned astronomy that it is not generally recognized as true of the others is probably one of the reasons why they are not in a more advanced state If what is called pure observation is at so great a disadvantage compared with artificial experimentation in one department of the direct exploration of phenomena there is another branch in which the advantage is all on the side of the former Inductive inquiry having for its object to ascertain what causes are connected with what effects we may begin this search at either end of the road which leads from the one point to the other we may either inquire into the effects of a given cause or into the causes of a given effect The fact that light blackens chloride of silver might have been discovered either by experiments on light trying what effect it would produce on various substances or by observing that portions of the chloride had repeatedly become black and inquiring into the circumstances The effect of the urali poison might have become known either by administering it to animals or by examining how it happened that the wounds which the Indians of Guiana inflict with their arrows prove so uniformly mortal Now it is manifest from the mere statement of the examples without any theoretical discussion that artificial experimentation is applicable only to the former of these modes of investigation We can take a cause and try what it will produce but we can not take an effect and try what it will be produced by We can only watch till we see it produced or are enabled to produce it by accident This would be of little importance if it always depended on our choice from which of the two ends of the sequence we would undertake our inquiries But we have seldom any option As we can only travel from the known to the unknown we are obliged to commence at whichever end we are best acquainted with If the agent is more familiar to us than its effects we watch for or contrive instances of the agent under such varieties of circumstances as are open to us and observe the result If on the contrary the conditions on which a phenomenon depends are obscure but the phenomenon itself familiar we must commence our inquiry from the effect If we are struck with the fact that chloride of silver has been blackened and have no suspicion of the cause we have no resource but to compare instances in which the fact has chanced to occur until by that comparison we discover that in all those instances the substances had been exposed to light If we knew nothing of the Indian arrows but their fatal effect accident alone could turn our attention to experiments on the urali in the regular course of investigation we could only inquire or try to observe what had been done to the arrows in particular instances Wherever having nothing to guide us to the cause we are obliged to set out from the effect and to apply the rule of varying the circumstances to the consequents not the antecedents we are necessarily destitute of the resource of artificial experimentation We can not at our choice obtain consequents as we can antecedents under any set of circumstances compatible with their nature There are no means of producing effects but through their causes and by the supposition the causes of the effect in question are not known to us We have therefore no expedient but to study it where it offers itself spontaneously If nature happens to present us with instances sufficiently varied in their circumstances and if we are able to discover either among the proximate antecedents or among some other order of antecedents something which is always found when the effect is found however various the circumstances and never found when it is not we may discover by mere observation without experiment a real uniformity in nature But though this is certainly the most favourable case for sciences of pure observation as contrasted with those in which artificial experiments are possible there is in reality no case which more strikingly illustrates the inherent imperfection of direct induction when not founded on experimentation Suppose that by a comparison of cases of the effect we have found an antecedent which appears to be and perhaps is invariably connected with it we have not yet proved that antecedent to be the cause until we have reversed the process and produced the effect by means of that antecedent If we can produce the antecedent artificially and if when we do so the effect follows the induction is complete that antecedent is the cause of that consequent But we have then added the evidence of experiment to that of simple observation Until we had done so we had only proved invariable antecedence within the limits of experience but not unconditional antecedence or causation Until it had been shown by the actual production of the antecedent under known circumstances and the occurrence thereupon of the consequent that the antecedent was really the condition on which it depended the uniformity of succession which was proved to exist between them might for aught we knew be like the succession of day and night not a case of causation at all both antecedent and consequent might be successive stages of the effect of an ulterior cause Observation in short without experiment supposing no aid from deduction can ascertain sequences and coexistences but can not prove causation In order to see these remarks verified by the actual state of the sciences we have only to think of the condition of natural history In zoology for example there is an immense number of uniformities ascertained some of coexistence others of succession to many of which notwithstanding considerable variations of the attendant circumstances we know not any exception but the antecedents for the most part are such as we can not artificially produce or if we can it is only by setting in motion the exact process by which nature produces them and this being to us a mysterious process of which the main circumstances are not only unknown but unobservable we do not succeed in obtaining the antecedents under known circumstances What is the result That on this vast subject which affords so much and such varied scope for observation we have made most scanty progress in ascertaining any laws of causation We know not with certainty in the case of most of the phenomena that we find conjoined which is the condition of the other which is cause and which effect or whether either of them is so or they are not rather conjunct effects of causes yet to be discovered complex results of laws hitherto unknown Although some of the foregoing observations may be in technical strictness of arrangement premature in this place it seemed that a few general remarks on the difference between sciences of mere observation and sciences of experimentation and the extreme disadvantage under which directly inductive inquiry is necessarily carried on in the former were the best preparation for discussing the methods of direct induction a preparation rendering superfluous much that must otherwise have been introduced with some inconvenience into the heart of that discussion To the consideration of these methods we now proceed The simplest and most obvious modes of singling out from among the circumstances which precede or follow a phenomenon those with which it is really connected by an invariable law are two in number One is by comparing together different instances in which the phenomenon occurs The other is by comparing instances in which the phenomenon does occur with instances in other respects similar in which it does not These two methods may be respectively denominated the Method of Agreement and the Method of Difference In illustrating these methods it will be necessary to bear in mind the twofold character of inquiries into the laws of phenomena which may be either inquiries into the cause of a given effect or into the effects or properties of a given cause We shall consider the methods in their application to either order of investigation and shall draw our examples equally from both We shall denote antecedents by the large letters of the alphabet and the consequents corresponding to them by the small Let A then be an agent or cause and let the object of our inquiry be to ascertain what are the effects of this cause If we can either find or produce the agent A in such varieties of circumstances that the different cases have no circumstance in common except A then whatever effect we find to be produced in all our trials is indicated as the effect of A Suppose for example that A is tried along with B and C and that the effect is a b c and suppose that A is next tried with D and E but without B and C and that the effect is a d e Then we may reason thus b and c are not effects of A for they were not produced by it in the second experiment nor are d and e for they were not produced in the first Whatever is really the effect of A must have been produced in both instances now this condition is fulfilled by no circumstance except a The phenomenon a can not have been the effect of B or C since it was produced where they were not nor of D or E since it was produced where they were not Therefore it is the effect of A For example let the antecedent A be the contact of an alkaline substance and an oil This combination being tried under several varieties of circumstances resembling each other in nothing else the results agree in the production of a greasy and detersive or saponaceous substance it is therefore concluded that the combination of an oil and an alkali causes the production of a soap It is thus we inquire by the Method of Agreement into the effect of a given cause In a similar manner we may inquire into the cause of a given effect Let a be the effect Here as shown in the last chapter we have only the resource of observation without experiment we can not take a phenomenon of which we know not the origin and try to find its mode of production by producing it if we succeeded in such a random trial it could only be by accident But if we can observe a in two different combinations a b c and a d e and if we know or can discover that the antecedent circumstances in these cases respectively were A B C and A D E we may conclude by a reasoning similar to that in the preceding example that A is the antecedent connected with the consequent a by a law of causation B and C we may say can not be causes of a since on its second occurrence they were not present nor are D and E for they were not present on its first occurrence A alone of the five circumstances was found among the antecedents of a in both instances For example let the effect a be crystallization We compare instances in which bodies are known to assume crystalline structure but which have no other point of agreement and we find them to have one and as far as we can observe only one antecedent in common the deposition of a solid matter from a liquid state either a state of fusion or of solution We conclude therefore that the solidification of a substance from a liquid state is an invariable antecedent of its crystallization In this example we may go further and say it is not only the invariable antecedent but the cause or at least the proximate event which completes the cause For in this case we are able after detecting the antecedent A to produce it artificially and by finding that a follows it verify the result of our induction The importance of thus reversing the proof was strikingly manifested when by keeping a phial of water charged with siliceous particles undisturbed for years a chemist I believe Dr Wollaston succeeded in obtaining crystals of quartz and in the equally interesting experiment in which Sir James Hall produced artificial marble by the cooling of its materials from fusion under immense pressure two admirable examples of the light which may be thrown upon the most secret processes of Nature by wellcontrived interrogation of her But if we can not artificially produce the phenomenon A the conclusion that it is the cause of a remains subject to very considerable doubt Though an invariable it may not be the unconditional antecedent of a but may precede it as day precedes night or night day This uncertainty arises from the impossibility of assuring ourselves that A is the only immediate antecedent common to both the instances If we could be certain of having ascertained all the invariable antecedents we might be sure that the unconditional invariable antecedent or cause must be found somewhere among them Unfortunately it is hardly ever possible to ascertain all the antecedents unless the phenomenon is one which we can produce artificially Even then the difficulty is merely lightened not removed men knew how to raise water in pumps long before they adverted to what was really the operating circumstance in the means they employed namely the pressure of the atmosphere on the open surface of the water It is however much easier to analyse completely a set of arrangements made by ourselves than the whole complex mass of the agencies which nature happens to be exerting at the moment of the production of a given phenomenon We may overlook some of the material circumstances in an experiment with an electrical machine but we shall at the worst be better acquainted with them than with those of a thunderstorm The mode of discovering and proving laws of nature which we have now examined proceeds on the following axiom Whatever circumstances can be excluded without prejudice to the phenomenon or can be absent notwithstanding its presence is not connected with it in the way of causation The casual circumstances being thus eliminated if only one remains that one is the cause which we are in search of if more than one they either are or contain among them the cause and so mutatis mutandis of the effect As this method proceeds by comparing different instances to ascertain in what they agree I have termed it the Method of Agreement and we may adopt as its regulating principal the following canon FIRST CANON If two or more instances of the phenomenon under investigation have only one circumstance in common the circumstance in which alone all the instances agree is the cause or effect of the given phenomenon Quitting for the present the Method of Agreement to which we shall almost immediately return we proceed to a still more potent instrument of the investigation of nature the Method of Difference In the Method of Agreement we endeavoured to obtain instances which agreed in the given circumstance but differed in every other in the present method we require on the contrary two instances resembling one another in every other respect but differing in the presence or absence of the phenomenon we wish to study If our object be to discover the effects of an agent A we must procure A in some set of ascertained circumstances as A B C and having noted the effects produced compare them with the effect of the remaining circumstances B C when A is absent If the effect of A B C is a b c and the effect of B C b c it is evident that the effect of A is a So again if we begin at the other end and desire to investigate the cause of an effect a we must select an instance as a b c in which the effect occurs and in which the antecedents were A B C and we must look out for another instance in which the remaining circumstances b c occur without a If the antecedents in that instance are B C we know that the cause of a must be A either A alone or A in conjunction with some of the other circumstances present It is scarcely necessary to give examples of a logical process to which we owe almost all the inductive conclusions we draw in daily life When a man is shot through the heart it is by this method we know that it was the gunshot which killed him for he was in the fullness of life immediately before all circumstances being the same except the wound The axioms implied in this method are evidently the following Whatever antecedent can not be excluded without preventing the phenomenon is the cause or a condition of that phenomenon whatever consequent can be excluded with no other difference in the antecedents than the absence of a particular one is the effect of that one Instead of comparing different instances of a phenomenon to discover in what they agree this method compares an instance of its occurrence with an instance of its nonoccurrence to discover in what they differ The canon which is the regulating principle of the Method of Difference may be expressed as follows SECOND CANON If an instance in which the phenomenon under investigation occurs and an instance in which it does not occur have every circumstance in common save one that one occurring only in the former the circumstance in which alone the two instances differ is the effect or the cause or an indispensable part of the cause of the phenomenon The two methods which we have now stated have many features of resemblance but there are also many distinctions between them Both are methods of elimination This term employed in the theory of equations to denote the process by which one after another of the elements of a question is excluded and the solution made to depend on the relation between the remaining elements only is well suited to express the operation analogous to this which has been understood since the time of Bacon to be the foundation of experimental inquiry namely the successive exclusion of the various circumstances which are found to accompany a phenomenon in a given instance in order to ascertain what are those among them which can be absent consistently with the existence of the phenomenon The Method of Agreement stands on the ground that whatever can be eliminated is not connected with the phenomenon by any law The Method of Difference has for its foundation that whatever can not be eliminated is connected with the phenomenon by a law Of these methods that of Difference is more particularly a method of artificial experiment while that of Agreement is more especially the resource employed where experimentation is impossible A few reflections will prove the fact and point out the reason of it It is inherent in the peculiar character of the Method of Difference that the nature of the combinations which it requires is much more strictly defined than in the Method of Agreement The two instances which are to be compared with one another must be exactly similar in all circumstances except the one which we are attempting to investigate they must be in the relation of A B C and B C or of a b c and b c It is true that this similarity of circumstances needs not extend to such as are already known to be immaterial to the result And in the case of most phenomena we learn at once from the commonest experience that most of the coexistent phenomena of the universe may be either present or absent without affecting the given phenomenon or if present are present indifferently when the phenomenon does not happen and when it does Still even limiting the identity which is required between the two instances A B C and B C to such circumstances as are not already known to be indifferent it is very seldom that nature affords two instances of which we can be assured that they stand in this precise relation to one another In the spontaneous operations of nature there is generally such complication and such obscurity they are mostly either on so overwhelmingly large or on so inaccessibly minute a scale we are so ignorant of a great part of the facts which really take place and even those of which we are not ignorant are so multitudinous and therefore so seldom exactly alike in any two cases that a spontaneous experiment of the kind required by the Method of Difference is commonly not to be found When on the contrary we obtain a phenomenon by an artificial experiment a pair of instances such as the method requires is obtained almost as a matter of course provided the process does not last a long time A certain state of surrounding circumstances existed before we commenced the experiment this is B C We then introduce A say for instance by merely bringing an object from another part of the room before there has been time for any change in the other elements It is in short as M Comt observes the very nature of an experiment to introduce into the preexisting state of circumstances a change perfectly definite We choose a previous state of things with which we are well acquainted so that no unforeseen alteration in that state is likely to pass unobserved and into this we introduce as rapidly as possible the phenomenon which we wish to study so that in general we are entitled to feel complete assurance that the preexisting state and the state which we have produced differ in nothing except the presence or absence of that phenomenon If a bird is taken from a cage and instantly plunged into carbonic acid gas the experimentalist may be fully assured at all events after one or two repetitions that no circumstance capable of causing suffocation had supervened in the interim except the change from immersion in the atmosphere to immersion in carbonic acid gas There is one doubt indeed which may remain in some cases of this description the effect may have been produced not by the change but by the means employed to produce the change The possibility however of this last supposition generally admits of being conclusively tested by other experiments It thus appears that in the study of the various kinds of phenomena which we can by our voluntary agency modify or control we can in general satisfy the requisitions of the Method of Difference but that by the spontaneous operations of nature those requisitions are seldom fulfilled The reverse of this is the case with the Method of Agreement We do not here require instances of so special and determinate a kind Any instances whatever in which nature presents us with a phenomenon may be examined for the purposes of this method and if all such instances agree in any thing a conclusion of considerable value is already attained We can seldom indeed be sure that the one point of agreement is the only one but this ignorance does not as in the Method of Difference vitiate the conclusion the certainty of the result as far as it goes is not affected We have ascertained one invariable antecedent or consequent however many other invariable antecedents or consequents may still remain unascertained If A B C A D E A F G are all equally followed by a then a is an invariable consequent of A If a b c a d e a f g all number A among their antecedents then A is connected as an antecedent by some invariable law with a But to determine whether this invariable antecedent is a cause or this invariable consequent an effect we must be able in addition to produce the one by means of the other or at least to obtain that which alone constitutes our assurance of having produced any thing namely an instance in which the effect a has come into existence with no other change in the preexisting circumstances than the addition of A And this if we can do it is an application of the Method of Difference not of the Method of Agreement It thus appears to be by the Method of Difference alone that we can ever in the way of direct experience arrive with certainty at causes The Method of Agreement leads only to laws of phenomena as some writers call them but improperly since laws of causation are also laws of phenomena that is to uniformities which either are not laws of causation or in which the question of causation must for the present remain undecided The Method of Agreement is chiefly to be resorted to as a means of suggesting applications of the Method of Difference as in the last example the comparison of A B C A D E A F G suggested that A was the antecedent on which to try the experiment whether it could produce a or as an inferior resource in case the Method of Difference is impracticable which as we before showed generally arises from the impossibility of artificially producing the phenomena And hence it is that the Method of Agreement though applicable in principle to either case is more emphatically the method of investigation on those subjects where artificial experimentation is impossible because on those it is generally our only resource of a directly inductive nature while in the phenomena which we can produce at pleasure the Method of Difference generally affords a more efficacious process which will ascertain causes as well as mere laws There are however many cases in which though our power of producing the phenomenon is complete the Method of Difference either can not be made available at all or not without a previous employment of the Method of Agreement This occurs when the agency by which we can produce the phenomenon is not that of one single antecedent but a combination of antecedents which we have no power of separating from each other and exhibiting apart For instance suppose the subject of inquiry to be the cause of the double refraction of light We can produce this phenomenon at pleasure by employing any one of the many substances which are known to refract light in that peculiar manner But if taking one of those substances as Iceland spar for example we wish to determine on which of the properties of Iceland spar this remarkable phenomenon depends we can make no use for that purpose of the Method of Difference for we can not find another substance precisely resembling Iceland spar except in some one property The only mode therefore of prosecuting this inquiry is that afforded by the Method of Agreement by which in fact through a comparison of all the known substances which have the property of doubly refracting light it was ascertained that they agree in the circumstance of being crystalline substances and though the converse does not hold though all crystalline substances have not the property of double refraction it was concluded with reason that there is a real connection between these two properties that either crystalline structure or the cause which gives rise to that structure is one of the conditions of double refraction Out of this employment of the Method of Agreement arises a peculiar modification of that method which is sometimes of great avail in the investigation of nature In cases similar to the above in which it is not possible to obtain the precise pair of instances which our second canon requires instances agreeing in every antecedent except A or in every consequent except a we may yet be able by a double employment of the Method of Agreement to discover in what the instances which contain A or a differ from those which do not If we compare various instances in which a occurs and find that they all have in common the circumstance A and as far as can be observed no other circumstance the Method of Agreement so far bears testimony to a connection between A and a In order to convert this evidence of connection into proof of causation by the direct Method of Difference we ought to be able in some one of these instances as for example A B C to leave out A and observe whether by doing so a is prevented Now supposing what is often the case that we are not able to try this decisive experiment yet provided we can by any means discover what would be its result if we could try it the advantage will be the same Suppose then that as we previously examined a variety of instances in which a occurred and found them to agree in containing A so we now observe a variety of instances in which a does not occur and find them agree in not containing A which establishes by the Method of Agreement the same connection between the absence of A and the absence of a which was before established between their presence As then it had been shown that whenever A is present a is present so it being now shown that when A is taken away a is removed along with it we have by the one proposition A B C a b c by the other B C b c the positive and negative instances which the Method of Difference requires This method may be called the Indirect Method of Difference or the Joint Method of Agreement and Difference and consists in a double employment of the Method of Agreement each proof being independent of the other and corroborating it But it is not equivalent to a proof by the direct Method of Difference For the requisitions of the Method of Difference are not satisfied unless we can be quite sure either that the instances affirmative of a agree in no antecedent whatever but A or that the instances negative of a agree in nothing but the negation of A Now if it were possible which it never is to have this assurance we should not need the joint method for either of the two sets of instances separately would then be sufficient to prove causation This indirect method therefore can only be regarded as a great extension and improvement of the Method of Agreement but not as participating in the more cogent nature of the Method of Difference The following may be stated as its canon THIRD CANON If two or more instances in which the phenomenon occurs have only one circumstance in common while two or more instances in which it does not occur have nothing in common save the absence of that circumstance the circumstance in which alone the two sets of instances differ is the effect or the cause or an indispensable part of the cause of the phenomenon We shall presently see that the Joint Method of Agreement and Difference constitutes in another respect not yet adverted to an improvement upon the common Method of Agreement namely in being unaffected by a characteristic imperfection of that method the nature of which still remains to be pointed out But as we can not enter into this exposition without introducing a new element of complexity into this long and intricate discussion I shall postpone it to a subsequent chapter and shall at once proceed to a statement of two other methods which will complete the enumeration of the means which mankind possess for exploring the laws of nature by specific observation and experience The first of these has been aptly denominated the Method of Residues Its principle is very simple Subducting from any given phenomenon all the portions which by virtue of preceding inductions can be assigned to known causes the remainder will be the effect of the antecedents which had been overlooked or of which the effect was as yet an unknown quantity Suppose as before that we have the antecedents A B C followed by the consequents a b c and that by previous inductions founded we will suppose on the Method of Difference we have ascertained the causes of some of these effects or the effects of some of these causes and are thence apprised that the effect of A is a and that the effect of B is b Subtracting the sum of these effects from the total phenomenon there remains c which now without any fresh experiments we may know to be the effect of C This Method of Residues is in truth a peculiar modification of the Method of Difference If the instance A B C a b c could have been compared with a single instance A B a b we should have proved C to be the cause of c by the common process of the Method of Difference In the present case however instead of a single instance A B we have had to study separately the causes A and B and to infer from the effects which they produce separately what effect they must produce in the case A B C where they act together Of the two instances therefore which the Method of Difference requires the one positive the other negative the negative one or that in which the given phenomenon is absent is not the direct result of observation and experiment but has been arrived at by deduction As one of the forms of the Method of Difference the Method of Residues partakes of its rigorous certainty provided the previous inductions those which gave the effects of A and B were obtained by the same infallible method and provided we are certain that C is the only antecedent to which the residual phenomenon c can be referred the only agent of which we had not already calculated and subducted the effect But as we can never be quite certain of this the evidence derived from the Method of Residues is not complete unless we can obtain C artificially and try it separately or unless its agency when once suggested can be accounted for and proved deductively from known laws Even with these reservations the Method of Residues is one of the most important among our instruments of discovery Of all the methods of investigating laws of nature this is the most fertile in unexpected results often informing us of sequences in which neither the cause nor the effect were sufficiently conspicuous to attract of themselves the attention of observers The agent C may be an obscure circumstance not likely to have been perceived unless sought for nor likely to have been sought for until attention had been awakened by the insufficiency of the obvious causes to account for the whole of the effect And c may be so disguised by its intermixture with a and b that it would scarcely have presented itself spontaneously as a subject of separate study Of these uses of the method we shall presently cite some remarkable examples The canon of the Method of Residues is as follows FOURTH CANON Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents and the residue of the phenomenon is the effect of the remaining antecedents There remains a class of laws which it is impracticable to ascertain by any of the three methods which I have attempted to characterize namely the laws of those Permanent Causes or indestructible natural agents which it is impossible either to exclude or to isolate which we can neither hinder from being present nor contrive that they shall be present alone It would appear at first sight that we could by no means separate the effects of these agents from the effects of those other phenomena with which they can not be prevented from coexisting In respect indeed to most of the permanent causes no such difficulty exists since though we can not eliminate them as coexisting facts we can eliminate them as influencing agents by simply trying our experiment in a local situation beyond the limits of their influence The pendulum for example has its oscillations disturbed by the vicinity of a mountain we remove the pendulum to a sufficient distance from the mountain and the disturbance ceases from these data we can determine by the Method of Difference the amount of effect due to the mountain and beyond a certain distance every thing goes on precisely as it would do if the mountain exercised no influence whatever which accordingly we with sufficient reason conclude to be the fact The difficulty therefore in applying the methods already treated of to determine the effects of Permanent Causes is confined to the cases in which it is impossible for us to get out of the local limits of their influence The pendulum can be removed from the influence of the mountain but it can not be removed from the influence of the earth we can not take away the earth from the pendulum nor the pendulum from the earth to ascertain whether it would continue to vibrate if the action which the earth exerts upon it were withdrawn On what evidence then do we ascribe its vibrations to the earth’s influence Not on any sanctioned by the Method of Difference for one of the two instances the negative instance is wanting Nor by the Method of Agreement for though all pendulums agree in this that during their oscillations the earth is always present why may we not as well ascribe the phenomenon to the sun which is equally a coexistent fact in all the experiments It is evident that to establish even so simple a fact of causation as this there was required some method over and above those which we have yet examined As another example let us take the phenomenon Heat Independently of all hypothesis as to the real nature of the agency so called this fact is certain that we are unable to exhaust any body of the whole of its heat It is equally certain that no one ever perceived heat not emanating from a body Being unable then to separate Body and Heat we can not effect such a variation of circumstances as the foregoing three methods require we can not ascertain by those methods what portion of the phenomena exhibited by any body is due to the heat contained in it If we could observe a body with its heat and the same body entirely divested of heat the Method of Difference would show the effect due to the heat apart from that due to the body If we could observe heat under circumstances agreeing in nothing but heat and therefore not characterized also by the presence of a body we could ascertain the effects of heat from an instance of heat with a body and an instance of heat without a body by the Method of Agreement or we could determine by the Method of Difference what effect was due to the body when the remainder which was due to the heat would be given by the Method of Residues But we can do none of these things and without them the application of any of the three methods to the solution of this problem would be illusory It would be idle for instance to attempt to ascertain the effect of heat by subtracting from the phenomena exhibited by a body all that is due to its other properties for as we have never been able to observe any bodies without a portion of heat in them effects due to that heat might form a part of the very results which we were affecting to subtract in order that the effect of heat might be shown by the residue If therefore there were no other methods of experimental investigation than these three we should be unable to determine the effects due to heat as a cause But we have still a resource Though we can not exclude an antecedent altogether we may be able to produce or nature may produce for us some modification in it By a modification is here meant a change in it not amounting to its total removal If some modification in the antecedent A is always followed by a change in the consequent a the other consequents b and c remaining the same or vic versa if every change in a is found to have been preceded by some modification in A none being observable in any of the other antecedents we may safely conclude that a is wholly or in part an effect traceable to A or at least in some way connected with it through causation For example in the case of heat though we can not expel it altogether from any body we can modify it in quantity we can increase or diminish it and doing so we find by the various methods of experimentation or observation already treated of that such increase or diminution of heat is followed by expansion or contraction of the body In this manner we arrive at the conclusion otherwise unattainable by us that one of the effects of heat is to enlarge the dimensions of bodies or what is the same thing in other words to widen the distances between their particles A change in a thing not amounting to its total removal that is a change which leaves it still the same thing it was must be a change either in its quantity or in some of its variable relations to other things of which variable relations the principal is its position in space In the previous example the modification which was produced in the antecedent was an alteration in its quantity Let us now suppose the question to be what influence the moon exerts on the surface of the earth We can not try an experiment in the absence of the moon so as to observe what terrestrial phenomena her annihilation would put an end to but when we find that all the variations in the position of the moon are followed by corresponding variations in the time and place of high water the place being always either the part of the earth which is nearest to or that which is most remote from the moon we have ample evidence that the moon is wholly or partially the cause which determines the tides It very commonly happens as it does in this instance that the variations of an effect are correspondent or analogous to those of its cause as the moon moves farther toward the east the highwater point does the same but this is not an indispensable condition as may be seen in the same example for along with that highwater point there is at the same instant another highwater point diametrically opposite to it and which therefore of necessity moves toward the west as the moon followed by the nearer of the tide waves advances toward the east and yet both these motions are equally effects of the moon’s motion That the oscillations of the pendulum are caused by the earth is proved by similar evidence Those oscillations take place between equidistant points on the two sides of a line which being perpendicular to the earth varies with every variation in the earth’s position either in space or relatively to the object Speaking accurately we only know by the method now characterized that all terrestrial bodies tend to the earth and not to some unknown fixed point lying in the same direction In every twentyfour hours by the earth’s rotation the line drawn from the body at right angles to the earth coincides successively with all the radii of a circle and in the course of six months the place of that circle varies by nearly two hundred millions of miles yet in all these changes of the earth’s position the line in which bodies tend to fall continues to be directed toward it which proves that terrestrial gravity is directed to the earth and not as was once fancied by some to a fixed point of space The method by which these results were obtained may be termed the Method of Concomitant Variations it is regulated by the following canon FIFTH CANON Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner is either a cause or an effect of that phenomenon or is connected with it through some fact of causation The last clause is subjoined because it by no means follows when two phenomena accompany each other in their variations that the one is cause and the other effect The same thing may and indeed must happen supposing them to be two different effects of a common cause and by this method alone it would never be possible to ascertain which of the suppositions is the true one The only way to solve the doubt would be that which we have so often adverted to viz by endeavouring to ascertain whether we can produce the one set of variations by means of the other In the case of heat for example by increasing the temperature of a body we increase its bulk but by increasing its bulk we do not increase its temperature on the contrary as in the rarefaction of air under the receiver of an airpump we generally diminish it therefore heat is not an effect but a cause of increase of bulk If we can not ourselves produce the variations we must endeavour though it is an attempt which is seldom successful to find them produced by nature in some case in which the preexisting circumstances are perfectly known to us It is scarcely necessary to say that in order to ascertain the uniform concomitance of variations in the effect with variations in the cause the same precautions must be used as in any other case of the determination of an invariable sequence We must endeavour to retain all the other antecedents unchanged while that particular one is subjected to the requisite series of variations or, in other words, that we may be warranted in inferring causation from concomitance of variations the concomitance itself must be proved by the Method of Difference It might at first appear that the Method of Concomitant Variations assumes a new axiom or law of causation in general namely that every modification of the cause is followed by a change in the effect And it does usually happen that when a phenomenon A causes a phenomenon a any variation in the quantity or in the various relations of A is uniformly followed by a variation in the quantity or relations of a To take a familiar instance that of gravitation The sun causes a certain tendency to motion in the earth here we have cause and effect but that tendency is toward the sun and therefore varies in direction as the sun varies in the relation of position and moreover the tendency varies in intensity in a certain numerical correspondence to the sun’s distance from the earth that is according to another relation of the sun Thus we see that there is not only an invariable connection between the sun and the earth’s gravitation but that two of the relations of the sun its position with respect to the earth and its distance from the earth are invariably connected as antecedents with the quantity and direction of the earth’s gravitation The cause of the earth’s gravitating at all is simply the sun but the cause of its gravitating with a given intensity and in a given direction is the existence of the sun in a given direction and at a given distance It is not strange that a modified cause which is in truth a different cause should produce a different effect Although it is for the most part true that a modification of the cause is followed by a modification of the effect the Method of Concomitant Variations does not however presuppose this as an axiom It only requires the converse proposition that any thing on whose modifications modifications of an effect are invariably consequent must be the cause or connected with the cause of that effect a proposition the truth of which is evident for if the thing itself had no influence on the effect neither could the modifications of the thing have any influence If the stars have no power over the fortunes of mankind it is implied in the very terms that the conjunctions or oppositions of different stars can have no such power Although the most striking applications of the Method of Concomitant Variations take place in the cases in which the Method of Difference strictly so called is impossible its use is not confined to those cases it may often usefully follow after the Method of Difference to give additional precision to a solution which that has found When by the Method of Difference it has first been ascertained that a certain object produces a certain effect the Method of Concomitant Variations may be usefully called in to determine according to what law the quantity or the different relations of the effect follow those of the cause The case in which this method admits of the most extensive employment is that in which the variations of the cause are variations of quantity Of such variations we may in general affirm with safety that they will be attended not only with variations but with similar variations of the effect the proposition that more of the cause is followed by more of the effect being a corollary from the principle of the Composition of Causes which as we have seen is the general rule of causation cases of the opposite description in which causes change their properties on being conjoined with one another being on the contrary special and exceptional Suppose then that when A changes in quantity a also changes in quantity and in such a manner that we can trace the numerical relation which the changes of the one bear to such changes of the other as take place within our limits of observation We may then with certain precautions safely conclude that the same numerical relation will hold beyond those limits If for instance we find that when A is double a is double that when A is treble or quadruple a is treble or quadruple we may conclude that if A were a half or a third a would be a half or a third and finally that if A were annihilated a would be annihilated and that a is wholly the effect of A or wholly the effect of the same cause with A And so with any other numerical relation according to which A and a would vanish simultaneously as for instance if a were proportional to the square of A If on the other hand a is not wholly the effect of A but yet varies when A varies it is probably a mathematical function not of A alone but of A and something else its changes for example may be such as would occur if part of it remained constant or varied on some other principle and the remainder varied in some numerical relations to the variations of A In that case when A diminishes a will be seen to approach not toward zero but toward some other limit and when the series of variations is such as to indicate what that limit is if constant or the law of its variation if variable the limit will exactly measure how much of a is the effect of some other and independent cause and the remainder will be the effect of A or of the cause of A These conclusions however must not be drawn without certain precautions In the first place the possibility of drawing them at all manifestly supposes that we are acquainted not only with the variations but with the absolute quantities both of A and a If we do not know the total quantities we can not of course determine the real numerical relation according to which those quantities vary It is therefore an error to conclude as some have concluded that because increase of heat expands bodies that is increases the distance between their particles therefore the distance is wholly the effect of heat and that if we could entirely exhaust the body of its heat the particles would be in complete contact This is no more than a guess and of the most hazardous sort not a legitimate induction for since we neither know how much heat there is in any body nor what is the real distance between any two of its particles we can not judge whether the contraction of the distance does or does not follow the diminution of the quantity of heat according to such a numerical relation that the two quantities would vanish simultaneously In contrast with this let us consider a case in which the absolute quantities are known the case contemplated in the first law of motion viz that all bodies in motion continue to move in a straight line with uniform velocity until acted upon by some new force This assertion is in open opposition to first appearances all terrestrial objects when in motion gradually abate their velocity and at last stop which accordingly the ancients with their inductio per enumerationem simplicem imagined to be the law Every moving body however encounters various obstacles as friction the resistance of the atmosphere etc which we know by daily experience to be causes capable of destroying motion It was suggested that the whole of the retardation might be owing to these causes How was this inquired into If the obstacles could have been entirely removed the case would have been amenable to the Method of Difference They could not be removed they could only be diminished and the case therefore admitted only of the Method of Concomitant Variations This accordingly being employed it was found that every diminution of the obstacles diminished the retardation of the motion and inasmuch as in this case unlike the case of heat the total quantities both of the antecedent and of the consequent were known it was practicable to estimate with an approach to accuracy both the amount of the retardation and the amount of the retarding causes or resistances and to judge how near they both were to being exhausted and it appeared that the effect dwindled as rapidly and at each step was as far on the road toward annihilation as the cause was The simple oscillation of a weight suspended from a fixed point and moved a little out of the perpendicular which in ordinary circumstances lasts but a few minutes was prolonged in Borda’s experiments to more than thirty hours by diminishing as much as possible the friction at the point of suspension and by making the body oscillate in a space exhausted as nearly as possible of its air There could therefore be no hesitation in assigning the whole of the retardation of motion to the influence of the obstacles and since after subducting this retardation from the total phenomenon the remainder was a uniform velocity the result was the proposition known as the first law of motion There is also another characteristic uncertainty affecting the inference that the law of variation which the quantities observe within our limits of observation will hold beyond those limits There is of course in the first instance, the possibility that beyond the limits and in circumstances therefore of which we have no direct experience some counteracting cause might develop itself either a new agent or a new property of the agents concerned which lies dormant in the circumstances we are able to observe This is an element of uncertainty which enters largely into all our predictions of effects but it is not peculiarly applicable to the Method of Concomitant Variations The uncertainty however of which I am about to speak is characteristic of that method especially in the cases in which the extreme limits of our observation are very narrow in comparison with the possible variations in the quantities of the phenomena Any one who has the slightest acquaintance with mathematics is aware that very different laws of variation may produce numerical results which differ but slightly from one another within narrow limits and it is often only when the absolute amounts of variation are considerable that the difference between the results given by one law and by another becomes appreciable When therefore such variations in the quantity of the antecedents as we have the means of observing are small in comparison with the total quantities there is much danger lest we should mistake the numerical law and be led to miscalculate the variations which would take place beyond the limits a miscalculation which would vitiate any conclusion respecting the dependence of the effect upon the cause that could be founded on those variations Examples are not wanting of such mistakes The formulae says Sir John Herschel which have been empirically deduced for the elasticity of steam till very recently and those for the resistance of fluids and other similar subjects when relied on beyond the limits of the observations from which they were deduced have almost invariably failed to support the theoretical structures which have been erected on them In this uncertainty the conclusion we may draw from the concomitant variations of a and A to the existence of an invariable and exclusive connection between them or to the permanency of the same numerical relation between their variations when the quantities are much greater or smaller than those which we have had the means of observing can not be considered to rest on a complete induction All that in such a case can be regarded as proved on the subject of causation is that there is some connection between the two phenomena that A or something which can influence A must be one of the causes which collectively determine a We may however feel assured that the relation which we have observed to exist between the variations of A and a will hold true in all cases which fall between the same extreme limits that is wherever the utmost increase or diminution in which the result has been found by observation to coincide with the law is not exceeded The four methods which it has now been attempted to describe are the only possible modes of experimental inquiry of direct induction a posteriori as distinguished from deduction at least I know not nor am able to imagine any others And even of these the Method of Residues as we have seen is not independent of deduction though as it also requires specific experience it may without impropriety be included among methods of direct observation and experiment These then with such assistance as can be obtained from Deduction compose the available resources of the human mind for ascertaining the laws of the succession of phenomena Before proceeding to point out certain circumstances by which the employment of these methods is subjected to an immense increase of complication and of difficulty it is expedient to illustrate the use of the methods by suitable examples drawn from actual physical investigations These accordingly will form the subject of the succeeding chapter I shall select as a first example an interesting speculation of one of the most eminent of theoretical chemists Baron Liebig The object in view is to ascertain the immediate cause of the death produced by metallic poisons Arsenious acid and the salts of lead bismuth copper and mercury if introduced into the animal organism except in the smallest doses destroy life These facts have long been known as insulated truths of the lowest order of generalization but it was reserved for Liebig by an apt employment of the first two of our methods of experimental inquiry to connect these truths together by a higher induction pointing out what property common to all these deleterious substances is the really operating cause of their fatal effect When solutions of these substances are placed in sufficiently close contact with many animal products albumen milk muscular fibre and animal membranes the acid or salt leaves the water in which it was dissolved and enters into combination with the animal substance which substance after being thus acted upon is found to have lost its tendency to spontaneous decomposition or putrefaction Observation also shows in cases where death has been produced by these poisons that the parts of the body with which the poisonous substances have been brought into contact do not afterward putrefy And finally when the poison has been supplied in too small a quantity to destroy life eschars are produced that is certain superficial portions of the tissues are destroyed which are afterward thrown off by the reparative process taking place in the healthy parts These three sets of instances admit of being treated according to the Method of Agreement In all of them the metallic compounds are brought into contact with the substances which compose the human or animal body and the instances do not seem to agree in any other circumstance The remaining antecedents are as different and even opposite as they could possibly be made for in some the animal substances exposed to the action of the poisons are in a state of life in others only in a state of organization in others not even in that And what is the result which follows in all the cases The conversion of the animal substance by combination with the poison into a chemical compound held together by so powerful a force as to resist the subsequent action of the ordinary causes of decomposition Now organic life the necessary condition of sensitive life consisting in a continual state of decomposition and recomposition of the different organs and tissues whatever incapacitates them for this decomposition destroys life And thus the proximate cause of the death produced by this description of poisons is ascertained as far as the Method of Agreement can ascertain it Let us now bring our conclusion to the test of the Method of Difference Setting out from the cases already mentioned in which the antecedent is the presence of substances forming with the tissues a compound incapable of putrefaction and a fortiori incapable of the chemical actions which constitute life and the consequent is death either of the whole organism or of some portion of it let us compare with these cases other cases as much resembling them as possible but in which that effect is not produced And first many insoluble basic salts of arsenious acid are known not to be poisonous The substance called alkargen discovered by Bunsen which contains a very large quantity of arsenic and approaches very closely in composition to the organic arsenious compounds found in the body has not the slightest injurious action upon the organism Now when these substances are brought into contact with the tissues in any way they do not combine with them they do not arrest their progress to decomposition As far therefore as these instances go it appears that when the effect is absent it is by reason of the absence of that antecedent which we had already good ground for considering as the proximate cause But the rigorous conditions of the Method of Difference are not yet satisfied for we can not be sure that these unpoisonous bodies agree with the poisonous substances in every property except the particular one of entering into a difficultly decomposable compound with the animal tissues To render the method strictly applicable we need an instance not of a different substance but of one of the very same substances in circumstances which would prevent it from forming with the tissues the sort of compound in question and then if death does not follow our case is made out Now such instances are afforded by the antidotes to these poisons For example in case of poisoning by arsenious acid if hydrated peroxide of iron is administered the destructive agency is instantly checked Now this peroxide is known to combine with the acid and form a compound which being insoluble can not act at all on animal tissues So again sugar is a wellknown antidote to poisoning by salts of copper and sugar reduces those salts either into metallic copper or into the red suboxide neither of which enters into combination with animal matter The disease called painter’s colic so common in manufactories of whitelead is unknown where the workmen are accustomed to take as a preservative sulphuric acid lemonade a solution of sugar rendered acid by sulphuric acid Now diluted sulphuric acid has the property of decomposing all compounds of lead with organic matter or of preventing them from being formed There is another class of instances of the nature required by the Method of Difference which seem at first sight to conflict with the theory Soluble salts of silver such for instance as the nitrate have the same stiffening antiseptic effect on decomposing animal substances as corrosive sublimate and the most deadly metallic poisons and when applied to the external parts of the body the nitrate is a powerful caustic depriving those parts of all active vitality and causing them to be thrown off by the neighboring living structures in the form of an eschar The nitrate and the other salts of silver ought then it would seem if the theory be correct to be poisonous yet they may be administered internally with perfect impunity From this apparent exception arises the strongest confirmation which the theory has yet received Nitrate of silver in spite of its chemical properties does not poison when introduced into the stomach but in the stomach as in all animal liquids there is common salt and in the stomach there is also free muriatic acid These substances operate as natural antidotes combining with the nitrate and if its quantity is not too great immediately converting it into chloride of silver a substance very slightly soluble and therefore incapable of combining with the tissues although to the extent of its solubility it has a medicinal influence though an entirely different class of organic actions The preceding instances have afforded an induction of a high order of conclusiveness illustrative of the two simplest of our four methods though not rising to the maximum of certainty which the Method of Difference in its most perfect exemplification is capable of affording For let us not forget the positive instance and the negative one which the rigor of that method requires ought to differ only in the presence or absence of one single circumstance Now in the preceding argument they differ in the presence or absence not of a single circumstance but of a single substance and as every substance has innumerable properties there is no knowing what number of real differences are involved in what is nominally and apparently only one difference It is conceivable that the antidote the peroxide of iron for example may counteract the poison through some other of its properties than that of forming an insoluble compound with it and if so the theory would fall to the ground so far as it is supported by that instance This source of uncertainty which is a serious hinderance to all extensive generalizations in chemistry is however reduced in the present case to almost the lowest degree possible when we find that not only one substance but many substances possess the capacity of acting as antidotes to metallic poisons and that all these agree in the property of forming insoluble compounds with the poisons while they can not be ascertained to agree in any other property whatsoever We have thus in favour of the theory all the evidence which can be obtained by what we termed the Indirect Method of Difference or the Joint Method of Agreement and Difference the evidence of which though it never can amount to that of the Method of Difference properly so called may approach indefinitely near to it Let the object be to ascertain the law of what is termed induced electricity to find under what conditions any electrified body whether positively or negatively electrified gives rise to a contrary electric state in some other body adjacent to it The most familiar exemplification of the phenomenon to be investigated is the following Around the prime conductors of an electrical machine the atmosphere to some distance or any conducting surface suspended in that atmosphere is found to be in an electric condition opposite to that of the prime conductor itself Near and around the positive prime conductor there is negative electricity and near and around the negative prime conductor there is positive electricity When pith balls are brought near to either of the conductors they become electrified with the opposite electricity to it either receiving a share from the already electrified atmosphere by conduction or acted upon by the direct inductive influence of the conductor itself they are then attracted by the conductor to which they are in opposition or if withdrawn in their electrified state they will be attracted by any other oppositely charged body In like manner the hand if brought near enough to the conductor receives or gives an electric discharge now we have no evidence that a charged conductor can be suddenly discharged unless by the approach of a body oppositely electrified In the case therefore of the electric machine it appears that the accumulation of electricity in an insulated conductor is always accompanied by the excitement of the contrary electricity in the surrounding atmosphere and in every conductor placed near the former conductor It does not seem possible in this case to produce one electricity by itself Let us now examine all the other instances which we can obtain resembling this instance in the given consequent namely the evolution of an opposite electricity in the neighborhood of an electrified body As one remarkable instance we have the Leyden jar and after the splendid experiments of Faraday in complete and final establishment of the substantial identity of magnetism and electricity we may cite the magnet both the natural and the electromagnet in neither of which it is possible to produce one kind of electricity by itself or to charge one pole without charging an opposite pole with the contrary electricity at the same time We can not have a magnet with one pole if we break a natural loadstone into a thousand pieces each piece will have its two oppositely electrified poles complete within itself In the voltaic circuit again we can not have one current without its opposite In the ordinary electric machine the glass cylinder or plate and the rubber acquire opposite electricities From all these instances treated by the Method of Agreement a general law appears to result The instances embrace all the known modes in which a body can become charged with electricity and in all of them there is found as a concomitant or consequent the excitement of the opposite electric state in some other body or bodies It seems to follow that the two facts are invariably connected and that the excitement of electricity in any body has for one of its necessary conditions the possibility of a simultaneous excitement of the opposite electricity in some neighboring body As the two contrary electricities can only be produced together so they can only cease together This may be shown by an application of the Method of Difference to the example of the Leyden jar It needs scarcely be here remarked that in the Leyden jar electricity can be accumulated and retained in considerable quantity by the contrivance of having two conducting surfaces of equal extent and parallel to each other through the whole of that extent with a nonconducting substance such as glass between them When one side of the jar is charged positively the other is charged negatively and it was by virtue of this fact that the Leyden jar served just now as an instance in our employment of the Method of Agreement Now it is impossible to discharge one of the coatings unless the other can be discharged at the same time A conductor held to the positive side can not convey away any electricity unless an equal quantity be allowed to pass from the negative side if one coating be perfectly insulated the charge is safe The dissipation of one must proceed pari passu with that of the other The law thus strongly indicated admits of corroboration by the Method of Concomitant Variations The Leyden jar is capable of receiving a much higher charge than can ordinarily be given to the conductor of an electrical machine Now in the case of the Leyden jar the metallic surface which receives the induced electricity is a conductor exactly similar to that which receives the primary charge and is therefore as susceptible of receiving and retaining the one electricity as the opposite surface of receiving and retaining the other but in the machine the neighboring body which is to be oppositely electrified is the surrounding atmosphere or any body casually brought near to the conductor and as these are generally much inferior in their capacity of becoming electrified to the conductor itself their limited power imposes a corresponding limit to the capacity of the conductor for being charged As the capacity of the neighboring body for supporting the opposition increases a higher charge becomes possible and to this appears to be owing the great superiority of the Leyden jar A further and most decisive confirmation by the Method of Difference is to be found in one of Faraday’s experiments in the course of his researches on the subject of Induced Electricity Since common or machine electricity and voltaic electricity may be considered for the present purpose to be identical Faraday wished to know whether as the prime conductor develops opposite electricity upon a conductor in its vicinity so a voltaic current running along a wire would induce an opposite current upon another wire laid parallel to it at a short distance Now this case is similar to the cases previously examined in every circumstance except the one to which we have ascribed the effect We found in the former instances that whenever electricity of one kind was excited in one body electricity of the opposite kind must be excited in a neighboring body But in Faraday’s experiment this indispensable opposition exists within the wire itself From the nature of a voltaic charge the two opposite currents necessary to the existence of each other are both accommodated in one wire and there is no need of another wire placed beside it to contain one of them in the same way as the Leyden jar must have a positive and a negative surface The exciting cause can and does produce all the effect which its laws require independently of any electric excitement of a neighboring body Now the result of the experiment with the second wire was that no opposite current was produced There was an instantaneous effect at the closing and breaking of the voltaic circuit electric inductions appeared when the two wires were moved to and from one another but these are phenomena of a different class There was no induced electricity in the sense in which this is predicated of the Leyden jar there was no sustained current running up the one wire while an opposite current ran down the neighboring wire and this alone would have been a true parallel case to the other It thus appears by the combined evidence of the Method of Agreement the Method of Concomitant Variations and the most rigorous form of the Method of Difference that neither of the two kinds of electricity can be excited without an equal excitement of the other and opposite kind that both are effects of the same cause that the possibility of the one is a condition of the possibility of the other and the quantity of the one an impassable limit to the quantity of the other A scientific result of considerable interest in itself and illustrating those three methods in a manner both characteristic and easily intelligible Our third example shall be extracted from Sir John Herschel’s Discourse course on the Study of Natural Philosophy a work replete with happilyselected exemplifications of inductive processes from almost every department of physical science and in which alone of all books which I have met with the four methods of induction are distinctly recognized though not so clearly characterized and defined nor their correlation so fully shown as has appeared to me desirable The present example is described by Sir John Herschel as one of the most beautiful specimens which can be cited of inductive experimental inquiry lying within a moderate compass the theory of dew first promulgated by the late Dr Wells and now universally adopted by scientific authorities The passages in inverted commas are extracted verbatim from the Discourse Suppose dew were the phenomenon proposed whose cause we would know In the first place we must determine precisely what we mean by dew what the fact really is whose cause we desire to investigate We must separate dew from rain and the moisture of fogs and limit the application of the term to what is really meant which is the spontaneous appearance of moisture on substances exposed in the open air when no rain or visible wet is falling This answers to a preliminary operation which will be characterized in the ensuing book treating of operations subsidiary to induction Now here we have analogous phenomena in the moisture which bedews a cold metal or stone when we breathe upon it that which appears on a glass of water fresh from the well in hot weather that which appears on the inside of windows when sudden rain or hail chills the external air that which runs down our walls when after a long frost a warm moist thaw comes on Comparing these cases we find that they all contain the phenomenon which was proposed as the subject of investigation Now all these instances agree in one point the coldness of the object dewed in comparison with the air in contact with it But there still remains the most important case of all that of nocturnal dew does the same circumstance exist in this case Is it a fact that the object dewed is colder than the air Certainly not one would at first be inclined to say for what is to make it so But the experiment is easy we have only to lay a thermometer in contact with the dewed substance and hang one at a little distance above it out of reach of its influence The experiment has been therefore made the question has been asked and the answer has been invariably in the affirmative Whenever an object contracts dew it is colder than the air Here then is a complete application of the Method of Agreement establishing the fact of an invariable connection between the deposition of dew on a surface and the coldness of that surface compared with the external air But which of these is cause and which effect or are they both effects of something else On this subject the Method of Agreement can afford us no light we must call in a more potent method We must collect more facts or which comes to the same thing vary the circumstances since every instance in which the circumstances differ is a fresh fact and especially we must note the contrary or negative cases ie where no dew is produced a comparison between instances of dew and instances of no dew being the condition necessary to bring the Method of Difference into play Now first no dew is produced on the surface of polished metals but it is very copiously on glass both exposed with their faces upward and in some cases the under side of a horizontal plate of glass is also dewed Here is an instance in which the effect is produced and another instance in which it is not produced but we can not yet pronounce as the canon of the Method of Difference requires that the latter instance agrees with the former in all its circumstances except one for the differences between glass and polished metals are manifold and the only thing we can as yet be sure of is that the cause of dew will be found among the circumstances by which the former substance is distinguished from the latter But if we could be sure that glass and the various other substances on which dew is deposited have only one quality in common and that polished metals and the other substances on which dew is not deposited have also nothing in common but the one circumstance of not having the one quality which the others have the requisitions of the Method of Difference would be completely satisfied and we should recognize in that quality of the substances the cause of dew This accordingly is the path of inquiry which is next to be pursued In the cases of polished metal and polished glass the contrast shows evidently that the substance has much to do with the phenomenon therefore let the substance alone be diversified as much as possible by exposing polished surfaces of various kinds This done a scale of intensity becomes obvious Those polished substances are found to be most strongly dewed which conduct heat worst while those which conduct heat well resist dew most effectually The complication increases here is the Method of Concomitant Variations called to our assistance and no other method was practicable on this occasion for the quality of conducting heat could not be excluded since all substances conduct heat in some degree The conclusion obtained is that caeteris paribus the deposition of dew is in some proportion to the power which the body possesses of resisting the passage of heat and that this therefore or something connected with this must be at least one of the causes which assist in producing the deposition of dew on the surface But if we expose rough surfaces instead of polished we sometimes find this law interfered with Thus roughened iron especially if painted over or blackened becomes dewed sooner than varnished paper the kind of surface therefore has a great influence Expose then the same material in very diversified states as to surface that is employ the Method of Difference to ascertain concomitance of variations and another scale of intensity becomes at once apparent those surfaces which part with their heat most readily by radiation are found to contract dew most copiously Here therefore are the requisites for a second employment of the Method of Concomitant Variations which in this case also is the only method available since all substances radiate heat in some degree or other The conclusion obtained by this new application of the method is that caeteris paribus the deposition of dew is also in some proportion to the power of radiating heat and that the quality of doing this abundantly or some cause on which that quality depends is another of the causes which promote the deposition of dew on the substance Again the influence ascertained to exist of substance and surface leads us to consider that of texture and here again we are presented on trial with remarkable differences and with a third scale of intensity pointing out substances of a close firm texture such as stones metals etc as unfavourable but those of a loose one as cloth velvet wool eiderdown cotton etc as eminently favourable to the contraction of dew The Method of Concomitant Variations is here for the third time had recourse to and as before from necessity since the texture of no substance is absolutely firm or absolutely loose Looseness of texture therefore or something which is the cause of that quality is another circumstance which promotes the deposition of dew but this third course resolves itself into the first viz the quality of resisting the passage of heat for substances of loose texture are precisely those which are best adapted for clothing or for impeding the free passage of heat from the skin into the air so as to allow their outer surfaces to be very cold while they remain warm within and this last is therefore an induction from fresh instances simply corroborative of a former induction It thus appears that the instances in which much dew is deposited which are very various agree in this and so far as we are able to observe in this only that they either radiate heat rapidly or conduct it slowly qualities between which there is no other circumstance of agreement than that by virtue of either the body tends to lose heat from the surface more rapidly than it can be restored from within The instances on the contrary in which no dew or but a small quantity of it is formed and which are also extremely various agree as far as we can observe in nothing except in not having this same property We seem therefore to have detected the characteristic difference between the substances on which dew is produced and those on which it is not produced And thus have been realized the requisitions of what we have termed the Indirect Method of Difference or the Joint Method of Agreement and Difference The example afforded of this indirect method and of the manner in which the data are prepared for it by the Methods of Agreement and of Concomitant Variations is the most important of all the illustrations of induction afforded by this interesting speculation We might now consider the question on what the deposition of dew depends to be completely solved if we could be quite sure that the substances on which dew is produced differ from those on which it is not in nothing but in the property of losing heat from the surface faster than the loss can be repaired from within And though we never can have that complete certainty this is not of so much importance as might at first be supposed for we have at all events ascertained that even if there be any other quality hitherto unobserved which is present in all the substances which contract dew and absent in those which do not this other property must be one which in all that great number of substances is present or absent exactly where the property of being a better radiator than conductor is present or absent an extent of coincidence which affords a strong presumption of a community of cause and a consequent invariable coexistence between the two properties so that the property of being a better radiator than conductor if not itself the cause almost certainly always accompanies the cause and for purposes of prediction no error is likely to be committed by treating it as if it were really such Reverting now to an earlier stage of the inquiry let us remember that we had ascertained that in every instance where dew is formed there is actual coldness of the surface below the temperature of the surrounding air but we were not sure whether this coldness was the cause of dew or its effect This doubt we are now able to resolve We have found that in every such instance the substance is one which by its own properties or laws would if exposed in the night become colder than the surrounding air The coldness therefore being accounted for independently of the dew while it is proved that there is a connection between the two it must be the dew which depends on the coldness or, in other words, the coldness is the cause of the dew This law of causation already so amply established admits however of efficient additional corroboration in no less than three ways First by deduction from the known laws of aqueous vapor when diffused through air or any other gas and though we have not yet come to the Deductive Method we will not omit what is necessary to render this speculation complete It is known by direct experiment that only a limited quantity of water can remain suspended in the state of vapor at each degree of temperature and that this maximum grows less and less as the temperature diminishes From this it follows deductively that if there is already as much vapor suspended as the air will contain at its existing temperature any lowering of that temperature will cause a portion of the vapor to be condensed and become water But again we know deductively from the laws of heat that the contact of the air with a body colder than itself will necessarily lower the temperature of the stratum of air immediately applied to its surface and will therefore cause it to part with a portion of its water which accordingly will by the ordinary laws of gravitation or cohesion attach itself to the surface of the body thereby constituting dew This deductive proof it will have been seen has the advantage of at once proving causation as well as coexistence and it has the additional advantage that it also accounts for the exceptions to the occurrence of the phenomenon the cases in which although the body is colder than the air yet no dew is deposited by showing that this will necessarily be the case when the air is so undersupplied with aqueous vapor comparatively to its temperature that even when somewhat cooled by the contact of the colder body it can still continue to hold in suspension all the vapor which was previously suspended in it thus in a very dry summer there are no dews in a very dry winter no hoarfrost Here therefore is an additional condition of the production of dew which the methods we previously made use of failed to detect and which might have remained still undetected if recourse had not been had to the plan of deducing the effect from the ascertained properties of the agents known to be present The second corroboration of the theory is by direct experiment according to the canon of the Method of Difference We can by cooling the surface of any body find in all cases some temperature more or less inferior to that of the surrounding air according to its hygrometric condition at which dew will begin to be deposited Here too therefore the causation is directly proved We can it is true accomplish this only on a small scale but we have ample reason to conclude that the same operation if conducted in nature’s great laboratory would equally produce the effect And finally even on that great scale we are able to verify the result The case is one of those rare cases as we have shown them to be in which nature works the experiment for us in the same manner in which we ourselves perform it introducing into the previous state of things a single and perfectly definite new circumstance and manifesting the effect so rapidly that there is not time for any other material change in the preexisting circumstances It is observed that dew is never copiously deposited in situations much screened from the open sky and not at all in a cloudy night but if the clouds withdraw even for a few minutes and leave a clear opening a deposition of dew presently begins and goes on increasing Dew formed in clear intervals will often even evaporate again when the sky becomes thickly overcast The proof therefore is complete that the presence or absence of an uninterrupted communication with the sky causes the deposition or nondeposition of dew Now since a clear sky is nothing but the absence of clouds and it is a known property of clouds as of all other bodies between which and any given object nothing intervenes but an elastic fluid that they tend to raise or keep up the superficial temperature of the object by radiating heat to it we see at once that the disappearance of clouds will cause the surface to cool so that nature in this case produces a change in the antecedent by definite and known means and the consequent follows accordingly a natural experiment which satisfies the requisitions of the Method of Difference The accumulated proof of which the Theory of Dew has been found susceptible is a striking instance of the fullness of assurance which the inductive evidence of laws of causation may attain in cases in which the invariable sequence is by no means obvious to a superficial view The admirable physiological investigations of Dr BrownSquard afford brilliant examples of the application of the Inductive Methods to a class of inquiries in which for reasons which will presently be given direct induction takes place under peculiar difficulties and disadvantages As one of the most apt instances I select his speculation in the proceedings of the Royal Society for May 16 1861 on the relations between muscular irritability cadaveric rigidity and putrefaction The law which Dr BrownSquard’s investigation tends to establish is the following The greater the degree of muscular irritability at the time of death the later the cadaveric rigidity sets in and the longer it lasts and the later also putrefaction appears and the slower it progresses One would say at first sight that the method here required must be that of Concomitant Variations But this is a delusive appearance arising from the circumstance that the conclusion to be tested is itself a fact of concomitant variations For the establishment of that fact any of the Methods may be put in requisition and it will be found that the fourth Method though really employed has only a subordinate place in this particular investigation The evidences by which Dr BrownSquard establishes the law may be enumerated as follows 1st Paralyzed muscles have greater irritability than healthy muscles Now paralyzed muscles are later in assuming the cadaveric rigidity than healthy muscles the rigidity lasts longer and putrefaction sets in later and proceeds more slowly Both these propositions had to be proved by experiment and for the experiments which prove them science is also indebted to Dr BrownSquard The former of the two that paralyzed muscles have greater irritability than healthy muscles he ascertained in various ways but most decisively by comparing the duration of irritability in a paralyzed muscle and in the corresponding healthy one of the opposite side while they are both submitted to the same excitation He often found in experimenting in that way that the paralyzed muscle remained irritable twice three times or even four times as long as the healthy one This is a case of induction by the Method of Difference The two limbs being those of the same animal were presumed to differ in no circumstance material to the case except the paralysis to the presence and absence of which therefore the difference in the muscular irritability was to be attributed This assumption of complete resemblance in all material circumstances save one evidently could not be safely made in any one pair of experiments because the two legs of any given animal might be accidentally in very different pathological conditions but if besides taking pains to avoid any such difference the experiment was repeated sufficiently often in different animals to exclude the supposition that any abnormal circumstance could be present in them all the conditions of the Method of Difference were adequately secured In the same manner in which Dr BrownSquard proved that paralyzed muscles have greater irritability he also proved the correlative proposition respecting cadaveric rigidity and putrefaction Having by section of the roots of the sciatic nerve and again of a lateral half of the spinal cord produced paralysis in one hind leg of an animal while the other remained healthy he found that not only did muscular irritability last much longer in the paralyzed limb but rigidity set in later and ended later and putrefaction began later and was less rapid than on the healthy side This is a common case of the Method of Difference requiring no comment A further and very important corroboration was obtained by the same method When the animal was killed not shortly after the section of the nerve but a month later the effect was reversed rigidity set in sooner and lasted a shorter time than in the healthy muscles But after this lapse of time the paralyzed muscles having been kept by the paralysis in a state of rest had lost a great part of their irritability and instead of more had become less irritable than those on the healthy side This gives the A B C a b c and B C b c of the Method of Difference One antecedent increased irritability being changed and the other circumstances being the same the consequence did not follow and moreover when a new antecedent contrary to the first was supplied it was followed by a contrary consequent This instance is attended with the special advantage of proving that the retardation and prolongation of the rigidity do not depend directly on the paralysis since that was the same in both the instances but specifically on one effect of the paralysis namely the increased irritability since they ceased when it ceased and were reversed when it was reversed 2d Diminution of the temperature of muscles before death increases their irritability But diminution of their temperature also retards cadaveric rigidity and putrefaction Both these truths were first made known by Dr BrownSquard himself through experiments which conclude according to the Method of Difference There is nothing in the nature of the process requiring specific analysis 3d Muscular exercise prolonged to exhaustion diminishes the muscular irritability This is a wellknown truth dependent on the most general laws of muscular action and proved by experiments under the Method of Difference constantly repeated Now it has been shown by observation that overdriven cattle if killed before recovery from their fatigue become rigid and putrefy in a surprisingly short time A similar fact has been observed in the case of animals hunted to death cocks killed during or shortly after a fight and soldiers slain in the field of battle These various cases agree in no circumstance directly connected with the muscles except that these have just been subjected to exhausting exercise Under the canon therefore of the Method of Agreement it may be inferred that there is a connection between the two facts The Method of Agreement indeed as has been shown is not competent to prove causation The present case however is already known to be a case of causation it being certain that the state of the body after death must somehow depend upon its state at the time of death We are therefore warranted in concluding that the single circumstance in which all the instances agree is the part of the antecedent which is the cause of that particular consequent 4th In proportion as the nutrition of muscles is in a good state their irritability is high This fact also rests on the general evidence of the laws of physiology grounded on many familiar applications of the Method of Difference Now in the case of those who die from accident or violence with their muscles in a good state of nutrition the muscular irritability continues long after death rigidity sets in late and persists long without the putrefactive change On the contrary in cases of disease in which nutrition has been diminished for a long time before death all these effects are reversed These are the conditions of the Joint Method of Agreement and Difference The cases of retarded and long continued rigidity here in question agree only in being preceded by a high state of nutrition of the muscles the cases of rapid and brief rigidity agree only in being preceded by a low state of muscular nutrition a connection is therefore inductively proved between the degree of the nutrition and the slowness and prolongation of the rigidity 5th Convulsions like exhausting exercise but in a still greater degree diminish the muscular irritability Now when death follows violent and prolonged convulsions as in tetanus hydrophobia some cases of cholera and certain poisons rigidity sets in very rapidly and after a very brief duration gives place to putrefaction This is another example of the Method of Agreement of the same character with No 3 6th The series of instances which we shall take last is of a more complex character and requires a more minute analysis It has long been observed that in some cases of death by lightning cadaveric rigidity either does not take place at all or is of such extremely brief duration as to escape notice and that in these cases putrefaction is very rapid In other cases however the usual cadaveric rigidity appears There must be some difference in the cause to account for this difference in the effect Now death by lightning may be the result of 1st a syncope by fright or in consequence of a direct or reflex influence of lightning on the par vagum 2d hemorrhage in or around the brain or in the lungs the pericardium etc 3d concussion or some other alteration in the brain none of which phenomena have any known property capable of accounting for the suppression or almost suppression of the cadaveric rigidity But the cause of death may also be that the lightning produces a violent convulsion of every muscle in the body of which if of sufficient intensity the known effect would be that muscular irritability ceases almost at once If Dr BrownSquard’s generalization is a true law these will be the very cases in which rigidity is so much abridged as to escape notice and the cases in which on the contrary rigidity takes place as usual will be those in which the stroke of lightning operates in some of the other modes which have been enumerated How then is this brought to the test By experiments not on lightning which can not be commanded at pleasure but on the same natural agency in a manageable form that of artificial galvanism Dr BrownSquard galvanized the entire bodies of animals immediately after death Galvanism can not operate in any of the modes in which the stroke of lightning may have operated except the single one of producing muscular convulsions If therefore after the bodies have been galvanized the duration of rigidity is much shortened and putrefaction much accelerated it is reasonable to ascribe the same effects when produced by lightning to the property which galvanism shares with lightning and not to those which it does not Now this Dr BrownSquard found to be the fact The galvanic experiment was tried with charges of very various degrees of strength and the more powerful the charge the shorter was found to be the duration of rigidity and the more speedy and rapid the putrefaction In the experiment in which the charge was strongest and the muscular irritability most promptly destroyed the rigidity only lasted fifteen minutes On the principle therefore of the Method of Concomitant Variations it may be inferred that the duration of the rigidity depends on the degree of the irritability and that if the charge had been as much stronger than Dr BrownSquard’s strongest as a stroke of lightning must be stronger than any electric shock which we can produce artificially the rigidity would have been shortened in a corresponding ratio and might have disappeared altogether This conclusion having been arrived at the case of an electric shock whether natural or artificial becomes an instance in addition to all those already ascertained of correspondence between the irritability of the muscle and the duration of rigidity All these instances are summed up in the following statement That when the degree of muscular irritability at the time of death is considerable either in consequence of a good state of nutrition as in persons who die in full health from an accidental cause or in consequence of rest as in cases of paralysis or on account of the influence of cold cadaveric rigidity in all these cases sets in late and lasts long and putrefaction appears late and progresses slowly but that when the degree of muscular irritability at the time of death is slight either in consequence of a bad state of nutrition or of exhaustion from overexertion or from convulsions caused by disease or poison cadaveric rigidity sets in and ceases soon and putrefaction appears and progresses quickly These facts present in all their completeness the conditions of the Joint Method of Agreement and Difference Early and brief rigidity takes place in cases which agree only in the circumstance of a low state of muscular irritability Rigidity begins late and lasts long in cases which agree only in the contrary circumstance of a muscular irritability high and unusually prolonged It follows that there is a connection through causation between the degree of muscular irritability after death and the tardiness and prolongation of the cadaveric rigidity This investigation places in a strong light the value and efficacy of the Joint Method For as we have already seen the defect of that Method is that like the Method of Agreement of which it is only an improved form it can not prove causation But in the present case as in one of the steps in the argument which led up to it causation is already proved since there could never be any doubt that the rigidity altogether and the putrefaction which follows it are caused by the fact of death the observations and experiments on which this rests are too familiar to need analysis and fall under the Method of Difference It being therefore beyond doubt that the aggregate antecedent the death is the actual cause of the whole train of consequents whatever of the circumstances attending the death can be shown to be followed in all its variations by variations in the effect under investigation must be the particular feature of the fact of death on which that effect depends The degree of muscular irritability at the time of death fulfills this condition The only point that could be brought into question would be whether the effect depended on the irritability itself or on something which always accompanied the irritability and this doubt is set at rest by establishing as the instances do that by whatever cause the high or low irritability is produced the effect equally follows and can not therefore depend upon the causes of irritability nor upon the other effects of those causes which are as various as the causes themselves but upon the irritability solely The last two examples will have conveyed to any one by whom they have been duly followed so clear a conception of the use and practical management of three of the four methods of experimental inquiry as to supersede the necessity of any further exemplification of them The remaining method that of Residues not having found a place in any of the preceding investigations I shall quote from Sir John Herschel some examples of that method with the remarks by which they are introduced It is by this process in fact that science in its present advanced state is chiefly promoted Most of the phenomena which Nature presents are very complicated and when the effects of all known causes are estimated with exactness and subducted the residual facts are constantly appearing in the form of phenomena altogether new and leading to the most important conclusions For example the return of the comet predicted by Professor Eucke a great many times in succession and the general good agreement of its calculated with its observed place during any one of its periods of visibility would lead us to say that its gravitation toward the sun and planets is the sole and sufficient cause of all the phenomena of its orbitual motion but when the effect of this cause is strictly calculated and subducted from the observed motion there is found to remain behind a residual phenomenon which would never have been otherwise ascertained to exist which is a small anticipation of the time of its reappearance or a diminution of its periodic time which can not be accounted for by gravity and whose cause is therefore to be inquired into Such an anticipation would be caused by the resistance of a medium disseminated through the celestial regions and as there are other good reasons for believing this to be a vera causa an actually existing antecedent it has therefore been ascribed to such a resistance M Arago having suspended a magnetic needle by a silk thread and set it in vibration observed that it came much sooner to a state of rest when suspended over a plate of copper than when no such plate was beneath it Now in both cases there were two verae causae antecedents known to exist why it should come at length to rest viz the resistance of the air which opposes and at length destroys all motions performed in it and the want of perfect mobility in the silk thread But the effect of these causes being exactly known by the observation made in the absence of the copper and being thus allowed for and subducted a residual phenomenon appeared in the fact that a retarding influence was exerted by the copper itself and this fact once ascertained speedily led to the knowledge of an entirely new and unexpected class of relations This example belongs however not to the Method of Residues but to the Method of Difference the law being ascertained by a direct comparison of the results of two experiments which differed in nothing but the presence or absence of the plate of copper To have made it exemplify the Method of Residues the effect of the resistance of the air and that of the rigidity of the silk should have been calculated a priori from the laws obtained by separate and foregone experiments Unexpected and peculiarly striking confirmations of inductive laws frequently occur in the form of residual phenomena in the course of investigations of a widely different nature from those which gave rise to the inductions themselves A very elegant example may be cited in the unexpected confirmation of the law of the development of heat in elastic fluids by compression which is afforded by the phenomena of sound The inquiry into the cause of sound had led to conclusions respecting its mode of propagation from which its velocity in the air could be precisely calculated The calculations were performed but when compared with fact though the agreement was quite sufficient to show the general correctness of the cause and mode of propagation assigned yet the whole velocity could not be shown to arise from this theory There was still a residual velocity to be accounted for which placed dynamical philosophers for a long time in great dilemma At length Laplace struck on the happy idea that this might arise from the heat developed in the act of that condensation which necessarily takes place at every vibration by which sound is conveyed The matter was subjected to exact calculation and the result was at once the complete explanation of the residual phenomenon and a striking confirmation of the general law of the development of heat by compression under circumstances beyond artificial imitation Many of the new elements of chemistry have been detected in the investigation of residual phenomena Thus Arfwedson discovered lithia by perceiving an excess of weight in the sulphate produced from a small portion of what he considered as magnesia present in a mineral he had analysed It is on this principle too that the small concentrated residues of great operations in the arts are almost sure to be the lurkingplaces of new chemical ingredients witness iodine brome selenium and the new metals accompanying platina in the experiments of Wollaston and Tennant It was a happy thought of Glauber to examine what every body else threw away Almost all the greatest discoveries in Astronomy says the same author have resulted from the consideration of residual phenomena of a quantitative or numerical kind It was thus that the grand discovery of the precession of the equinoxes resulted as a residual phenomenon from the imperfect explanation of the return of the seasons by the return of the sun to the same apparent place among the fixed stars Thus also aberration and nutation resulted as residual phenomena from that portion of the changes of the apparent places of the fixed stars which was left unaccounted for by precession And thus again the apparent proper motions of the stars are the observed residues of their apparent movements outstanding and unaccounted for by strict calculation of the effects of precession nutation and aberration The nearest approach which human theories can make to perfection is to diminish this residue this caput mortuum of observation as it may be considered as much as practicable and if possible to reduce it to nothing either by showing that something has been neglected in our estimation of known causes or by reasoning upon it as a new fact and on the principle of the inductive philosophy ascending from the effect to its cause or causes The disturbing effects mutually produced by the earth and planets upon each other’s motions were first brought to light as residual phenomena by the difference which appeared between the observed places of those bodies and the places calculated on a consideration solely of their gravitation toward the sun It was this which determined astronomers to consider the law of gravitation as obtaining between all bodies whatever and therefore between all particles of matter their first tendency having been to regard it as a force acting only between each planet or satellite and the central body to whose system it belonged Again the catastrophists in geology be their opinion right or wrong support it on the plea that after the effect of all causes now in operation has been allowed for there remains in the existing constitution of the earth a large residue of facts proving the existence at former periods either of other forces or of the same forces in a much greater degree of intensity To add one more example those who assert what no one has shown any real ground for believing that there is in one human individual one sex or one race of mankind over another an inherent and inexplicable superiority in mental faculties could only substantiate their proposition by subtracting from the differences of intellect which we in fact see all that can be traced by known laws either to the ascertained differences of physical organization or to the differences which have existed in the outward circumstances in which the subjects of the comparison have hitherto been placed What these causes might fail to account for would constitute a residual phenomenon which and which alone would be evidence of an ulterior original distinction and the measure of its amount But the asserters of such supposed differences have not provided themselves with these necessary logical conditions of the establishment of their doctrine The spirit of the Method of Residues being it is hoped sufficiently intelligible from these examples and the other three methods having already been so fully exemplified we may here close our exposition of the four methods considered as employed in the investigation of the simpler and more elementary order of the combinations of phenomena Dr Whewell has expressed a very unfavourable opinion of the utility of the Four Methods as well as of the aptness of the examples by which I have attempted to illustrate them His words are these Upon these methods the obvious thing to remark is that they take for granted the very thing which is most difficult to discover the reduction of the phenomena to formulae such as are here presented to us When we have any set of complex facts offered to us for instance those which were offered in the cases of discovery which I have mentioned the facts of the planetary paths of falling bodies of refracted rays of cosmical motions of chemical analysis and when in any of these cases we would discover the law of nature which governs them or if any one chooses so to term it the feature in which all the cases agree where are we to look for our A B C and a b c Nature does not present to us the cases in this form and how are we to reduce them to this form You say when we find the combination of A B C with a b c and A B D with a b d then we may draw our inference Granted but when and where are we to find such combinations Even now that the discoveries are made who will point out to us what are the A B C and a b c elements of the cases which have just been enumerated Who will tell us which of the methods of inquiry those historically real and successful inquiries exemplify Who will carry these formulae through the history of the sciences as they have really grown up and show us that these four methods have been operative in their formation or that any light is thrown upon the steps of their progress by reference to these formulae He adds that in this work the methods have not been applied to a large body of conspicuous and undoubted examples of discovery extending along the whole history of science which ought to have been done in order that the methods might be shown to possess the advantage which he claims as belonging to his own of being those by which all great discoveries in science have really been made P 277 There is a striking similarity between the objections here made against Canons of Induction and what was alleged in the last century by as able men as Dr Whewell against the acknowledged Canon of Ratiocination Those who protested against the Aristotelian Logic said of the Syllogism what Dr Whewell says of the Inductive Methods that it takes for granted the very thing which is most difficult to discover the reduction of the argument to formulae such as are here presented to us The grand difficulty they said is to obtain your syllogism not to judge of its correctness when obtained On the matter of fact both they and Dr Whewell are right The greatest difficulty in both cases is first that of obtaining the evidence and next of reducing it to the form which tests its conclusiveness But if we try to reduce it without knowing what it is to be reduced to we are not likely to make much progress It is a more difficult thing to solve a geometrical problem than to judge whether a proposed solution is correct but if people were not able to judge of the solution when found they would have little chance of finding it And it can not be pretended that to judge of an induction when found is perfectly easy is a thing for which aids and instruments are superfluous for erroneous inductions false inferences from experience are quite as common on some subjects much commoner than true ones The business of Inductive Logic is to provide rules and models such as the Syllogism and its rules are for ratiocination to which if inductive arguments conform those arguments are conclusive and not otherwise This is what the Four Methods profess to be and what I believe they are universally considered to be by experimental philosophers who had practiced all of them long before any one sought to reduce the practice to theory The assailants of the Syllogism had also anticipated Dr Whewell in the other branch of his argument They said that no discoveries were ever made by syllogism and Dr Whewell says or seems to say that none were ever made by the Four Methods of Induction To the former objectors Archbishop Whately very pertinently answered that their argument if good at all was good against the reasoning process altogether for whatever can not be reduced to syllogism is not reasoning And Dr Whewell’s argument if good at all is good against all inferences from experience In saying that no discoveries were ever made by the Four Methods he affirms that none were ever made by observation and experiment for assuredly if any were it was by processes reducible to one or other of those methods This difference between us accounts for the dissatisfaction which my examples give him for I did not select them with a view to satisfy any one who required to be convinced that observation and experiment are modes of acquiring knowledge I confess that in the choice of them I thought only of illustration and of facilitating the conception of the Methods by concrete instances If it had been my object to justify the processes themselves as means of investigation there would have been no need to look far off or make use of recondite or complicated instances As a specimen of a truth ascertained by the Method of Agreement I might have chosen the proposition Dogs bark This dog and that dog and the other dog answer to A B C A D E A F G The circumstance of being a dog answers to A Barking answers to a As a truth made known by the Method of Difference Fire burns might have sufficed Before I touch the fire I am not burned this is B C I touch it and am burned this is A B C a B C Such familiar experimental processes are not regarded as inductions by Dr Whewell but they are perfectly homogeneous with those by which even on his own showing the pyramid of science is supplied with its base In vain he attempts to escape from this conclusion by laying the most arbitrary restrictions on the choice of examples admissible as instances of Induction they must neither be such as are still matter of discussion p 265 nor must any of them be drawn from mental and social subjects p 269 nor from ordinary observation and practical life pp 241247 They must be taken exclusively from the generalizations by which scientific thinkers have ascended to great and comprehensive laws of natural phenomena Now it is seldom possible in these complicated inquiries to go much beyond the initial steps without calling in the instrument of Deduction and the temporary aid of hypothesis as I myself in common with Dr Whewell have maintained against the purely empirical school Since therefore such cases could not conveniently be selected to illustrate the principles of mere observation and experiment Dr Whewell is misled by their absence into representing the Experimental Methods as serving no purpose in scientific investigation forgetting that if those methods had not supplied the first generalizations there would have been no materials for his own conception of Induction to work upon His challenge however to point out which of the four methods are exemplified in certain important cases of scientific inquiry is easily answered The planetary paths as far as they are a case of induction at all fall under the Method of Agreement The law of falling bodies namely that they describe spaces proportional to the squares of the times was historically a deduction from the first law of motion but the experiments by which it was verified and by which it might have been discovered were examples of the Method of Agreement and the apparent variation from the true law caused by the resistance of the air was cleared up by experiments in vacuo constituting an application of the Method of Difference The law of refracted rays the constancy of the ratio between the sines of incidence and of refraction for each refracting substance was ascertained by direct measurement and therefore by the Method of Agreement The cosmical motions were determined by highly complex processes of thought in which Deduction was predominant but the Methods of Agreement and of Concomitant Variations had a large part in establishing the empirical laws Every case without exception of chemical analysis constitutes a wellmarked example of the Method of Difference To any one acquainted with the subjects to Dr Whewell himself there would not be the smallest difficulty in setting out the A B C and a b c elements of these cases If discoveries are ever made by observation and experiment without Deduction the four methods are methods of discovery but even if they were not methods of discovery it would not be the less true that they are the sole methods of Proof and in that character even the results of deduction are amenable to them The great generalizations which begin as Hypotheses must end by being proved and are in reality as will be shown hereafter proved by the Four Methods Now it is with Proof as such that Logic is principally concerned This distinction has indeed no chance of finding favour with Dr Whewell for it is the peculiarity of his system not to recognize in cases of Induction any necessity for proof If after assuming an hypothesis and carefully collating it with facts nothing is brought to light inconsistent with it that is if experience does not disprove it he is content at least until a simpler hypothesis equally consistent with experience presents itself If this be Induction doubtless there is no necessity for the four methods But to suppose that it is so appears to me a radical misconception of the nature of the evidence of physical truths So real and practical is the need of a test for induction similar to the syllogistic test of ratiocination that inferences which bid defiance to the most elementary notions of inductive logic are put forth without misgiving by persons eminent in physical science as soon as they are off the ground on which they are conversant with the facts and not reduced to judge only by the arguments and as for educated persons in general it may be doubted if they are better judges of a good or a bad induction than they were before Bacon wrote The improvement in the results of thinking has seldom extended to the processes or has reached if any process that of investigation only not that of proof A knowledge of many laws of nature has doubtless been arrived at by framing hypotheses and finding that the facts corresponded to them and many errors have been got rid of by coming to a knowledge of facts which were inconsistent with them but not by discovering that the mode of thought which led to the errors was itself faulty and might have been known to be such independently of the facts which disproved the specific conclusion Hence it is that while the thoughts of mankind have on many subjects worked themselves practically right the thinking power remains as weak as ever and on all subjects on which the facts which would check the result are not accessible as in what relates to the invisible world and even as has been seen lately to the visible world of the planetary regions men of the greatest scientific acquirements argue as pitiably as the merest ignoramus For though they have made many sound inductions they have not learned from them and Dr Whewell thinks there is no necessity that they should learn the principles of inductive evidence In the preceding exposition of the four methods of observation and experiment by which we contrive to distinguish among a mass of coexistent phenomena the particular effect due to a given cause or the particular cause which gave birth to a given effect it has been necessary to suppose in the first instance, for the sake of simplification that this analytical operation is encumbered by no other difficulties than what are essentially inherent in its nature and to represent to ourselves therefore every effect on the one hand as connected exclusively with a single cause and on the other hand as incapable of being mixed and confounded with any other coexistent effect We have regarded a b c d e the aggregate of the phenomena existing at any moment as consisting of dissimilar facts a b c d and e for each of which one and only one cause needs be sought the difficulty being only that of singling out this one cause from the multitude of antecedent circumstances A B C D and E The cause indeed may not be simple it may consist of an assemblage of conditions but we have supposed that there was only one possible assemblage of conditions from which the given effect could result If such were the fact it would be comparatively an easy task to investigate the laws of nature But the supposition does not hold in either of its parts In the first place it is not true that the same phenomenon is always produced by the same cause the effect a may sometimes arise from A sometimes from B And secondly the effects of different causes are often not dissimilar but homogeneous and marked out by no assignable boundaries from one another A and B may produce not a and b but different portions of an effect a The obscurity and difficulty of the investigation of the laws of phenomena is singularly increased by the necessity of adverting to these two circumstances Intermixture of Effects and Plurality of Causes To the latter being the simpler of the two considerations we shall first direct our attention It is not true then that one effect must be connected with only one cause or assemblage of conditions that each phenomenon can be produced only in one way There are often several independent modes in which the same phenomenon could have originated One fact may be the consequent in several invariable sequences it may follow with equal uniformity any one of several antecedents or collections of antecedents Many causes may produce mechanical motion many causes may produce some kinds of sensation many causes may produce death A given effect may really be produced by a certain cause and yet be perfectly capable of being produced without it One of the principal consequences of this fact of Plurality of Causes is to render the first of the inductive methods that of Agreement uncertain To illustrate that method we supposed two instances A B C followed by a b c and A D E followed by a d e From these instances it might apparently be concluded that A is an invariable antecedent of a and even that it is the unconditional invariable antecedent or cause if we could be sure that there is no other antecedent common to the two cases That this difficulty may not stand in the way let us suppose the two cases positively ascertained to have no antecedent in common except A The moment however that we let in the possibility of a plurality of causes the conclusion fails For it involves a tacit supposition that a must have been produced in both instances by the same cause If there can possibly have been two causes those two may for example be C and E the one may have been the cause of a in the former of the instances the other in the latter A having no influence in either case Suppose for example that two great artists or great philosophers that two extremely selfish or extremely generous characters were compared together as to the circumstances of their education and history and the two cases were found to agree only in one circumstance would it follow that this one circumstance was the cause of the quality which characterized both those individuals Not at all for the causes which may produce any type of character are very numerous and the two persons might equally have agreed in their character though there had been no manner of resemblance in their previous history This therefore is a characteristic imperfection of the Method of Agreement from which imperfection the Method of Difference is free For if we have two instances A B C and B C of which B C gives b c and A being added converts it into a b c it is certain that in this instance at least A was either the cause of a or an indispensable portion of its cause even though the cause which produces it in other instances may be altogether different Plurality of Causes therefore not only does not diminish the reliance due to the Method of Difference but does not even render a greater number of observations or experiments necessary two instances the one positive and the other negative are still sufficient for the most complete and rigorous induction Not so however with the Method of Agreement The conclusions which that yields when the number of instances compared is small are of no real value except as in the character of suggestions they may lead either to experiments bringing them to the test of the Method of Difference or to reasonings which may explain and verify them deductively It is only when the instances being indefinitely multiplied and varied continue to suggest the same result that this result acquires any high degree of independent value If there are but two instances A B C and A D E though these instances have no antecedent in common except A yet as the effect may possibly have been produced in the two cases by different causes the result is at most only a slight probability in favour of A there may be causation but it is almost equally probable that there was only a coincidence But the oftener we repeat the observation varying the circumstances the more we advance toward a solution of this doubt For if we try A F G A H K etc all unlike one another except in containing the circumstance A and if we find the effect a entering into the result in all these cases we must suppose one of two things either that it is caused by A or that it has as many different causes as there are instances With each addition therefore to the number of instances the presumption is strengthened in favour of A The inquirer of course will not neglect if an opportunity present itself to exclude A from some one of these combinations from A H K for instance and by trying H K separately appeal to the Method of Difference in aid of the Method of Agreement By the Method of Difference alone can it be ascertained that A is the cause of a but that it is either the cause or another effect of the same cause may be placed beyond any reasonable doubt by the Method of Agreement provided the instances are very numerous as well as sufficiently various After how great a multiplication then of varied instances all agreeing in no other antecedent except A is the supposition of a plurality of causes sufficiently rebutted and the conclusion that a is connected with A divested of the characteristic imperfection and reduced to a virtual certainty This is a question which we can not be exempted from answering but the consideration of it belongs to what is called the Theory of Probability which will form the subject of a chapter hereafter It is seen however at once that the conclusion does amount to a practical certainty after a sufficient number of instances and that the method therefore is not radically vitiated by the characteristic imperfection The result of these considerations is only in the first place to point out a new source of inferiority in the Method of Agreement as compared with other modes of investigation and new reasons for never resting contented with the results obtained by it without attempting to confirm them either by the Method of Difference or by connecting them deductively with some law or laws already ascertained by that superior method And in the second place we learn from this the true theory of the value of mere number of instances in inductive inquiry The Plurality of Causes is the only reason why mere number is of any importance The tendency of unscientific inquirers is to rely too much on number without analyzing the instances without looking closely enough into their nature to ascertain what circumstances are or are not eliminated by means of them Most people hold their conclusions with a degree of assurance proportioned to the mere mass of the experience on which they appear to rest not considering that by the addition of instances to instances all of the same kind that is differing from one another only in points already recognized as immaterial nothing whatever is added to the evidence of the conclusion A single instance eliminating some antecedent which existed in all the other cases is of more value than the greatest multitude of instances which are reckoned by their number alone It is necessary no doubt to assure ourselves by repetition of the observation or experiment that no error has been committed concerning the individual facts observed and until we have assured ourselves of this instead of varying the circumstances we can not too scrupulously repeat the same experiment or observation without any change But when once this assurance has been obtained the multiplication of instances which do not exclude any more circumstances is entirely useless provided there have been already enough to exclude the supposition of Plurality of Causes It is of importance to remark that the peculiar modification of the Method of Agreement which as partaking in some degree of the nature of the Method of Difference I have called the Joint Method of Agreement and Difference is not affected by the characteristic imperfection now pointed out For in the joint method it is supposed not only that the instances in which a is agree only in containing A but also that the instances in which a is not agree only in not containing A Now if this be so A must be not only the cause of a but the only possible cause for if there were another as for example B then in the instances in which a is not B must have been absent as well as A and it would not be true that these instances agree only in not containing A This therefore constitutes an immense advantage of the joint method over the simple Method of Agreement It may seem indeed that the advantage does not belong so much to the joint method as to one of its two premises if they may be so called the negative premise The Method of Agreement when applied to negative instances or those in which a phenomenon does not take place is certainly free from the characteristic imperfection which affects it in the affirmative case The negative premise it might therefore be supposed could be worked as a simple case of the Method of Agreement without requiring an affirmative premise to be joined with it But though this is true in principle it is generally altogether impossible to work the Method of Agreement by negative instances without positive ones it is so much more difficult to exhaust the field of negation than that of affirmation For instance let the question be what is the cause of the transparency of bodies with what prospect of success could we set ourselves to inquire directly in what the multifarious substances which are not transparent agree But we might hope much sooner to seize some point of resemblance among the comparatively few and definite species of objects which are transparent and this being attained we should quite naturally be put upon examining whether the absence of this one circumstance be not precisely the point in which all opaque substances will be found to resemble The Joint Method of Agreement and Difference therefore or as I have otherwise called it the Indirect Method of Difference because like the Method of Difference properly socalled it proceeds by ascertaining how and in what the cases where the phenomenon is present differ from those in which it is absent is after the Direct Method of Difference the most powerful of the remaining instruments of inductive investigation and in the sciences which depend on pure observation with little or no aid from experiment this method so well exemplified in the speculation on the cause of dew is the primary resource so far as direct appeals to experience are concerned We have thus far treated Plurality of Causes only as a possible supposition which until removed renders our inductions uncertain and have only considered by what means where the plurality does not really exist we may be enabled to disprove it But we must also consider it as a case actually occurring in nature and which as often as it does occur our methods of induction ought to be capable of ascertaining and establishing For this however there is required no peculiar method When an effect is really producible by two or more causes the process for detecting them is in no way different from that by which we discover single causes They may first be discovered as separate sequences by separate sets of instances One set of observations or experiments shows that the sun is a cause of heat another that friction is a source of it another that percussion another that electricity another that chemical action is such a source Or secondly the plurality may come to light in the course of collating a number of instances when we attempt to find some circumstance in which they all agree and fail in doing so We find it impossible to trace in all the cases in which the effect is met with any common circumstance We find that we can eliminate all the antecedents that no one of them is present in all the instances no one of them indispensable to the effect On closer scrutiny however it appears that though no one is always present one or other of several always is If on further analysis we can detect in these any common element we may be able to ascend from them to some one cause which is the really operative circumstance in them all Thus it is now thought that in the production of heat by friction percussion chemical action etc the ultimate source is one and the same. But if as continually happens we can not take this ulterior step the different antecedents must be set down provisionally as distinct causes each sufficient of itself to produce the effect We here close our remarks on the Plurality of Causes and proceed to the still more peculiar and more complex case of the Intermixture of Effects and the interference of causes with one another a case constituting the principal part of the complication and difficulty of the study of nature and with which the four only possible methods of directly inductive investigation by observation and experiment are for the most part as will appear presently quite unequal to cope The instrument of Deduction alone is adequate to unravel the complexities proceeding from this source and the four methods have little more in their power than to supply premises for and a verification of our deductions A concurrence of two or more causes not separately producing each its own effect but interfering with or modifying the effects of one another takes place as has already been explained in two different ways In the one which is exemplified by the joint operation of different forces in mechanics the separate effects of all the causes continue to be produced but are compounded with one another and disappear in one total In the other illustrated by the case of chemical action the separate effects cease entirely and are succeeded by phenomena altogether different and governed by different laws Of these cases the former is by far the more frequent and this case it is which for the most part eludes the grasp of our experimental methods The other and exceptional case is essentially amenable to them When the laws of the original agents cease entirely and a phenomenon makes its appearance which with reference to those laws is quite heterogeneous when for example two gaseous substances hydrogen and oxygen on being brought together throw off their peculiar properties and produce the substance called water in such cases the new fact may be subjected to experimental inquiry like any other phenomenon and the elements which are said to compose it may be considered as the mere agents of its production the conditions on which it depends the facts which make up its cause The effects of the new phenomenon the properties of water for instance are as easily found by experiment as the effects of any other cause But to discover the cause of it that is the particular conjunction of agents from which it results is often difficult enough In the first place the origin and actual production of the phenomenon are most frequently inaccessible to our observation If we could not have learned the composition of water until we found instances in which it was actually produced from oxygen and hydrogen we should have been forced to wait until the casual thought struck some one of passing an electric spark through a mixture of the two gases or inserting a lighted taper into it merely to try what would happen Besides many substances though they can be analysed can not by any known artificial means be recompounded Further even if we could have ascertained by the Method of Agreement that oxygen and hydrogen were both present when water is produced no experimentation on oxygen and hydrogen separately no knowledge of their laws could have enabled us deductively to infer that they would produce water We require a specific experiment on the two combined Under these difficulties we should generally have been indebted for our knowledge of the causes of this class of effects not to any inquiry directed specifically toward that end but either to accident or to the gradual progress of experimentation on the different combinations of which the producing agents are susceptible if it were not for a peculiarity belonging to effects of this description that they often under some particular combination of circumstances reproduce their causes If water results from the juxtaposition of hydrogen and oxygen whenever this can be made sufficiently close and intimate so on the other hand if water itself be placed in certain situations hydrogen and oxygen are reproduced from it an abrupt termination is put to the new laws and the agents reappear separately with their own properties as at first What is called chemical analysis is the process of searching for the causes of a phenomenon among its effects or rather among the effects produced by the action of some other causes upon it Lavoisier by heating mercury to a high temperature in a close vessel containing air found that the mercury increased in weight and became what was then called red precipitate while the air on being examined after the experiment proved to have lost weight and to have become incapable of supporting life or combustion When red precipitate was exposed to a still greater heat it became mercury again and gave off a gas which did support life and flame Thus the agents which by their combination produced red precipitate namely the mercury and the gas reappear as effects resulting from that precipitate when acted upon by heat So if we decompose water by means of iron filings we produce two effects rust and hydrogen Now rust is already known by experiments upon the component substances to be an effect of the union of iron and oxygen the iron we ourselves supplied but the oxygen must have been produced from the water The result therefore is that water has disappeared and hydrogen and oxygen have appeared in its stead or, in other words, the original laws of these gaseous agents which had been suspended by the superinduction of the new laws called the properties of water have again started into existence and the causes of water are found among its effects Where two phenomena between the laws or properties of which considered in themselves no connection can be traced are thus reciprocally cause and effect each capable in its turn of being produced from the other and each when it produces the other ceasing itself to exist as water is produced from oxygen and hydrogen and oxygen and hydrogen are reproduced from water this causation of the two phenomena by one another each being generated by the other’s destruction is properly transformation The idea of chemical composition is an idea of transformation but of a transformation which is incomplete since we consider the oxygen and hydrogen to be present in the water as oxygen and hydrogen and capable of being discovered in it if our senses were sufficiently keen a supposition for it is no more grounded solely on the fact that the weight of the water is the sum of the separate weights of the two ingredients If there had not been this exception to the entire disappearance in the compound of the laws of the separate ingredients if the combined agents had not in this one particular of weight preserved their own laws and produced a joint result equal to the sum of their separate results we should never probably have had the notion now implied by the words chemical composition and in the facts of water produced from hydrogen and oxygen and hydrogen and oxygen produced from water as the transformation would have been complete we should have seen only a transformation In these cases where the heteropathic effect as we called it in a former chapter is but a transformation of its cause or in other words, where the effect and its cause are reciprocally such and mutually convertible into each other the problem of finding the cause resolves itself into the far easier one of finding an effect which is the kind of inquiry that admits of being prosecuted by direct experiment But there are other cases of heteropathic effects to which this mode of investigation is not applicable Take for instance the heteropathic laws of mind that portion of the phenomena of our mental nature which are analogous to chemical rather than to dynamical phenomena as when a complex passion is formed by the coalition of several elementary impulses or a complex emotion by several simple pleasures or pains of which it is the result without being the aggregate or in any respect homogeneous with them The product in these cases is generated by its various factors but the factors can not be reproduced from the product just as a youth can grow into an old man but an old man can not grow into a youth We can not ascertain from what simple feelings any of our complex states of mind are generated as we ascertain the ingredients of a chemical compound by making it in its turn generate them We can only therefore discover these laws by the slow process of studying the simple feelings themselves and ascertaining synthetically by experimenting on the various combinations of which they are susceptible what they by their mutual action upon one another are capable of generating It might have been supposed that the other and apparently simpler variety of the mutual interference of causes where each cause continues to produce its own proper effect according to the same laws to which it conforms in its separate state would have presented fewer difficulties to the inductive inquirer than that of which we have just finished the consideration It presents however so far as direct induction apart from deduction is concerned infinitely greater difficulties When a concurrence of causes gives rise to a new effect bearing no relation to the separate effects of those causes the resulting phenomenon stands forth undisguised inviting attention to its peculiarity and presenting no obstacle to our recognizing its presence or absence among any number of surrounding phenomena It admits therefore of being easily brought under the canons of Induction provided instances can be obtained such as those canons require and the nonoccurrence of such instances or the want of means to produce them artificially is the real and only difficulty in such investigations a difficulty not logical but in some sort physical It is otherwise with cases of what in a preceding chapter has been denominated the Composition of Causes There the effects of the separate causes do not terminate and give place to others thereby ceasing to form any part of the phenomenon to be investigated on the contrary they still take place but are intermingled with and disguised by the homogeneous and closely allied effects of other causes They are no longer a b c d e existing side by side and continuing to be separately discernible they are a a b b 2b etc some of which cancel one another while many others do not appear distinguishably but merge in one sum forming altogether a result between which and the causes whereby it was produced there is often an insurmountable difficulty in tracing by observation any fixed relation whatever The general idea of the Composition of Causes has been seen to be that though two or more laws interfere with one another and apparently frustrate or modify one another’s operation yet in reality all are fulfilled the collective effect being the exact sum of the effects of the causes taken separately A familiar instance is that of a body kept in equilibrium by two equal and contrary forces One of the forces if acting alone would carry the body in a given time a certain distance to the west the other if acting alone would carry it exactly as far toward the east and the result is the same as if it had been first carried to the west as far as the one force would carry it and then back toward the east as far as the other would carry it that is precisely the same distance being ultimately left where it was found at first All laws of causation are liable to be in this manner counteracted and seemingly frustrated by coming into conflict with other laws the separate result of which is opposite to theirs or more or less inconsistent with it And hence with almost every law many instances in which it really is entirely fulfilled do not at first sight appear to be cases of its operation at all It is so in the example just adduced a force in mechanics means neither more nor less than a cause of motion yet the sum of the effects of two causes of motion may be rest Again a body solicited by two forces in directions making an angle with one another moves in the diagonal and it seems a paradox to say that motion in the diagonal is the sum of two motions in two other lines Motion however is but change of place and at every instant the body is in the exact place it would have been in if the forces had acted during alternate instants instead of acting in the same instant saving that if we suppose two forces to act successively which are in truth simultaneous we must of course allow them double the time It is evident therefore that each force has had during each instant all the effect which belonged to it and that the modifying influence which one of two concurrent causes is said to exercise with respect to the other may be considered as exerted not over the action of the cause itself but over the effect after it is completed For all purposes of predicting calculating or explaining their joint result causes which compound their effects may be treated as if they produced simultaneously each of them its own effect and all these effects coexisted visibly Since the laws of causes are as really fulfilled when the causes are said to be counteracted by opposing causes as when they are left to their own undisturbed action we must be cautious not to express the laws in such terms as would render the assertion of their being fulfilled in those cases a contradiction If for instance it were stated as a law of nature that a body to which a force is applied moves in the direction of the force with a velocity proportioned to the force directly and to its own mass inversely when in point of fact some bodies to which a force is applied do not move at all and those which do move at least in the region of our earth are from the very first retarded by the action of gravity and other resisting forces and at last stopped altogether it is clear that the general proposition though it would be true under a certain hypothesis would not express the facts as they actually occur To accommodate the expression of the law to the real phenomena we must say not that the object moves but that it tends to move in the direction and with the velocity specified We might indeed guard our expression in a different mode by saying that the body moves in that manner unless prevented or except in so far as prevented by some counteracting cause But the body does not only move in that manner unless counteracted it tends to move in that manner even when counteracted it still exerts in the original direction the same energy of movement as if its first impulse had been undisturbed and produces by that energy an exactly equivalent quantity of effect This is true even when the force leaves the body as it found it in a state of absolute rest as when we attempt to raise a body of three tons’ weight with a force equal to one ton For if while we are applying this force wind or water or any other agent supplies an additional force just exceeding two tons the body will be raised thus proving that the force we applied exerted its full effect by neutralizing an equivalent portion of the weight which it was insufficient altogether to overcome And if while we are exerting this force of one ton upon the object in a direction contrary to that of gravity it be put into a scale and weighed it will be found to have lost a ton of its weight or, in other words, to press downward with a force only equal to the difference of the two forces These facts are correctly indicated by the expression tendency All laws of causation in consequence of their liability to be counteracted require to be stated in words affirmative of tendencies only and not of actual results In those sciences of causation which have an accurate nomenclature there are special words which signify a tendency to the particular effect with which the science is conversant thus pressure in mechanics is synonymous with tendency to motion and forces are not reasoned on as causing actual motion but as exerting pressure A similar improvement in terminology would be very salutary in many other branches of science The habit of neglecting this necessary element in the precise expression of the laws of nature has given birth to the popular prejudice that all general truths have exceptions and much unmerited distrust has thence accrued to the conclusions of science when they have been submitted to the judgment of minds insufficiently disciplined and cultivated The rough generalizations suggested by common observation usually have exceptions but principles of science or, in other words, laws of causation have not What is thought to be an exception to a principle to quote words used on a different occasion is always some other and distinct principle cutting into the former some other force which impinges against the first force and deflects it from its direction There are not a law and an exception to that law the law acting in ninetynine cases and the exception in one There are two laws each possibly acting in the whole hundred cases and bringing about a common effect by their conjunct operation If the force which being the less conspicuous of the two is called the disturbing force prevails sufficiently over the other force in some one case to constitute that case what is commonly called an exception the same disturbing force probably acts as a modifying cause in many other cases which no one will call exceptions Thus if it were stated to be a law of nature that all heavy bodies fall to the ground it would probably be said that the resistance of the atmosphere which prevents a balloon from falling constitutes the balloon an exception to that pretended law of nature But the real law is that all heavy bodies tend to fall and to this there is no exception not even the sun and moon for even they as every astronomer knows tend toward the earth with a force exactly equal to that with which the earth tends toward them The resistance of the atmosphere might in the particular case of the balloon from a misapprehension of what the law of gravitation is be said to prevail over the law but its disturbing effect is quite as real in every other case since though it does not prevent it retards the fall of all bodies whatever The rule and the socalled exception do not divide the cases between them each of them is a comprehensive rule extending to all cases To call one of these concurrent principles an exception to the other is superficial and contrary to the correct principles of nomenclature and arrangement An effect of precisely the same kind and arising from the same cause ought not to be placed in two different categories merely as there does or does not exist another cause preponderating over it We have now to consider according to what method these complex effects compounded of the effects of many causes are to be studied how we are enabled to trace each effect to the concurrence of causes in which it originated and ascertain the conditions of its recurrence the circumstances in which it may be expected again to occur The conditions of a phenomenon which arises from a composition of causes may be investigated either deductively or experimentally The case it is evident is naturally susceptible of the deductive mode of investigation The law of an effect of this description is a result of the laws of the separate causes on the combination of which it depends and is therefore in itself capable of being deduced from these laws This is called the method a priori The other or a posteriori method professes to proceed according to the canons of experimental inquiry Considering the whole assemblage of concurrent causes which produced the phenomenon as one single cause it attempts to ascertain the cause in the ordinary manner by a comparison of instances This second method subdivides itself into two different varieties If it merely collates instances of the effect it is a method of pure observation If it operates upon the causes and tries different combinations of them in hopes of ultimately hitting the precise combination which will produce the given total effect it is a method of experiment In order more completely to clear up the nature of each of these three methods and determine which of them deserves the preference it will be expedient conformably to a favourite maxim of Lord Chancellor Eldon to which though it has often incurred philosophical ridicule a deeper philosophy will not refuse its sanction to clothe them in circumstances We shall select for this purpose a case which as yet furnishes no very brilliant example of the success of any of the three methods but which is all the more suited to illustrate the difficulties inherent in them Let the subject of inquiry be the conditions of health and disease in the human body or for greater simplicity the conditions of recovery from a given disease and in order to narrow the question still more let it be limited in the first instance, to this one inquiry Is or is not some particular medicament mercury for instance a remedy for the given disease Now the deductive method would set out from known properties of mercury and known laws of the human body and by reasoning from these would attempt to discover whether mercury will act upon the body when in the morbid condition supposed in such a manner as would tend to restore health The experimental method would simply administer mercury in as many cases as possible noting the age sex temperament and other peculiarities of bodily constitution the particular form or variety of the disease the particular stage of its progress etc remarking in which of these cases it was attended with a salutary effect and with what circumstances it was on those occasions combined The method of simple observation would compare instances of recovery to find whether they agreed in having been preceded by the administration of mercury or would compare instances of recovery with instances of failure to find cases which agreeing in all other respects differed only in the fact that mercury had been administered or that it had not That the last of these three modes of investigation is applicable to the case no one has ever seriously contended No conclusions of value on a subject of such intricacy ever were obtained in that way The utmost that could result would be a vague general impression for or against the efficacy of mercury of no avail for guidance unless confirmed by one of the other two methods Not that the results which this method strives to obtain would not be of the utmost possible value if they could be obtained If all the cases of recovery which presented themselves in an examination extending to a great number of instances were cases in which mercury had been administered we might generalize with confidence from this experience and should have obtained a conclusion of real value But no such basis for generalization can we in a case of this description hope to obtain The reason is that which we have spoken of as constituting the characteristic imperfection of the Method of Agreement Plurality of Causes Supposing even that mercury does tend to cure the disease so many other causes both natural and artificial also tend to cure it that there are sure to be abundant instances of recovery in which mercury has not been administered unless indeed the practice be to administer it in all cases on which supposition it will equally be found in the cases of failure When an effect results from the union of many causes the share which each has in the determination of the effect can not in general be great and the effect is not likely even in its presence or absence still less in its variations to follow even approximately any one of the causes Recovery from a disease is an event to which in every case many influences must concur Mercury may be one such influence but from the very fact that there are many other such it will necessarily happen that although mercury is administered the patient for want of other concurring influences will often not recover and that he often will recover when it is not administered the other favourable influences being sufficiently powerful without it Neither therefore will the instances of recovery agree in the administration of mercury nor will the instances of failure agree in its nonadministration It is much if by multiplied and accurate returns from hospitals and the like we can collect that there are rather more recoveries and rather fewer failures when mercury is administered than when it is not a result of very secondary value even as a guide to practice and almost worthless as a contribution to the theory of the subject The inapplicability of the method of simple observation to ascertain the conditions of effects dependent on many concurring causes being thus recognized we shall next inquire whether any greater benefit can be expected from the other branch of the a posteriori method that which proceeds by directly trying different combinations of causes either artificially produced or found in nature and taking notice what is their effect as for example by actually trying the effect of mercury in as many different circumstances as possible This method differs from the one which we have just examined in turning our attention directly to the causes or agents instead of turning it to the effect recovery from the disease And since as a general rule the effects of causes are far more accessible to our study than the causes of effects it is natural to think that this method has a much better chance of proving successful than the former The method now under consideration is called the Empirical Method and in order to estimate it fairly we must suppose it to be completely not incompletely empirical We must exclude from it every thing which partakes of the nature not of an experimental but of a deductive operation If for instance we try experiments with mercury upon a person in health in order to ascertain the general laws of its action upon the human body and then reason from these laws to determine how it will act upon persons affected with a particular disease this may be a really effectual method but this is deduction The experimental method does not derive the law of a complex case from the simpler laws which conspire to produce it but makes its experiments directly upon the complex case We must make entire abstraction of all knowledge of the simpler tendencies the modi operandi of mercury in detail Our experimentation must aim at obtaining a direct answer to the specific question Does or does not mercury tend to cure the particular disease Let us see therefore how far the case admits of the observance of those rules of experimentation which it is found necessary to observe in other cases When we devise an experiment to ascertain the effect of a given agent there are certain precautions which we never if we can help it omit In the first place we introduce the agent into the midst of a set of circumstances which we have exactly ascertained It needs hardly be remarked how far this condition is from being realized in any case connected with the phenomena of life how far we are from knowing what are all the circumstances which preexist in any instance in which mercury is administered to a living being This difficulty however though insuperable in most cases may not be so in all there are sometimes concurrences of many causes in which we yet know accurately what the causes are Moreover the difficulty may be attenuated by sufficient multiplication of experiments in circumstances rendering it improbable that any of the unknown causes should exist in them all But when we have got clear of this obstacle we encounter another still more serious In other cases when we intend to try an experiment we do not reckon it enough that there be no circumstance in the case the presence of which is unknown to us We require also that none of the circumstances which we do know shall have effects susceptible of being confounded with those of the agents whose properties we wish to study We take the utmost pains to exclude all causes capable of composition with the given cause or if forced to let in any such causes we take care to make them such that we can compute and allow for their influence so that the effect of the given cause may after the subduction of those other effects be apparent as a residual phenomenon These precautions are inapplicable to such cases as we are now considering The mercury of our experiment being tried with an unknown multitude or even let it be a known multitude of other influencing circumstances the mere fact of their being influencing circumstances implies that they disguise the effect of the mercury and preclude us from knowing whether it has any effect or not Unless we already knew what and how much is owing to every other circumstance that is unless we suppose the very problem solved which we are considering the means of solving we can not tell that those other circumstances may not have produced the whole of the effect independently or even in spite of the mercury The Method of Difference in the ordinary mode of its use namely by comparing the state of things following the experiment with the state which preceded it is thus in the case of intermixture of effects entirely unavailing because other causes than that whose effect we are seeking to determine have been operating during the transition As for the other mode of employing the Method of Difference namely by comparing not the same case at two different periods but different cases this in the present instance is quite chimerical In phenomena so complicated it is questionable if two cases similar in all respects but one ever occurred and were they to occur we could not possibly know that they were so exactly similar Any thing like a scientific use of the method of experiment in these complicated cases is therefore out of the question We can generally even in the most favourable cases only discover by a succession of trials that a certain cause is very often followed by a certain effect For in one of these conjunct effects the portion which is determined by any one of the influencing agents is usually as we before remarked but small and it must be a more potent cause than most if even the tendency which it really exerts is not thwarted by other tendencies in nearly as many cases as it is fulfilled Some causes indeed there are which are more potent than any counteracting causes to which they are commonly exposed and accordingly there are some truths in medicine which are sufficiently proved by direct experiment Of these the most familiar are those that relate to the efficacy of the substances known as Specifics for particular diseases quinine colchicum limejuice codliver oil and a few others Even these are not invariably followed by success but they succeed in so large a proportion of cases and against such powerful obstacles that their tendency to restore health in the disorders for which they are prescribed may be regarded as an experimental truth If so little can be done by the experimental method to determine the conditions of an effect of many combined causes in the case of medical science still less is this method applicable to a class of phenomena more complicated than even those of physiology the phenomena of politics and history There Plurality of Causes exists in almost boundless excess and effects are for the most part inextricably interwoven with one another To add to the embarrassment most of the inquiries in political science relate to the production of effects of a most comprehensive description such as the public wealth public security public morality and the like results liable to be affected directly or indirectly either in plus or in minus by nearly every fact which exists or event which occurs in human society The vulgar notion that the safe methods on political subjects are those of Baconian induction that the true guide is not general reasoning but specific experience will one day be quoted as among the most unequivocal marks of a low state of the speculative faculties in any age in which it is accredited Nothing can be more ludicrous than the sort of parodies on experimental reasoning which one is accustomed to meet with not in popular discussion only but in grave treatises when the affairs of nations are the theme How it is asked can an institution be bad when the country has prospered under it How can such or such causes have contributed to the prosperity of one country when another has prospered without them Whoever makes use of an argument of this kind not intending to deceive should be sent back to learn the elements of some one of the more easy physical sciences Such reasoners ignore the fact of Plurality of Causes in the very case which affords the most signal example of it So little could be concluded in such a case from any possible collation of individual instances that even the impossibility in social phenomena of making artificial experiments a circumstance otherwise so prejudicial to directly inductive inquiry hardly affords in this case additional reason of regret For even if we could try experiments upon a nation or upon the human race with as little scruple as M Magendie tried them on dogs and rabbits we should never succeed in making two instances identical in every respect except the presence or absence of some one definite circumstance The nearest approach to an experiment in the philosophical sense which takes place in politics is the introduction of a new operative element into national affairs by some special and assignable measure of government such as the enactment or repeal of a particular law But where there are so many influences at work it requires some time for the influence of any new cause upon national phenomena to become apparent and as the causes operating in so extensive a sphere are not only infinitely numerous but in a state of perpetual alteration it is always certain that before the effect of the new cause becomes conspicuous enough to be a subject of induction so many of the other influencing circumstances will have changed as to vitiate the experiment Two therefore of the three possible methods for the study of phenomena resulting from the composition of many causes being from the very nature of the case inefficient and illusory there remains only the third that which considers the causes separately and infers the effect from the balance of the different tendencies which produce it in short the deductive or a priori method The more particular consideration of this intellectual process requires a chapter to itself The mode of investigation which from the proved inapplicability of direct methods of observation and experiment remains to us as the main source of the knowledge we possess or can acquire respecting the conditions and laws of recurrence of the more complex phenomena is called in its most general expression the Deductive Method and consists of three operations the first one of direct induction the second of ratiocination the third of verification I call the first step in the process an inductive operation because there must be a direct induction as the basis of the whole though in many particular investigations the place of the induction may be supplied by a prior deduction but the premises of this prior deduction must have been derived from induction The problem of the Deductive Method is to find the law of an effect from the laws of the different tendencies of which it is the joint result The first requisite therefore is to know the laws of those tendencies the law of each of the concurrent causes and this supposes a previous process of observation or experiment upon each cause separately or else a previous deduction which also must depend for its ultimate premises on observation or experiment Thus if the subject be social or historical phenomena the premises of the Deductive Method must be the laws of the causes which determine that class of phenomena and those causes are human actions together with the general outward circumstances under the influence of which mankind are placed and which constitute man’s position on the earth The Deductive Method applied to social phenomena must begin therefore by investigating or must suppose to have been already investigated the laws of human action and those properties of outward things by which the actions of human beings in society are determined Some of these general truths will naturally be obtained by observation and experiment others by deduction the more complex laws of human action for example may be deduced from the simpler ones but the simple or elementary laws will always and necessarily have been obtained by a directly inductive process To ascertain then the laws of each separate cause which takes a share in producing the effect is the first desideratum of the Deductive Method To know what the causes are which must be subjected to this process of study may or may not be difficult In the case last mentioned this first condition is of easy fulfilment That social phenomena depend on the acts and mental impressions of human beings never could have been a matter of any doubt however imperfectly it may have been known either by what laws those impressions and actions are governed or to what social consequences their laws naturally lead Neither again after physical science had attained a certain development could there be any real doubt where to look for the laws on which the phenomena of life depend since they must be the mechanical and chemical laws of the solid and fluid substances composing the organized body and the medium in which it subsists together with the peculiar vital laws of the different tissues constituting the organic structure In other cases really far more simple than these it was much less obvious in what quarter the causes were to be looked for as in the case of the celestial phenomena Until by combining the laws of certain causes it was found that those laws explained all the facts which experience had proved concerning the heavenly motions and led to predictions which it always verified mankind never knew that those were the causes But whether we are able to put the question before or not until after we have become capable of answering it in either case it must be answered the laws of the different causes must be ascertained before we can proceed to deduce from them the conditions of the effect The mode of ascertaining those laws neither is nor can be any other than the fourfold method of experimental inquiry already discussed A few remarks on the application of that method to cases of the Composition of Causes are all that is requisite It is obvious that we can not expect to find the law of a tendency by an induction from cases in which the tendency is counteracted The laws of motion could never have been brought to light from the observation of bodies kept at rest by the equilibrium of opposing forces Even where the tendency is not in the ordinary sense of the word counteracted but only modified by having its effects compounded with the effects arising from some other tendency or tendencies we are still in an unfavourable position for tracing by means of such cases the law of the tendency itself It would have been scarcely possible to discover the law that every body in motion tends to continue moving in a straight line by an induction from instances in which the motion is deflected into a curve by being compounded with the effect of an accelerating force Notwithstanding the resources afforded in this description of cases by the Method of Concomitant Variations the principles of a judicious experimentation prescribe that the law of each of the tendencies should be studied if possible in cases in which that tendency operates alone or in combination with no agencies but those of which the effect can from previous knowledge be calculated and allowed for Accordingly in the cases unfortunately very numerous and important in which the causes do not suffer themselves to be separated and observed apart there is much difficulty in laying down with due certainty the inductive foundation necessary to support the deductive method This difficulty is most of all conspicuous in the case of physiological phenomena it being seldom possible to separate the different agencies which collectively compose an organized body without destroying the very phenomena which it is our object to investigate following life in creatures we dissect We lose it in the moment we detect And for this reason I am inclined to the opinion that physiology greatly and rapidly progressive as it now is is embarrassed by greater natural difficulties and is probably susceptible of a less degree of ultimate perfection than even the social science inasmuch as it is possible to study the laws and operations of one human mind apart from other minds much less imperfectly than we can study the laws of one organ or tissue of the human body apart from the other organs or tissues It has been judiciously remarked that pathological facts or to speak in common language diseases in their different forms and degrees afford in the case of physiological investigation the most valuable equivalent to experimentation properly so called inasmuch as they often exhibit to us a definite disturbance in some one organ or organic function the remaining organs and functions being in the first instance at least unaffected It is true that from the perpetual actions and reactions which are going on among all parts of the organic economy there can be no prolonged disturbance in any one function without ultimately involving many of the others and when once it has done so the experiment for the most part loses its scientific value All depends on observing the early stages of the derangement which unfortunately are of necessity the least marked If however the organs and functions not disturbed in the first instance become affected in a fixed order of succession some light is thereby thrown upon the action which one organ exercises over another and we occasionally obtain a series of effects which we can refer with some confidence to the original local derangement but for this it is necessary that we should know that the original derangement was local If it was what is termed constitutional that is if we do not know in what part of the animal economy it took its rise or the precise nature of the disturbance which took place in that part we are unable to determine which of the various derangements was cause and which effect which of them were produced by one another and which by the direct though perhaps tardy action of the original cause Besides natural pathological facts we can produce pathological facts artificially we can try experiments even in the popular sense of the term by subjecting the living being to some external agent such as the mercury of our former example or the section of a nerve to ascertain the functions of different parts of the nervous system As this experimentation is not intended to obtain a direct solution of any practical question but to discover general laws from which afterward the conditions of any particular effect may be obtained by deduction the best cases to select are those of which the circumstances can be best ascertained and such are generally not those in which there is any practical object in view The experiments are best tried not in a state of disease which is essentially a changeable state but in the condition of health comparatively a fixed state In the one unusual agencies are at work the results of which we have no means of predicting in the other the course of the accustomed physiological phenomena would it may generally be presumed remain undisturbed were it not for the disturbing cause which we introduce Such with the occasional aid of the Method of Concomitant Variations the latter not less encumbered than the more elementary methods by the peculiar difficulties of the subject are our inductive resources for ascertaining the laws of the causes considered separately when we have it not in our power to make trial of them in a state of actual separation The insufficiency of these resources is so glaring that no one can be surprised at the backward state of the science of physiology in which indeed our knowledge of causes is so imperfect that we can neither explain nor could without specific experience have predicted many of the facts which are certified to us by the most ordinary observation Fortunately we are much better informed as to the empirical laws of the phenomena that is the uniformities respecting which we can not yet decide whether they are cases of causation or mere results of it Not only has the order in which the facts of organization and life successively manifest themselves from the first germ of existence to death been found to be uniform and very accurately ascertainable but by a great application of the Method of Concomitant Variations to the entire facts of comparative anatomy and physiology the characteristic organic structure corresponding to each class of functions has been determined with considerable precision Whether these organic conditions are the whole of the conditions and in many cases whether they are conditions at all or mere collateral effects of some common cause we are quite ignorant nor are we ever likely to know unless we could construct an organized body and try whether it would live Under such disadvantages do we in cases of this description attempt the initial or inductive step in the application of the Deductive Method to complex phenomena But such fortunately is not the common case In general the laws of the causes on which the effect depends may be obtained by an induction from comparatively simple instances or at the worst by deduction from the laws of simpler causes so obtained By simple instances are meant of course those in which the action of each cause was not intermixed or interfered with or not to any great extent by other causes whose laws were unknown And only when the induction which furnished the premises to the Deductive method rested on such instances has the application of such a method to the ascertainment of the laws of a complex effect been attended with brilliant results When the laws of the causes have been ascertained and the first stage of the great logical operation now under discussion satisfactorily accomplished the second part follows that of determining from the laws of the causes what effect any given combination of those causes will produce This is a process of calculation in the wider sense of the term and very often involves processes of calculation in the narrowest sense It is a ratiocination and when our knowledge of the causes is so perfect as to extend to the exact numerical laws which they observe in producing their effects the ratiocination may reckon among its premises the theorems of the science of number in the whole immense extent of that science Not only are the most advanced truths of mathematics often required to enable us to compute an effect the numerical law of which we already know but even by the aid of those most advanced truths we can go but a little way In so simple a case as the common problem of three bodies gravitating toward one another with a force directly as their mass and inversely as the square of the distance all the resources of the calculus have not hitherto sufficed to obtain any general solution but an approximate one In a case a little more complex but still one of the simplest which arise in practice that of the motion of a projectile the causes which affect the velocity and range for example of a cannonball may be all known and estimated the force of the gunpowder the angle of elevation the density of the air the strength and direction of the wind but it is one of the most difficult of mathematical problems to combine all these so as to determine the effect resulting from their collective action Besides the theorems of number those of geometry also come in as premises where the effects take place in space and involve motion and extension as in mechanics optics acoustics astronomy But when the complication increases and the effects are under the influence of so many and such shifting causes as to give no room either for fixed numbers or for straight lines and regular curves as in the case of physiological to say nothing of mental and social phenomena the laws of number and extension are applicable if at all only on that large scale on which precision of details becomes unimportant Although these laws play a conspicuous part in the most striking examples of the investigation of nature by the Deductive Method as for example in the Newtonian theory of the celestial motions they are by no means an indispensable part of every such process All that is essential in it is reasoning from a general law to a particular case that is determining by means of the particular circumstances of that case what result is required in that instance to fulfill the law Thus in the Torricellian experiment if the fact that air has weight had been previously known it would have been easy without any numerical data to deduce from the general law of equilibrium that the mercury would stand in the tube at such a height that the column of mercury would exactly balance a column of the atmosphere of equal diameter because otherwise equilibrium would not exist By such ratiocinations from the separate laws of the causes we may to a certain extent succeed in answering either of the following questions Given a certain combination of causes what effect will follow and What combination of causes if it existed would produce a given effect In the one case we determine the effect to be expected in any complex circumstances of which the different elements are known in the other case we learn according to what law under what antecedent conditions a given complex effect will occur But it may here be asked are not the same arguments by which the methods of direct observation and experiment were set aside as illusory when applied to the laws of complex phenomena applicable with equal force against the Method of Deduction When in every single instance a multitude often an unknown multitude of agencies are clashing and combining what security have we that in our computation a priori we have taken all these into our reckoning How many must we not generally be ignorant of Among those which we know how probable that some have been overlooked and even were all included how vain the pretense of summing up the effects of many causes unless we know accurately the numerical law of each a condition in most cases not to be fulfilled and even when it is fulfilled to make the calculation transcends in any but very simple cases the utmost power of mathematical science with all its most modern improvements These objections have real weight and would be altogether unanswerable if there were no test by which when we employ the Deductive Method we might judge whether an error of any of the above descriptions had been committed or not Such a test however there is and its application forms under the name of Verification the third essential component part of the Deductive Method without which all the results it can give have little other value than that of conjecture To warrant reliance on the general conclusions arrived at by deduction these conclusions must be found on careful comparison to accord with the results of direct observation wherever it can be had If when we have experience to compare with them this experience confirms them we may safely trust to them in other cases of which our specific experience is yet to come But if our deductions have led to the conclusion that from a particular combination of causes a given effect would result then in all known cases where that combination can be shown to have existed and where the effect has not followed we must be able to show or at least to make a probable surmise what frustrated it if we can not the theory is imperfect and not yet to be relied upon Nor is the verification complete unless some of the cases in which the theory is borne out by the observed result are of at least equal complexity with any other cases in which its application could be called for If direct observation and collation of instances have furnished us with any empirical laws of the effect whether true in all observed cases or only true for the most part the most effectual verification of which the theory could be susceptible would be that it led deductively to those empirical laws that the uniformities whether complete or incomplete which were observed to exist among the phenomena were accounted for by the laws of the causes were such as could not but exist if those be really the causes by which the phenomena are produced Thus it was very reasonably deemed an essential requisite of any true theory of the causes of the celestial motions that it should lead by deduction to Kepler’s laws which accordingly the Newtonian theory did In order therefore to facilitate the verification of theories obtained by deduction it is important that as many as possible of the empirical laws of the phenomena should be ascertained by a comparison of instances conformably to the Method of Agreement as well as it must be added that the phenomena themselves should be described in the most comprehensive as well as accurate manner possible by collecting from the observation of parts the simplest possible correct expressions for the corresponding wholes as when the series of the observed places of a planet was first expressed by a circle then by a system of epicycles and subsequently by an ellipse It is worth remarking that complex instances which would have been of no use for the discovery of the simple laws into which we ultimately analyse their phenomena nevertheless when they have served to verify the analysis become additional evidence of the laws themselves Although we could not have got at the law from complex cases still when the law got at otherwise is found to be in accordance with the result of a complex case that case becomes a new experiment on the law and helps to confirm what it did not assist to discover It is a new trial of the principle in a different set of circumstances and occasionally serves to eliminate some circumstance not previously excluded and the exclusion of which might require an experiment impossible to be executed This was strikingly conspicuous in the example formerly quoted in which the difference between the observed and the calculated velocity of sound was ascertained to result from the heat extricated by the condensation which takes place in each sonorous vibration This was a trial in new circumstances of the law of the development of heat by compression and it added materially to the proof of the universality of that law Accordingly any law of nature is deemed to have gained in point of certainty by being found to explain some complex case which had not previously been thought of in connection with it and this indeed is a consideration to which it is the habit of scientific inquirers to attach rather too much value than too little To the Deductive Method thus characterized in its three constituent parts Induction Ratiocination and Verification the human mind is indebted for its most conspicuous triumphs in the investigation of nature To it we owe all the theories by which vast and complicated phenomena are embraced under a few simple laws which considered as the laws of those great phenomena could never have been detected by their direct study We may form some conception of what the method has done for us from the case of the celestial motions one of the simplest among the greater instances of the Composition of Causes since except in a few cases not of primary importance each of the heavenly bodies may be considered without material inaccuracy to be never at one time influenced by the attraction of more than two bodies the sun and one other planet or satellite making with the reaction of the body itself and the force generated by the body’s own motion and acting in the direction of the tangent only four different agents on the concurrence of which the motions of that body depend a much smaller number no doubt than that by which any other of the great phenomena of nature is determined or modified Yet how could we ever have ascertained the combination of forces on which the motions of the earth and planets are dependent by merely comparing the orbits or velocities of different planets or the different velocities or positions of the same planet Notwithstanding the regularity which manifests itself in those motions in a degree so rare among the effects of concurrence of causes and although the periodical recurrence of exactly the same effect affords positive proof that all the combinations of causes which occur at all recur periodically we should not have known what the causes were if the existence of agencies precisely similar on our own earth had not fortunately brought the causes themselves within the reach of experimentation under simple circumstances As we shall have occasion to analyse further on this great example of the Method of Deduction we shall not occupy any time with it here but shall proceed to that secondary application of the Deductive Method the result of which is not to prove laws of phenomena but to explain them The deductive operation by which we derive the law of an effect from the laws of the causes the concurrence of which gives rise to it may be undertaken either for the purpose of discovering the law or of explaining a law already discovered The word explanation occurs so continually and holds so important a place in philosophy that a little time spent in fixing the meaning of it will be profitably employed An individual fact is said to be explained by pointing out its cause that is by stating the law or laws of causation of which its production is an instance Thus a conflagration is explained when it is proved to have arisen from a spark falling into the midst of a heap of combustibles And in a similar manner a law or uniformity in nature is said to be explained when another law or laws are pointed out of which that law itself is but a case and from which it could be deduced There are three distinguishable sets of circumstances in which a law of causation may be explained from or as it also is often expressed resolved into other laws The first is the case already so fully considered an intermixture of laws producing a joint effect equal to the sum of the effects of the causes taken separately The law of the complex effect is explained by being resolved into the separate laws of the causes which contribute to it Thus the law of the motion of a planet is resolved into the law of the acquired force which tends to produce a uniform motion in the tangent and the law of the centripetal force which tends to produce an accelerating motion toward the sun the real motion being a compound of the two It is necessary here to remark that in this resolution of the law of a complex effect the laws of which it is compounded are not the only elements It is resolved into the laws of the separate causes together with the fact of their coexistence The one is as essential an ingredient as the other whether the object be to discover the law of the effect or only to explain it To deduce the laws of the heavenly motions we require not only to know the law of a rectilinear and that of a gravitative force but the existence of both these forces in the celestial regions and even their relative amount The complex laws of causation are thus resolved into two distinct kinds of elements the one simpler laws of causation the other in the aptly selected expression of Dr Chalmers collocations the collocations consisting in the existence of certain agents or powers in certain circumstances of place and time We shall hereafter have occasion to return to this distinction and to dwell on it at such length as dispenses with the necessity of further insisting on it here The first mode then of the explanation of Laws of Causation is when the law of an effect is resolved into the various tendencies of which it is the result together with the laws of those tendencies A second case is when between what seemed the cause and what was supposed to be its effect further observation detects an intermediate link a fact caused by the antecedent and in its turn causing the consequent so that the cause at first assigned is but the remote cause operating through the intermediate phenomenon A seemed the cause of C but it subsequently appeared that A was only the cause of B and that it is B which was the cause of C For example mankind were aware that the act of touching an outward object caused a sensation It was subsequently discovered that after we have touched the object and before we experience the sensation some change takes place in a kind of thread called a nerve which extends from our outward organs to the brain Touching the object therefore is only the remote cause of our sensation that is not the cause properly speaking but the cause of the cause the real cause of the sensation is the change in the state of the nerve Future experience may not only give us more knowledge than we now have of the particular nature of this change but may also interpolate another link between the contact for example of the object with our outward organs and the production of the change of state in the nerve there may take place some electric phenomenon or some phenomenon of a nature not resembling the effects of any known agency Hitherto however no such intermediate link has been discovered and the touch of the object must be considered provisionally as the proximate cause of the affection of the nerve The sequence therefore of a sensation of touch on contact with an object is ascertained not to be an ultimate law it is resolved as the phrase is into two other laws the law that contact with an object produces an affection of the nerve and the law that an affection of the nerve produces sensation To take another example the more powerful acids corrode or blacken organic compounds This is a case of causation but of remote causation and is said to be explained when it is shown that there is an intermediate link namely the separation of some of the chemical elements of the organic structure from the rest and their entering into combination with the acid The acid causes this separation of the elements and the separation of the elements causes the disorganization and often the charring of the structure So again chlorine extracts coloring matters whence its efficacy in bleaching and purifies the air from infection This law is resolved into the two following laws Chlorine has a powerful affinity for bases of all kinds particularly metallic bases and hydrogen such bases are essential elements of coloring matters and contagious compounds which substances therefore are decomposed and destroyed by chlorine It is of importance to remark that when a sequence of phenomena is thus resolved into other laws they are always laws more general than itself The law that A is followed by C is less general than either of the laws which connect B with C and A with B This will appear from very simple considerations All laws of causation are liable to be counteracted or frustrated by the nonfulfilment of some negative condition the tendency therefore of B to produce C may be defeated Now the law that A produces B is equally fulfilled whether B is followed by C or not but the law that A produces C by means of B is of course only fulfilled when B is really followed by C and is therefore less general than the law that A produces B It is also less general than the law that B produces C For B may have other causes besides A and as A produces C only by means of B while B produces C whether it has itself been produced by A or by any thing else the second law embraces a greater number of instances covers as it were a greater space of ground than the first Thus in our former example the law that the contact of an object causes a change in the state of the nerve is more general than the law that contact with an object causes sensation since for aught we know the change in the nerve may equally take place when from a counteracting cause as for instance strong mental excitement the sensation does not follow as in a battle where wounds are sometimes received without any consciousness of receiving them And again the law that change in the state of a nerve produces sensation is more general than the law that contact with an object produces sensation since the sensation equally follows the change in the nerve when not produced by contact with an object but by some other cause as in the wellknown case when a person who has lost a limb feels the same sensation which he has been accustomed to call a pain in the limb Not only are the laws of more immediate sequence into which the law of a remote sequence is resolved laws of greater generality than that law is but as a consequence of or rather as implied in their greater generality they are more to be relied on there are fewer chances of their being ultimately found not to be universally true From the moment when the sequence of A and C is shown not to be immediate but to depend on an intervening phenomenon then however constant and invariable the sequence of A and C has hitherto been found possibilities arise of its failure exceeding those which can effect either of the more immediate sequences A B and B C The tendency of A to produce C may be defeated by whatever is capable of defeating either the tendency of A to produce B or the tendency of B to produce C it is therefore twice as liable to failure as either of those more elementary tendencies and the generalization that A is always followed by C is twice as likely to be found erroneous And so of the converse generalization that C is always preceded and caused by A which will be erroneous not only if there should happen to be a second immediate mode of production of C itself but moreover if there be a second mode of production of B the immediate antecedent of C in the sequence The resolution of the one generalization into the other two not only shows that there are possible limitations of the former from which its two elements are exempt but shows also where these are to be looked for As soon as we know that B intervenes between A and C we also know that if there be cases in which the sequence of A and C does not hold these are most likely to be found by studying the effects or the conditions of the phenomenon B It appears then that in the second of the three modes in which a law may be resolved into other laws the latter are more general that is extend to more cases and are also less likely to require limitation from subsequent experience than the law which they serve to explain They are more nearly unconditional they are defeated by fewer contingencies they are a nearer approach to the universal truth of nature The same observations are still more evidently true with regard to the first of the three modes of resolution When the law of an effect of combined forces is resolved into the separate laws of the causes the nature of the case implies that the law of the effect is less general than the law of any of the causes since it only holds when they are combined while the law of any one of the causes holds good both then and also when that cause acts apart from the rest It is also manifest that the complex law is liable to be oftener unfulfilled than any one of the simpler laws of which it is the result since every contingency which defeats any of the laws prevents so much of the effect as depends on it and thereby defeats the complex law The mere rusting for example of some small part of a great machine often suffices entirely to prevent the effect which ought to result from the joint action of all the parts The law of the effect of a combination of causes is always subject to the whole of the negative conditions which attach to the action of all the causes severally There is another and an equally strong reason why the law of a complex effect must be less general than the laws of the causes which conspire to produce it The same causes acting according to the same laws and differing only in the proportions in which they are combined often produce effects which differ not merely in quantity but in kind The combination of a centripetal with a projectile force in the proportions which obtain in all the planets and satellites of our solar system gives rise to an elliptical motion but if the ratio of the two forces to each other were slightly altered it is demonstrated that the motion produced would be in a circle or a parabola or an hyperbola and it is thought that in the case of some comets one of these is probably the fact Yet the law of the parabolic motion would be resolvable into the very same simple laws into which that of the elliptical motion is resolved namely the law of the permanence of rectilinear motion and the law of gravitation If therefore in the course of ages some circumstance were to manifest itself which without defeating the law of either of those forces should merely alter their proportion to one another such as the shock of some solid body or even the accumulating effect of the resistance of the medium in which astronomers have been led to surmise that the motions of the heavenly bodies take place the elliptical motion might be changed into a motion in some other conic section and the complex law that the planetary motions take place in ellipses would be deprived of its universality though the discovery would not at all detract from the universality of the simpler laws into which that complex law is resolved The law in short of each of the concurrent causes remains the same however their collocations may vary but the law of their joint effect varies with every difference in the collocations There needs no more to show how much more general the elementary laws must be than any of the complex laws which are derived from them Besides the two modes which have been treated of there is a third mode in which laws are resolved into one another and in this it is selfevident that they are resolved into laws more general than themselves This third mode is the subsumption as it has been called of one law under another or what comes to the same thing the gathering up of several laws into one more general law which includes them all The most splendid example of this operation was when terrestrial gravity and the central force of the solar system were brought together under the general law of gravitation It had been proved antecedently that the earth and the other planets tend to the sun and it had been known from the earliest times that terrestrial bodies tend toward the earth These were similar phenomena and to enable them both to be subsumed under one law it was only necessary to prove that as the effects were similar in quality so also they as to quantity conform to the same rules This was first shown to be true of the moon which agreed with terrestrial objects not only in tending to a centre but in the fact that this centre was the earth The tendency of the moon toward the earth being ascertained to vary as the inverse square of the distance it was deduced from this by direct calculation that if the moon were as near to the earth as terrestrial objects are and the acquired force in the direction of the tangent were suspended the moon would fall toward the earth through exactly as many feet in a second as those objects do by virtue of their weight Hence the inference was irresistible that the moon also tends to the earth by virtue of its weight and that the two phenomena the tendency of the moon to the earth and the tendency of terrestrial objects to the earth being not only similar in quality but when in the same circumstances identical in quantity are cases of one and the same law of causation But the tendency of the moon to the earth and the tendency of the earth and planets to the sun were already known to be cases of the same law of causation and thus the law of all these tendencies and the law of terrestrial gravity were recognized as identical and were subsumed under one general law that of gravitation In a similar manner the laws of magnetic phenomena have more recently been subsumed under known laws of electricity It is thus that the most general laws of nature are usually arrived at we mount to them by successive steps For to arrive by correct induction at laws which hold under such an immense variety of circumstances laws so general as to be independent of any varieties of space or time which we are able to observe requires for the most part many distinct sets of experiments or observations conducted at different times and by different people One part of the law is first ascertained afterward another part one set of observations teaches us that the law holds good under some conditions another that it holds good under other conditions by combining which observations we find that it holds good under conditions much more general or even universally The general law in this case is literally the sum of all the partial ones it is a recognition of the same sequence in different sets of instances and may in fact be regarded as merely one step in the process of elimination The tendency of bodies toward one another which we now call gravity had at first been observed only on the earth’s surface where it manifested itself only as a tendency of all bodies toward the earth and might therefore be ascribed to a peculiar property of the earth itself one of the circumstances namely the proximity of the earth had not been eliminated To eliminate this circumstance required a fresh set of instances in other parts of the universe these we could not ourselves create and though nature had created them for us we were placed in very unfavourable circumstances for observing them To make these observations fell naturally to the lot of a different set of persons from those who studied terrestrial phenomena and had indeed been a matter of great interest at a time when the idea of explaining celestial facts by terrestrial laws was looked upon as the confounding of an indefeasible distinction When however the celestial motions were accurately ascertained and the deductive processes performed from which it appeared that their laws and those of terrestrial gravity corresponded those celestial observations became a set of instances which exactly eliminated the circumstance of proximity to the earth and proved that in the original case that of terrestrial objects it was not the earth as such that caused the motion or the pressure but the circumstance common to that case with the celestial instances namely the presence of some great body within certain limits of distance There are then three modes of explaining laws of causation or which is the same thing resolving them into other laws First when the law of an effect of combined causes is resolved into the separate laws of the causes together with the fact of their combination Secondly when the law which connects any two links not proximate in a chain of causation is resolved into the laws which connect each with the intermediate links Both of these are cases of resolving one law into two or more in the third two or more are resolved into one when after the law has been shown to hold good in several different classes of cases we decide that what is true in each of these classes of cases is true under some more general supposition consisting of what all those classes of cases have in common We may here remark that this last operation involves none of the uncertainties attendant on induction by the Method of Agreement since we need not suppose the result to be extended by way of inference to any new class of cases different from those by the comparison of which it was engendered In all these three processes laws are as we have seen resolved into laws more general than themselves laws extending to all the cases which the former extended to and others besides In the first two modes they are also resolved into laws more certain in other words more universally true than themselves they are in fact proved not to be themselves laws of nature the character of which is to be universally true but results of laws of nature which may be only true conditionally and for the most part No difference of this sort exists in the third case since here the partial laws are in fact the very same law as the general one and any exception to them would be an exception to it too By all the three processes the range of deductive science is extended since the laws thus resolved may be thenceforth deduced demonstratively from the laws into which they are resolved As already remarked the same deductive process which proves a law or fact of causation if unknown serves to explain it when known The word explanation is here used in its philosophical sense What is called explaining one law of nature by another is but substituting one mystery for another and does nothing to render the general course of nature other than mysterious we can no more assign a why for the more extensive laws than for the partial ones The explanation may substitute a mystery which has become familiar and has grown to seem not mysterious for one which is still strange And this is the meaning of explanation in common parlance But the process with which we are here concerned often does the very contrary it resolves a phenomenon with which we are familiar into one of which we previously knew little or nothing as when the common fact of the fall of heavy bodies was resolved into the tendency of all particles of matter toward one another It must be kept constantly in view therefore that in science those who speak of explaining any phenomenon mean or should mean pointing out not some more familiar but merely some more general phenomenon of which it is a partial exemplification or some laws of causation which produce it by their joint or successive action and from which therefore its conditions may be determined deductively Every such operation brings us a step nearer toward answering the question which was stated in a previous chapter as comprehending the whole problem of the investigation of nature viz what are the fewest assumptions which being granted the order of nature as it exists would be the result What are the fewest general propositions from which all the uniformities existing in nature could be deduced The laws thus explained or resolved are sometimes said to be accounted for but the expression is incorrect if taken to mean any thing more than what has been already stated In minds not habituated to accurate thinking there is often a confused notion that the general laws are the causes of the partial ones that the law of general gravitation for example causes the phenomenon of the fall of bodies to the earth But to assert this would be a misuse of the word cause terrestrial gravity is not an effect of general gravitation but a case of it that is one kind of the particular instances in which that general law obtains To account for a law of nature means and can mean nothing more than to assign other laws more general together with collocations which laws and collocations being supposed the partial law follows without any additional supposition The most striking example which the history of science presents of the explanation of laws of causation and other uniformities of sequence among special phenomena by resolving them into laws of greater simplicity and generality is the great Newtonian generalization respecting which typical instance so much having already been said it is sufficient to call attention to the great number and variety of the special observed uniformities which are in this case accounted for either as particular cases or as consequences of one very simple law of universal nature The simple fact of a tendency of every particle of matter toward every other particle varying inversely as the square of the distance explains the fall of bodies to the earth the revolutions of the planets and satellites the motions so far as known of comets and all the various regularities which have been observed in these special phenomena such as the elliptical orbits and the variations from exact ellipses the relation between the solar distances of the planets and the duration of their revolutions the precession of the equinoxes the tides and a vast number of minor astronomical truths Mention has also been made in the preceding chapter of the explanation of the phenomena of magnetism from laws of electricity the special laws of magnetic agency having been affiliated by deduction to observed laws of electric action in which they have ever since been considered to be included as special cases An example not so complete in itself but even more fertile in consequences having been the startingpoint of the really scientific study of physiology is the affiliation commenced by Bichat and carried on by subsequent biologists of the properties of the bodily organs to the elementary properties of the tissues into which they are anatomically decomposed Another striking instance is afforded by Dalton’s generalization commonly known as the atomic theory It had been known from the very commencement of accurate chemical observation that any two bodies combine chemically with one another in only a certain number of proportions but those proportions were in each case expressed by a percentage so many parts by weight of each ingredient in 100 of the compound say 35 and a fraction of one element 64 and a fraction of the other in which mode of statement no relation was perceived between the proportion in which a given element combines with one substance and that in which it combines with others The great step made by Dalton consisted in perceiving that a unit of weight might be established for each substance such that by supposing the substance to enter into all its combinations in the ratio either of that unit or of some low multiple of that unit all the different proportions previously expressed by percentages were found to result Thus 1 being assumed as the unit of hydrogen if 8 were then taken as that of oxygen the combination of one unit of hydrogen with one unit of oxygen would produce the exact proportion of weight between the two substances which is known to exist in water the combination of one unit of hydrogen with two units of oxygen would produce the proportion which exists in the other compound of the same two elements called peroxide of hydrogen and the combinations of hydrogen and of oxygen with all other substances would correspond with the supposition that those elements enter into combination by single units or twos or threes of the numbers assigned to them 1 and 8 and the other substances by ones or twos or threes of other determinate numbers proper to each The result is that a table of the equivalent numbers or as they are called atomic weights of all the elementary substances comprises in itself and scientifically explains all the proportions in which any substance elementary or compound is found capable of entering into chemical combination with any other substance whatever Some interesting cases of the explanation of old uniformities by newly ascertained laws are afforded by the researches of Professor Graham That eminent chemist was the first who drew attention to the distinction which may be made of all substances into two classes termed by him crystalloids and colloids or rather of all states of matter into the crystalloid and the colloidal states for many substances are capable of existing in either When in the colloidal state their sensible properties are very different from those of the same substance when crystallized or when in a state easily susceptible of crystallization Colloid substances pass with extreme difficulty and slowness into the crystalline state and are extremely inert in all the ordinary chemical relations Substances in the colloid state are almost always when combined with water more or less viscous or gelatinous The most prominent examples of the state are certain animal and vegetable substances particularly gelatine albumen starch the gums caramel tannin and some others Among substances not of organic origin the most notable instances are hydrated silicic acid and hydrated alumina with other metallic peroxides of the aluminous class Now it is found that while colloidal substances are easily penetrated by water and by the solutions of crystalloid substances they are very little penetrable by one another which enabled Professor Graham to introduce a highly effective process termed dialysis for separating the crystalloid substances contained in any liquid mixture by passing them through a thin septum of colloidal matter which does not suffer any thing colloidal to pass or suffers it only in very minute quantity This property of colloids enabled Mr Graham to account for a number of special results of observation not previously explained For instance while soluble crystalloids are always highly sapid soluble colloids are singularly insipid as might be expected for as the sentient extremities of the nerves of the palate are probably protected by a colloidal membrane impermeable to other colloids a colloid when tasted probably never reaches those nerves Again it has been observed that vegetable gum is not digested in the stomach the coats of that organ dialyse the soluble food absorbing crystalloids and rejecting all colloids One of the mysterious processes accompanying digestion the secretion of free muriatic acid by the coats of the stomach obtains a probable hypothetical explanation through the same law Finally much light is thrown upon the observed phenomena of osmose the passage of fluids outward and inward through animal membranes by the fact that the membranes are colloidal In consequence the water and saline solutions contained in the animal body pass easily and rapidly through the membranes while the substances directly applicable to nutrition which are mostly colloidal are detained by them The property which salt possesses of preserving animal substances from putrefaction is resolved by Liebig into two more general laws the strong attraction of salt for water and the necessity of the presence of water as a condition of putrefaction The intermediate phenomenon which is interpolated between the remote cause and the effect can here be not merely inferred but seen for it is a familiar fact that flesh upon which salt has been thrown is speedily found swimming in brine The second of the two factors as they may be termed into which the preceding law has been resolved the necessity of water to putrefaction itself affords an additional example of the Resolution of Laws The law itself is proved by the Method of Difference since flesh completely dried and kept in a dry atmosphere does not putrefy as we see in the case of dried provisions and human bodies in very dry climates A deductive explanation of this same law results from Liebig’s speculations The putrefaction of animal and other azotized bodies is a chemical process by which they are gradually dissipated in a gaseous form chiefly in that of carbonic acid and ammonia now to convert the carbon of the animal substance into carbonic acid requires oxygen and to convert the azote into ammonia requires hydrogen which are the elements of water The extreme rapidity of the putrefaction of azotized substances compared with the gradual decay of nonazotized bodies such as wood and the like by the action of oxygen alone he explains from the general law that substances are much more easily decomposed by the action of two different affinities upon two of their elements than by the action of only one Among the many important properties of the nervous system which have either been first discovered or strikingly illustrated by Dr BrownSquard I select the reflex influence of the nervous system on nutrition and secretion By reflex nervous action is meant action which one part of the nervous system exerts over another part without any intermediate action on the brain and consequently without consciousness or which if it does pass through the brain at least produces its effects independently of the will There are many experiments which prove that irritation of a nerve in one part of the body may in this manner excite powerful action in another part for example food injected into the stomach through a divided Ïsophagus nevertheless produces secretion of saliva warm water injected into the bowels and various other irritations of the lower intestines have been found to excite secretion of the gastric juice and so forth The reality of the power being thus proved its agency explains a great variety of apparently anomalous phenomena of which I select the following from Dr BrownSquard’s Lectures on the Nervous System The production of tears by irritation of the eye or of the mucous membrane of the nose The secretions of the eye and nose increased by exposure of other parts of the body to cold Inflammation of the eye especially when of traumatic origin very frequently excites a similar affection in the other eye which may be cured by section of the intervening nerve Loss of sight sometimes produced by neuralgia and has been known to be at once cured by the extirpation for instance of a carious tooth Even cataract has been produced in a healthy eye by cataract in the other eye or by neuralgia or by a wound of the frontal nerve The wellknown phenomenon of a sudden stoppage of the heart’s action and consequent death produced by irritation of some of the nervous extremities eg by drinking very cold water or by a blow on the abdomen or other sudden excitation of the abdominal sympathetic nerve though this nerve may be irritated to any extent without stopping the heart’s action if a section be made of the communicating nerves The extraordinary effects produced on the internal organs by an extensive burn on the surface of the body consisting in violent inflammation of the tissues of the abdomen chest or head which when death ensues from this kind of injury is one of the most frequent causes of it Paralysis and anaesthesia of one part of the body from neuralgia in another part and muscular atrophy from neuralgia even when there is no paralysis Tetanus produced by the lesion of a nerve Dr BrownSquard thinks it highly probable that hydrophobia is a phenomenon of a similar nature Morbid changes in the nutrition of the brain and spinal cord manifesting themselves by epilepsy chorea hysteria and other diseases occasioned by lesion of some of the nervous extremities in remote places as by worms calculi tumors carious bones and in some cases even by very slight irritations of the skin From the foregoing and similar instances we may see the importance when a law of nature previously unknown has been brought to light or when new light has been thrown upon a known law by experiment of examining all cases which present the conditions necessary for bringing that law into action a process fertile in demonstrations of special laws previously unsuspected and explanations of others already empirically known For instance Faraday discovered by experiment that voltaic electricity could be evolved from a natural magnet provided a conducting body were set in motion at right angles to the direction of the magnet and this he found to hold not only of small magnets but of that great magnet the earth The law being thus established experimentally that electricity is evolved by a magnet and a conductor moving at right angles to the direction of its poles we may now look out for fresh instances in which these conditions meet Wherever a conductor moves or revolves at right angles to the direction of the earth’s magnetic poles there we may expect an evolution of electricity In the northern regions where the polar direction is nearly perpendicular to the horizon all horizontal motions of conductors will produce electricity horizontal wheels for example made of metal likewise all running streams will evolve a current of electricity which will circulate round them and the air thus charged with electricity may be one of the causes of the Aurora Borealis In the equatorial regions on the contrary upright wheels placed parallel to the equator will originate a voltaic circuit and waterfalls will naturally become electric For a second example it has been proved chiefly by the researches of Professor Graham that gases have a strong tendency to permeate animal membranes and diffuse themselves through the spaces which such membranes enclose notwithstanding the presence of other gases in those spaces Proceeding from this general law and reviewing a variety of cases in which gases lie contiguous to membranes we are enabled to demonstrate or to explain the following more special laws 1st The human or animal body when surrounded with any gas not already contained within the body absorbs it rapidly such for instance as the gases of putrefying matters which helps to explain malaria 2d The carbonic acid gas of effervescing drinks evolved in the stomach permeates its membranes and rapidly spreads through the system 3d Alcohol taken into the stomach passes into vapor and spreads through the system with great rapidity which combined with the high combustibility of alcohol or in other words its ready combination with oxygen may perhaps help to explain the bodily warmth immediately consequent on drinking spirituous liquors 4th In any state of the body in which peculiar gases are formed within it these will rapidly exhale through all parts of the body and hence the rapidity with which in certain states of disease the surrounding atmosphere becomes tainted 5th The putrefaction of the interior parts of a carcass will proceed as rapidly as that of the exterior from the ready passage outward of the gaseous products 6th The exchange of oxygen and carbonic acid in the lungs is not prevented but rather promoted by the intervention of the membrane of the lungs and the coats of the bloodvessels between the blood and the air It is necessary however that there should be a substance in the blood with which the oxygen of the air may immediately combine otherwise instead of passing into the blood it would permeate the whole organism and it is necessary that the carbonic acid as it is formed in the capillaries should also find a substance in the blood with which it can combine otherwise it would leave the body at all points instead of being discharged through the lungs The following is a deduction which confirms by explaining the empirical generalization that soda powders weaken the human system These powders consisting of a mixture of tartaric acid with bicarbonate of soda from which the carbonic acid is set free must pass into the stomach as tartrate of soda Now neutral tartrates citrates and acetates of the alkalis are found in their passage through the system to be changed into carbonates and to convert a tartrate into a carbonate requires an additional quantity of oxygen the abstraction of which must lessen the oxygen destined for assimilation with the blood on the quantity of which the vigorous action of the human system partly depends The instances of new theories agreeing with and explaining old empiricisms are innumerable All the just remarks made by experienced persons on human character and conduct are so many special laws which the general laws of the human mind explain and resolve The empirical generalizations on which the operations of the arts have usually been founded are continually justified and confirmed on the one hand or corrected and improved on the other by the discovery of the simpler scientific laws on which the efficacy of those operations depends The effects of the rotation of crops of the various manures and other processes of improved agriculture have been for the first time resolved in our own day into known laws of chemical and organic action by Davy Liebig and others The processes of the medical art are even now mostly empirical their efficacy is concluded in each instance from a special and most precarious experimental generalization but as science advances in discovering the simple laws of chemistry and physiology progress is made in ascertaining the intermediate links in the series of phenomena and the more general laws on which they depend and thus while the old processes are either exploded or their efficacy in so far as real explained better processes founded on the knowledge of proximate causes are continually suggested and brought into use Many even of the truths of geometry were generalizations from experience before they were deduced from first principles The quadrature of the cycloid is said to have been first effected by measurement or rather by weighing a cycloidal card and comparing its weight with that of a piece of similar card of known dimensions To the foregoing examples from physical science let us add another from mental The following is one of the simple laws of mind Ideas of a pleasurable or painful character form associations more easily and strongly than other ideas that is they become associated after fewer repetitions and the association is more durable This is an experimental law grounded on the Method of Difference By deduction from this law many of the more special laws which experience shows to exist among particular mental phenomena may be demonstrated and explained the ease and rapidity for instance with which thoughts connected with our passions or our more cherished interests are excited and the firm hold which the facts relating to them have on our memory the vivid recollection we retain of minute circumstances which accompanied any object or event that deeply interested us and of the times and places in which we have been very happy or very miserable the horror with which we view the accidental instrument of any occurrence which shocked us or the locality where it took place and the pleasure we derive from any memorial of past enjoyment all these effects being proportional to the sensibility of the individual mind and to the consequent intensity of the pain or pleasure from which the association originated It has been suggested by the able writer of a biographical sketch of Dr Priestley in a monthly periodical that the same elementary law of our mental constitution suitably followed out would explain a variety of mental phenomena previously inexplicable and in particular some of the fundamental diversities of human character and genius Associations being of two sorts either between synchronous or between successive impressions and the influence of the law which renders associations stronger in proportion to the pleasurable or painful character of the impressions being felt with peculiar force in the synchronous class of associations it is remarked by the writer referred to that in minds of strong organic sensibility synchronous associations will be likely to predominate producing a tendency to conceive things in pictures and in the concrete richly clothed in attributes and circumstances a mental habit which is commonly called Imagination and is one of the peculiarities of the painter and the poet while persons of more moderate susceptibility to pleasure and pain will have a tendency to associate facts chiefly in the order of their succession and such persons if they possess mental superiority will addict themselves to history or science rather than to creative art This interesting speculation the author of the present work has endeavoured on another occasion to pursue further and to examine how far it will avail toward explaining the peculiarities of the poetical temperament It is at least an example which may serve instead of many others to show the extensive scope which exists for deductive investigation in the important and hitherto so imperfect Science of Mind The copiousness with which the discovery and explanation of special laws of phenomena by deduction from simpler and more general ones has here been exemplified was prompted by a desire to characterize clearly and place in its due position of importance the Deductive Method which in the present state of knowledge is destined henceforth irrevocably to predominate in the course of scientific investigation A revolution is peaceably and progressively effecting itself in philosophy the reverse of that to which Bacon has attached his name That great man changed the method of the sciences from deductive to experimental and it is now rapidly reverting from experimental to deductive But the deductions which Bacon abolished were from premises hastily snatched up or arbitrarily assumed The principles were neither established by legitimate canons of experimental inquiry nor the results tested by that indispensable element of a rational Deductive Method verification by specific experience Between the primitive method of Deduction and that which I have attempted to characterize there is all the difference which exists between the Aristotelian physics and the Newtonian theory of the heavens It would however be a mistake to expect that those great generalizations from which the subordinate truths of the more backward sciences will probably at some future period be deduced by reasoning as the truths of astronomy are deduced from the generalities of the Newtonian theory will be found in all or even in most cases among truths now known and admitted We may rest assured that many of the most general laws of nature are as yet entirely unthought of and that many others destined hereafter to assume the same character are known if at all only as laws or properties of some limited class of phenomena just as electricity now recognized as one of the most universal of natural agencies was once known only as a curious property which certain substances acquired by friction of first attracting and then repelling light bodies If the theories of heat cohesion crystallization and chemical action are destined as there can be little doubt that they are to become deductive the truths which will then be regarded as the principia of those sciences would probably if now announced appear quite as novel as the law of gravitation appeared to the contemporaries of Newton possibly even more so since Newton’s law after all was but an extension of the law of weight that is of a generalization familiar from of old and which already comprehended a not inconsiderable body of natural phenomena The general laws of a similarly commanding character which we still look forward to the discovery of may not always find so much of their foundations already laid These general truths will doubtless make their first appearance in the character of hypotheses not proved nor even admitting of proof in the first instance, but assumed as premises for the purpose of deducing from them the known laws of concrete phenomena But this though their initial can not be their final state To entitle an hypothesis to be received as one of the truths of nature and not as a mere technical help to the human faculties it must be capable of being tested by the canons of legitimate induction and must actually have been submitted to that test When this shall have been done and done successfully premises will have been obtained from which all the other propositions of the science will thenceforth be presented as conclusions and the science will by means of a new and unexpected Induction be rendered Deductive The preceding considerations have led us to recognize a distinction between two kinds of laws or observed uniformities in nature ultimate laws and what may be termed derivative laws Derivative laws are such as are deducible from and may in any of the modes which we have pointed out be resolved into other and more general ones Ultimate laws are those which can not We are not sure that any of the uniformities with which we are yet acquainted are ultimate laws but we know that there must be ultimate laws and that every resolution of a derivative law into more general laws brings us nearer to them Since we are continually discovering that uniformities not previously known to be other than ultimate are derivative and resolvable into more general laws since in other words we are continually discovering the explanation of some sequence which was previously known only as a fact it becomes an interesting question whether there are any necessary limits to this philosophical operation or whether it may proceed until all the uniform sequences in nature are resolved into some one universal law For this seems at first sight to be the ultimatum toward which the progress of induction by the Deductive Method resting on a basis of observation and experiment is tending Projects of this kind were universal in the infancy of philosophy any speculations which held out a less brilliant prospect being in these early times deemed not worth pursuing And the idea receives so much apparent countenance from the nature of the most remarkable achievements of modern science that speculators are even now frequently appearing who profess either to have solved the problem or to suggest modes in which it may one day be solved Even where pretensions of this magnitude are not made the character of the solutions which are given or sought of particular classes of phenomena often involves such conceptions of what constitutes explanation as would render the notion of explaining all phenomena whatever by means of some one cause or law perfectly admissible It is therefore useful to remark that the ultimate Laws of Nature can not possibly be less numerous than the distinguishable sensations or other feelings of our nature those I mean which are distinguishable from one another in quality and not merely in quantity or degree For example since there is a phenomenon sui generis called colour which our consciousness testifies to be not a particular degree of some other phenomenon as heat or odor or motion but intrinsically unlike all others it follows that there are ultimate laws of colour that though the facts of colour may admit of explanation they never can be explained from laws of heat or odor alone or of motion alone but that however far the explanation may be carried there will always remain in it a law of colour I do not mean that it might not possibly be shown that some other phenomenon some chemical or mechanical action for example invariably precedes and is the cause of every phenomenon of colour But though this if proved would be an important extension of our knowledge of nature it would not explain how or why a motion or a chemical action can produce a sensation of colour and however diligent might be our scrutiny of the phenomena whatever number of hidden links we might detect in the chain of causation terminating in the colour the last link would still be a law of colour not a law of motion nor of any other phenomenon whatever Nor does this observation apply only to colour as compared with any other of the great classes of sensations it applies to every particular colour as compared with others White colour can in no manner be explained exclusively by the laws of the production of red colour In any attempt to explain it we can not but introduce as one element of the explanation the proposition that some antecedent or other produces the sensation of white The ideal limit therefore of the explanation of natural phenomena toward which as toward other ideal limits we are constantly tending without the prospect of ever completely attaining it would be to show that each distinguishable variety of our sensations or other states of consciousness has only one sort of cause that for example whenever we perceive a white colour there is some one condition or set of conditions which is always present and the presence of which always produces in us that sensation As long as there are several known modes of production of a phenomenon several different substances for instance which have the property of whiteness and between which we can not trace any other resemblance so long it is not impossible that one of these modes of production may be resolved into another or that all of them may be resolved into some more general mode of production not hitherto recognized But when the modes of production are reduced to one we can not in point of simplification go any further This one may not after all be the ultimate mode there may be other links to be discovered between the supposed cause and the effect but we can only further resolve the known law by introducing some other law hitherto unknown which will not diminish the number of ultimate laws In what cases accordingly has science been most successful in explaining phenomena by resolving their complex laws into laws of greater simplicity and generality Hitherto chiefly in cases of the propagation of various phenomena through space and first and principally the most extensive and important of all facts of that description mechanical motion Now this is exactly what might be expected from the principles here laid down Not only is motion one of the most universal of all phenomena it is also as might be expected from that circumstance one of those which apparently at least are produced in the greatest number of ways but the phenomenon itself is always to our sensations the same in every respect but degree Differences of duration or of velocity are evidently differences in degree only and differences of direction in space which alone has any semblance of being a distinction in kind entirely disappear so far as our sensations are concerned by a change in our own position indeed the very same motion appears to us according to our position to take place in every variety of direction and motions in every different direction to take place in the same And again motion in a straight line and in a curve are no otherwise distinct than that the one is motion continuing in the same direction the other is motion which at each instant changes its direction There is therefore according to the principles I have stated no absurdity in supposing that all motion may be produced in one and the same way by the same kind of cause Accordingly the greatest achievements in physical science have consisted in resolving one observed law of the production of motion into the laws of other known modes of production or the laws of several such modes into one more general mode as when the fall of bodies to the earth and the motions of the planets were brought under the one law of the mutual attraction of all particles of matter when the motions said to be produced by magnetism were shown to be produced by electricity when the motions of fluids in a lateral direction or even contrary to the direction of gravity were shown to be produced by gravity and the like There is an abundance of distinct causes of motion still unresolved into one another gravitation heat electricity chemical action nervous action and so forth but whether the efforts of the present generation of savants to resolve all these different modes of production into one are ultimately successful or not the attempt so to resolve them is perfectly legitimate For though these various causes produce in other respects sensations intrinsically different and are not therefore capable of being resolved into one another yet in so far as they all produce motion it is quite possible that the immediate antecedent of the motion may in all these different cases be the same nor is it impossible that these various agencies themselves may as the new doctrines assert all of them have for their own immediate antecedent modes of molecular motion We need not extend our illustration to other cases as for instance to the propagation of light sound heat electricity etc through space or any of the other phenomena which have been found susceptible of explanation by the resolution of their observed laws into more general laws Enough has been said to display the difference between the kind of explanation and resolution of laws which is chimerical and that of which the accomplishment is the great aim of science and to show into what sort of elements the resolution must be effected if at all As however there is scarcely any one of the principles of a true method of philosophizing which does not require to be guarded against errors on both sides I must enter a caveat against another misapprehension of a kind directly contrary to the preceding M Comte among other occasions on which he has condemned with some asperity any attempt to explain phenomena which are evidently primordial meaning apparently no more than that every peculiar phenomenon must have at least one peculiar and therefore inexplicable law has spoken of the attempt to furnish any explanation of the colour belonging to each substance la couleur lmentaire propre ˆ chaque substance as essentially illusory No one says he in our time attempts to explain the particular specific gravity of each substance or of each structure Why should it be otherwise as to the specific colour the notion of which is undoubtedly no less primordial Now although as he elsewhere observes a colour must always remain a different thing from a weight or a sound varieties of colour might nevertheless follow or correspond to given varieties of weight or sound or some other phenomenon as different as these are from colour itself It is one question what a thing is and another what it depends on and though to ascertain the conditions of an elementary phenomenon is not to obtain any new insight into the nature of the phenomenon itself that is no reason against attempting to discover the conditions The interdict against endeavouring to reduce distinctions of colour to any common principle would have held equally good against a like attempt on the subject of distinctions of sound which nevertheless have been found to be immediately preceded and caused by distinguishable varieties in the vibrations of elastic bodies though a sound no doubt is quite as different as a colour is from any motion of particles vibratory or otherwise We might add that in the case of colours there are strong positive indications that they are not ultimate properties of the different kinds of substances but depend on conditions capable of being superinduced upon all substances since there is no substance which can not according to the kind of light thrown upon it be made to assume almost any colour and since almost every change in the mode of aggregation of the particles of the same substance is attended with alterations in its colour and in its optical properties generally The really weak point in the attempts which have been made to account for colours by the vibrations of a fluid is not that the attempt itself is unphilosophical but that the existence of the fluid and the fact of its vibratory motion are not proved but are assumed on no other ground than the facility they are supposed to afford of explaining the phenomena And this consideration leads to the important question of the proper use of scientific hypotheses the connection of which with the subject of the explanation of the phenomena of nature and of the necessary limits to that explanation need not be pointed out An hypothesis is any supposition which we make either without actual evidence or on evidence avowedly insufficient in order to endeavour to deduce from it conclusions in accordance with facts which are known to be real under the idea that if the conclusions to which the hypothesis leads are known truths the hypothesis itself either must be or at least is likely to be true If the hypothesis relates to the cause or mode of production of a phenomenon it will serve if admitted to explain such facts as are found capable of being deduced from it And this explanation is the purpose of many if not most hypotheses Since explaining in the scientific sense means resolving a uniformity which is not a law of causation into the laws of causation from which it results or a complex law of causation into simpler and more general ones from which it is capable of being deductively inferred if there do not exist any known laws which fulfill this requirement we may feign or imagine some which would fulfill it and this is making an hypothesis An hypothesis being a mere supposition there are no other limits to hypotheses than those of the human imagination we may if we please imagine by way of accounting for an effect some cause of a kind utterly unknown and acting according to a law altogether fictitious But as hypotheses of this sort would not have any of the plausibility belonging to those which ally themselves by analogy with known laws of nature and besides would not supply the want which arbitrary hypotheses are generally invented to satisfy by enabling the imagination to represent to itself an obscure phenomenon in a familiar light there is probably no hypothesis in the history of science in which both the agent itself and the law of its operation were fictitious Either the phenomenon assigned as the cause is real but the law according to which it acts merely supposed or the cause is fictitious but is supposed to produce its effects according to laws similar to those of some known class of phenomena An instance of the first kind is afforded by the different suppositions made respecting the law of the planetary central force anterior to the discovery of the true law that the force varies as the inverse square of the distance which also suggested itself to Newton in the first instance, as an hypothesis and was verified by proving that it led deductively to Kepler’s laws Hypotheses of the second kind are such as the vortices of Descartes which were fictitious but were supposed to obey the known laws of rotatory motion or the two rival hypotheses respecting the nature of light the one ascribing the phenomena to a fluid emitted from all luminous bodies the other now generally received attributing them to vibratory motions among the particles of an ether pervading all space Of the existence of either fluid there is no evidence save the explanation they are calculated to afford of some of the phenomena but they are supposed to produce their effects according to known laws the ordinary laws of continued locomotion in the one case and in the other those of the propagation of undulatory movements among the particles of an elastic fluid According to the foregoing remarks hypotheses are invented to enable the Deductive Method to be earlier applied to phenomena But in order to discover the cause of any phenomenon by the Deductive Method the process must consist of three parts induction ratiocination and verification Induction the place of which however may be supplied by a prior deduction to ascertain the laws of the causes ratiocination to compute from those laws how the causes will operate in the particular combination known to exist in the case in hand verification by comparing this calculated effect with the actual phenomenon No one of these three parts of the process can be dispensed with In the deduction which proves the identity of gravity with the central force of the solar system all the three are found First it is proved from the moon’s motions that the earth attracts her with a force varying as the inverse square of the distance This though partly dependent on prior deductions corresponds to the first or purely inductive step the ascertainment of the law of the cause Secondly from this law and from the knowledge previously obtained of the moon’s mean distance from the earth and of the actual amount of her deflection from the tangent it is ascertained with what rapidity the earth’s attraction would cause the moon to fall if she were no further off and no more acted upon by extraneous forces than terrestrial bodies are that is the second step the ratiocination Finally this calculated velocity being compared with the observed velocity with which all heavy bodies fall by mere gravity toward the surface of the earth sixteen feet in the first second fortyeight in the second and so forth in the ratio of the odd numbers 1 3 5 etc the two quantities are found to agree The order in which the steps are here presented was not that of their discovery but it is their correct logical order as portions of the proof that the same attraction of the earth which causes the moon’s motion causes also the fall of heavy bodies to the earth a proof which is thus complete in all its parts Now the Hypothetical Method suppresses the first of the three steps the induction to ascertain the law and contents itself with the other two operations ratiocination and verification the law which is reasoned from being assumed instead of proved This process may evidently be legitimate on one supposition namely if the nature of the case be such that the final step the verification shall amount to and fulfill the conditions of a complete induction We want to be assured that the law we have hypothetically assumed is a true one and its leading deductively to true results will afford this assurance provided the case be such that a false law can not lead to a true result provided no law except the very one which we have assumed can lead deductively to the same conclusions which that leads to And this proviso is often realized For example in the very complete specimen of deduction which we just cited the original major premise of the ratiocination the law of the attractive force was ascertained in this mode by this legitimate employment of the Hypothetical Method Newton began by an assumption that the force which at each instant deflects a planet from its rectilinear course and makes it describe a curve round the sun is a force tending directly toward the sun He then proved that if this be so the planet will describe as we know by Kepler’s first law that it does describe equal areas in equal times and lastly he proved that if the force acted in any other direction whatever the planet would not describe equal areas in equal times It being thus shown that no other hypothesis would accord with the facts the assumption was proved the hypothesis became an inductive truth Not only did Newton ascertain by this hypothetical process the direction of the deflecting force he proceeded in exactly the same manner to ascertain the law of variation of the quantity of that force He assumed that the force varied inversely as the square of the distance showed that from this assumption the remaining two of Kepler’s laws might be deduced and finally that any other law of variation would give results inconsistent with those laws and inconsistent therefore with the real motions of the planets of which Kepler’s laws were known to be a correct expression I have said that in this case the verification fulfills the conditions of an induction but an induction of what sort On examination we find that it conforms to the canon of the Method of Difference It affords the two instances A B C a b c and B C b c A represents central force A B C the planets plus a central force B C the planets apart from a central force The planets with a central force give a areas proportional to the times the planets without a central force give b c a set of motions without a or with something else instead of a This is the Method of Difference in all its strictness It is true the two instances which the method requires are obtained in this case not by experiment but by a prior deduction But that is of no consequence It is immaterial what is the nature of the evidence from which we derive the assurance that A B C will produce a b c and B C only b c it is enough that we have that assurance In the present case a process of reasoning furnished Newton with the very instances which if the nature of the case had admitted of it he would have sought by experiment It is thus perfectly possible and indeed is a very common occurrence that what was an hypothesis at the beginning of the inquiry becomes a proved law of nature before its close But in order that this should happen we must be able either by deduction or experiment to obtain both the instances which the Method of Difference requires That we are able from the hypothesis to deduce the known facts gives only the affirmative instance A B C a b c It is equally necessary that we should be able to obtain as Newton did the negative instance B C b c by showing that no antecedent except the one assumed in the hypothesis would in conjunction with B C produce a Now it appears to me that this assurance can not be obtained when the cause assumed in the hypothesis is an unknown cause imagined solely to account for a When we are only seeking to determine the precise law of a cause already ascertained or to distinguish the particular agent which is in fact the cause among several agents of the same kind one or other of which it is already known to be we may then obtain the negative instance An inquiry which of the bodies of the solar system causes by its attraction some particular irregularity in the orbit or periodic time of some satellite or comet would be a case of the second description Newton’s was a case of the first If it had not been previously known that the planets were hindered from moving in straight lines by some force tending toward the interior of their orbit though the exact direction was doubtful or if it had not been known that the force increased in some proportion or other as the distance diminished and diminished as it increased Newton’s argument would not have proved his conclusion These facts however being already certain the range of admissible suppositions was limited to the various possible directions of a line and the various possible numerical relations between the variations of the distance and the variations of the attractive force Now among these it was easily shown that different suppositions could not lead to identical consequences Accordingly Newton could not have performed his second great scientific operation that of identifying terrestrial gravity with the central force of the solar system by the same hypothetical method When the law of the moon’s attraction had been proved from the data of the moon itself then on finding the same law to accord with the phenomena of terrestrial gravity he was warranted in adopting it as the law of those phenomena likewise but it would not have been allowable for him without any lunar data to assume that the moon was attracted toward the earth with a force as the inverse square of the distance merely because that ratio would enable him to account for terrestrial gravity for it would have been impossible for him to prove that the observed law of the fall of heavy bodies to the earth could not result from any force save one extending to the moon and proportional to the inverse square It appears then to be a condition of the most genuinely scientific hypothesis that it be not destined always to remain an hypothesis but be of such a nature as to be either proved or disproved by comparison with observed facts This condition is fulfilled when the effect is already known to depend on the very cause supposed and the hypothesis relates only to the precise mode of dependence the law of the variation of the effect according to the variations in the quantity or in the relations of the cause With these may be classed the hypotheses which do not make any supposition with regard to causation but only with regard to the law of correspondence between facts which accompany each other in their variations though there may be no relation of cause and effect between them Such were the different false hypotheses which Kepler made respecting the law of the refraction of light It was known that the direction of the line of refraction varied with every variation in the direction of the line of incidence but it was not known how that is what changes of the one corresponded to the different changes of the other In this case any law different from the true one must have led to false results And lastly we must add to these all hypothetical modes of merely representing or describing phenomena such as the hypothesis of the ancient astronomers that the heavenly bodies moved in circles the various hypotheses of eccentrics deferents and epicycles which were added to that original hypothesis the nineteen false hypotheses which Kepler made and abandoned respecting the form of the planetary orbits and even the doctrine in which he finally rested that those orbits are ellipses which was but an hypothesis like the rest until verified by facts In all these cases verification is proof if the supposition accords with the phenomena there needs no other evidence of it But in order that this may be the case I conceive it to be necessary when the hypothesis relates to causation that the supposed cause should not only be a real phenomenon something actually existing in nature but should be already known to exercise or at least to be capable of exercising an influence of some sort over the effect In any other case it is no sufficient evidence of the truth of the hypothesis that we are able to deduce the real phenomena from it Is it then never allowable in a scientific hypothesis to assume a cause but only to ascribe an assumed law to a known cause I do not assert this I only say that in the latter case alone can the hypothesis be received as true merely because it explains the phenomena In the former case it may be very useful by suggesting a line of investigation which may possibly terminate in obtaining real proof But for this purpose as is justly remarked by M Comte it is indispensable that the cause suggested by the hypothesis should be in its own nature susceptible of being proved by other evidence This seems to be the philosophical import of Newton’s maxim so often cited with approbation by subsequent writers that the cause assigned for any phenomenon must not only be such as if admitted would explain the phenomenon but must also be a vera causa What he meant by a vera causa Newton did not indeed very explicitly define and Dr Whewell who dissents from the propriety of any such restriction upon the latitude of framing hypotheses has had little difficulty in showing that his conception of it was neither precise nor consistent with itself accordingly his optical theory was a signal instance of the violation of his own rule It is certainly not necessary that the cause assigned should be a cause already known otherwise we should sacrifice our best opportunities of becoming acquainted with new causes But what is true in the maxim is that the cause though not known previously should be capable of being known thereafter that its existence should be capable of being detected and its connection with the effect ascribed to it should be susceptible of being proved by independent evidence The hypothesis by suggesting observations and experiments puts us on the road to that independent evidence if it be really attainable and till it be attained the hypothesis ought only to count for a more or less plausible conjecture This function however of hypotheses is one which must be reckoned absolutely indispensable in science When Newton said Hypotheses non fingo he did not mean that he deprived himself of the facilities of investigation afforded by assuming in the first instance what he hoped ultimately to be able to prove Without such assumptions science could never have attained its present state they are necessary steps in the progress to something more certain and nearly every thing which is now theory was once hypothesis Even in purely experimental science some inducement is necessary for trying one experiment rather than another and though it is abstractedly possible that all the experiments which have been tried might have been produced by the mere desire to ascertain what would happen in certain circumstances without any previous conjecture as to the result yet in point of fact, those unobvious delicate and often cumbrous and tedious processes of experiment which have thrown most light upon the general constitution of nature would hardly ever have been undertaken by the persons or at the time they were unless it had seemed to depend on them whether some general doctrine or theory which had been suggested but not yet proved should be admitted or not If this be true even of merely experimental inquiry the conversion of experimental into deductive truths could still less have been effected without large temporary assistance from hypotheses The process of tracing regularity in any complicated and at first sight confused set of appearances is necessarily tentative we begin by making any supposition even a false one to see what consequences will follow from it and by observing how these differ from the real phenomena we learn what corrections to make in our assumption The simplest supposition which accords with the more obvious facts is the best to begin with because its consequences are the most easily traced This rude hypothesis is then rudely corrected and the operation repeated and the comparison of the consequences deducible from the corrected hypothesis with the observed facts suggests still further correction until the deductive results are at last made to tally with the phenomena Some fact is as yet little understood or some law is unknown we frame on the subject an hypothesis as accordant as possible with the whole of the data already possessed and the science being thus enabled to move forward freely always ends by leading to new consequences capable of observation which either confirm or refute unequivocally the first supposition Neither induction nor deduction would enable us to understand even the simplest phenomena if we did not often commence by anticipating on the results by making a provisional supposition at first essentially conjectural as to some of the very notions which constitute the final object of the inquiry Let any one watch the manner in which he himself unravels a complicated mass of evidence let him observe how for instance he elicits the true history of any occurrence from the involved statements of one or of many witnesses he will find that he does not take all the items of evidence into his mind at once and attempt to weave them together he extemporizes from a few of the particulars a first rude theory of the mode in which the facts took place and then looks at the other statements one by one to try whether they can be reconciled with that provisional theory or what alterations or additions it requires to make it square with them In this way which has been justly compared to the Methods of Approximation of mathematicians we arrive by means of hypotheses at conclusions not hypothetical It is perfectly consistent with the spirit of the method to assume in this provisional manner not only an hypothesis respecting the law of what we already know to be the cause but an hypothesis respecting the cause itself It is allowable useful and often even necessary to begin by asking ourselves what cause may have produced the effect in order that we may know in what direction to look out for evidence to determine whether it actually did The vortices of Descartes would have been a perfectly legitimate hypothesis if it had been possible by any mode of exploration which we could entertain the hope of ever possessing to bring the reality of the vortices as a fact in nature conclusively to the test of observation The vice of the hypothesis was that it could not lead to any course of investigation capable of converting it from an hypothesis into a proved fact It might chance to be disproved either by some want of correspondence with the phenomena it purported to explain or as actually happened by some extraneous fact The free passage of comets through the spaces in which these vortices should have been convinced men that these vortices did not exist But the hypothesis would have been false though no such direct evidence of its falsity had been procurable Direct evidence of its truth there could not be The prevailing hypothesis of a luminiferous ether in other respects not without analogy to that of Descartes is not in its own nature entirely cut off from the possibility of direct evidence in its favour It is well known that the difference between the calculated and the observed times of the periodical return of Encke’s comet has led to a conjecture that a medium capable of opposing resistance to motion is diffused through space If this surmise should be confirmed in the course of ages by the gradual accumulation of a similar variance in the case of the other bodies of the solar system the luminiferous ether would have made a considerable advance toward the character of a vera causa since the existence would have been ascertained of a great cosmical agent possessing some of the attributes which the hypothesis assumes though there would still remain many difficulties and the identification of the ether with the resisting medium would even I imagine give rise to new ones At present however this supposition can not be looked upon as more than a conjecture the existence of the ether still rests on the possibility of deducing from its assumed laws a considerable number of actual phenomena and this evidence I can not regard as conclusive because we can not have in the case of such an hypothesis the assurance that if the hypothesis be false it must lead to results at variance with the true facts Accordingly most thinkers of any degree of sobriety allow that an hypothesis of this kind is not to be received as probably true because it accounts for all the known phenomena since this is a condition sometimes fulfilled tolerably well by two conflicting hypotheses while there are probably many others which are equally possible but which for want of any thing analogous in our experience our minds are unfitted to conceive But it seems to be thought that an hypothesis of the sort in question is entitled to a more favourable reception if besides accounting for all the facts previously known it has led to the anticipation and prediction of others which experience afterward verified as the undulatory theory of light led to the prediction subsequently realized by experiment that two luminous rays might meet each other in such a manner as to produce darkness Such predictions and their fulfilment are indeed well calculated to impress the uninformed whose faith in science rests solely on similar coincidences between its prophecies and what comes to pass But it is strange that any considerable stress should be laid upon such a coincidence by persons of scientific attainments If the laws of the propagation of light accord with those of the vibrations of an elastic fluid in as many respects as is necessary to make the hypothesis afford a correct expression of all or most of the phenomena known at the time it is nothing strange that they should accord with each other in one respect more Though twenty such coincidences should occur they would not prove the reality of the undulatory ether it would not follow that the phenomena of light were results of the laws of elastic fluids but at most that they are governed by laws partially identical with these which we may observe is already certain from the fact that the hypothesis in question could be for a moment tenable Cases may be cited even in our imperfect acquaintance with nature where agencies that we have good reason to consider as radically distinct produce their effects or some of their effects according to laws which are identical The law for example of the inverse square of the distance is the measure of the intensity not only of gravitation but it is believed of illumination and of heat diffused from a centre Yet no one looks upon this identity as proving similarity in the mechanism by which the three kinds of phenomena are produced According to Dr Whewell the coincidence of results predicted from an hypothesis with facts afterward observed amounts to a conclusive proof of the truth of the theory If I copy a long series of letters of which the last halfdozen are concealed and if I guess these aright as is found to be the case when they are afterward uncovered this must be because I have made out the import of the inscription To say that because I have copied all that I could see it is nothing strange that I should guess those which I can not see would be absurd without supposing such a ground for guessing If any one from examining the greater part of a long inscription can interpret the characters so that the inscription gives a rational meaning in a known language there is a strong presumption that his interpretation is correct but I do not think the presumption much increased by his being able to guess the few remaining letters without seeing them for we should naturally expect when the nature of the case excludes chance that even an erroneous interpretation which accorded with all the visible parts of the inscription would accord also with the small remainder as would be the case for example if the inscription had been designedly so contrived as to admit of a double sense I assume that the uncovered characters afford an amount of coincidence too great to be merely casual otherwise the illustration is not a fair one No one supposes the agreement of the phenomena of light with the theory of undulations to be merely fortuitous It must arise from the actual identity of some of the laws of undulations with some of those of light and if there be that identity it is reasonable to suppose that its consequences would not end with the phenomena which first suggested the identification nor be even confined to such phenomena as were known at the time But it does not follow because some of the laws agree with those of undulations that there are any actual undulations no more than it followed because some though not so many of the same laws agreed with those of the projection of particles that there was actual emission of particles Even the undulatory hypothesis does not account for all the phenomena of light The natural colours of objects the compound nature of the solar ray the absorption of light and its chemical and vital action the hypothesis leaves as mysterious as it found them and some of these facts are at least apparently more reconcilable with the emission theory than with that of Young and Fresnel Who knows but that some third hypothesis including all these phenomena may in time leave the undulatory theory as far behind as that has left the theory of Newton and his successors To the statement that the condition of accounting for all the known phenomena is often fulfilled equally well by two conflicting hypotheses Dr Whewell makes answer that he knows of no such case in the history of science where the phenomena are at all numerous and complicated Such an affirmation by a writer of Dr Whewell’s minute acquaintance with the history of science would carry great authority if he had not a few pages before taken pains to refute it by maintaining that even the exploded scientific hypotheses might always or almost always have been so modified as to make them correct representations of the phenomena The hypothesis of vortices he tells us was by successive modifications brought to coincide in its results with the Newtonian theory and with the facts The vortices did not indeed explain all the phenomena which the Newtonian theory was ultimately found to account for such as the precession of the equinoxes but this phenomenon was not at the time in the contemplation of either party as one of the facts to be accounted for All the facts which they did contemplate we may believe on Dr Whewell’s authority to have accorded as accurately with the Cartesian hypothesis in its finally improved state as with Newton’s But it is not I conceive a valid reason for accepting any given hypothesis that we are unable to imagine any other which will account for the facts There is no necessity for supposing that the true explanation must be one which with only our present experience we could imagine Among the natural agents with which we are acquainted the vibrations of an elastic fluid may be the only one whose laws bear a close resemblance to those of light but we can not tell that there does not exist an unknown cause other than an elastic ether diffused through space yet producing effects identical in some respects with those which would result from the undulations of such an ether To assume that no such cause can exist appears to me an extreme case of assumption without evidence And at the risk of being charged with want of modesty I can not help expressing astonishment that a philosopher of Dr Whewell’s abilities and attainments should have written an elaborate treatise on the philosophy of induction in which he recognizes absolutely no mode of induction except that of trying hypothesis after hypothesis until one is found which fits the phenomena which one when found is to be assumed as true with no other reservation than that if on reexamination it should appear to assume more than is needful for explaining the phenomena the superfluous part of the assumption should be cut off And this without the slightest distinction between the cases in which it may be known beforehand that two different hypotheses can not lead to the same result and those in which for aught we can ever know the range of suppositions all equally consistent with the phenomena may be infinite Nevertheless I do not agree with M Comte in condemning those who employ themselves in working out into detail the application of these hypotheses to the explanation of ascertained facts provided they bear in mind that the utmost they can prove is not that the hypothesis is but that it may be true The ether hypothesis has a very strong claim to be so followed out a claim greatly strengthened since it has been shown to afford a mechanism which would explain the mode of production not of light only but also of heat Indeed the speculation has a smaller element of hypothesis in its application to heat than in the case for which it was originally framed We have proof by our senses of the existence of molecular movement among the particles of all heated bodies while we have no similar experience in the case of light When therefore heat is communicated from the sun to the earth across apparently empty space the chain of causation has molecular motion both at the beginning and end The hypothesis only makes the motion continuous by extending it to the middle Now motion in a body is known to be capable of being imparted to another body contiguous to it and the intervention of a hypothetical elastic fluid occupying the space between the sun and the earth supplies the contiguity which is the only condition wanting and which can be supplied by no supposition but that of an intervening medium The supposition notwithstanding is at best a probable conjecture not a proved truth For there is no proof that contiguity is absolutely required for the communication of motion from one body to another Contiguity does not always exist to our senses at least in the cases in which motion produces motion The forces which go under the name of attraction especially the greatest of all gravitation are examples of motion producing motion without apparent contiguity When a planet moves its distant satellites accompany its motion The sun carries the whole solar system along with it in the progress which it is ascertained to be executing through space And even if we were to accept as conclusive the geometrical reasonings strikingly similar to those by which the Cartesians defended their vortices by which it has been attempted to show that the motions of the ether may account for gravitation itself even then it would only have been proved that the supposed mode of production may be but not that no other mode can be the true one It is necessary before quitting the subject of hypotheses to guard against the appearance of reflecting upon the scientific value of several branches of physical inquiry which though only in their infancy I hold to be strictly inductive There is a great difference between inventing agencies to account for classes of phenomena and endeavouring in conformity with known laws to conjecture what former collocations of known agents may have given birth to individual facts still in existence The latter is the legitimate operation of inferring from an observed effect the existence in time past of a cause similar to that by which we know it to be produced in all cases in which we have actual experience of its origin This for example is the scope of the inquiries of geology and they are no more illogical or visionary than judicial inquiries which also aim at discovering a past event by inference from those of its effects which still subsist As we can ascertain whether a man was murdered or died a natural death from the indications exhibited by the corpse the presence or absence of signs of struggling on the ground or on the adjacent objects the marks of blood the footsteps of the supposed murderers and so on proceeding throughout on uniformities ascertained by a perfect induction without any mixture of hypothesis so if we find on and beneath the surface of our planet masses exactly similar to deposits from water or to results of the cooling of matter melted by fire we may justly conclude that such has been their origin and if the effects though similar in kind are on a far larger scale than any which are now produced we may rationally and without hypothesis conclude either that the causes existed formerly with greater intensity or that they have operated during an enormous length of time Further than this no geologist of authority has since the rise of the present enlightened school of geological speculation attempted to go In many geological inquiries it doubtless happens that though the laws to which the phenomena are ascribed are known laws and the agents known agents those agents are not known to have been present in the particular case In the speculation respecting the igneous origin of trap or granite the fact does not admit of direct proof that those substances have been actually subjected to intense heat But the same thing might be said of all judicial inquiries which proceed on circumstantial evidence We can conclude that a man was murdered though it is not proved by the testimony of eyewitnesses that some person who had the intention of murdering him was present on the spot It is enough for most purposes if no other known cause could have generated the effects shown to have been produced The celebrated speculation of Laplace concerning the origin of the earth and planets participates essentially in the inductive character of modern geological theory The speculation is that the atmosphere of the sun originally extended to the present limits of the solar system from which by the process of cooling it has contracted to its present dimensions and since by the general principles of mechanics the rotation of the sun and of its accompanying atmosphere must increase in rapidity as its volume diminishes the increased centrifugal force generated by the more rapid rotation overbalancing the action of gravitation has caused the sun to abandon successive rings of vaporous matter which are supposed to have condensed by cooling and to have become the planets There is in this theory no unknown substance introduced on supposition nor any unknown property or law ascribed to a known substance The known laws of matter authorize us to suppose that a body which is constantly giving out so large an amount of heat as the sun is must be progressively cooling and that by the process of cooling it must contract if therefore we endeavour from the present state of that luminary to infer its state in a time long past we must necessarily suppose that its atmosphere extended much farther than at present and we are entitled to suppose that it extended as far as we can trace effects such as it might naturally leave behind it on retiring and such the planets are These suppositions being made it follows from known laws that successive zones of the solar atmosphere might be abandoned that these would continue to revolve round the sun with the same velocity as when they formed part of its substance and that they would cool down long before the sun itself to any given temperature and consequently to that at which the greater part of the vaporous matter of which they consisted would become liquid or solid The known law of gravitation would then cause them to agglomerate in masses which would assume the shape our planets actually exhibit would acquire each about its own axis a rotatory movement and would in that state revolve as the planets actually do about the sun in the same direction with the sun’s rotation but with less velocity because in the same periodic time which the sun’s rotation occupied when his atmosphere extended to that point There is thus in Laplace’s theory nothing strictly speaking hypothetical it is an example of legitimate reasoning from a present effect to a possible past cause according to the known laws of that cause The theory therefore is as I have said of a similar character to the theories of geologists but considerably inferior to them in point of evidence Even if it were proved which it is not that the conditions necessary for determining the breaking off of successive rings would certainly occur there would still be a much greater chance of error in assuming that the existing laws of nature are the same which existed at the origin of the solar system than in merely presuming with geologists that those laws have lasted through a few revolutions and transformations of a single one among the bodies of which that system is composed In the last four chapters we have traced the general outlines of the theory of the generation of derivative laws from ultimate ones In the present chapter our attention will be directed to a particular case of the derivation of laws from other laws but a case so general and so important as not only to repay but to require a separate examination This is the case of a complex phenomenon resulting from one simple law by the continual addition of an effect to itself There are some phenomena some bodily sensations for example which are essentially instantaneous and whose existence can only be prolonged by the prolongation of the existence of the cause by which they are produced But most phenomena are in their own nature permanent having begun to exist they would exist forever unless some cause intervened having a tendency to alter or destroy them Such for example are all the facts of phenomena which we call bodies Water once produced will not of itself relapse into a state of hydrogen and oxygen such a change requires some agent having the power of decomposing the compound Such again are the positions in space and the movements of bodies No object at rest alters its position without the intervention of some conditions extraneous to itself and when once in motion no object returns to a state of rest or alters either its direction or its velocity unless some new external conditions are superinduced It therefore perpetually happens that a temporary cause gives rise to a permanent effect The contact of iron with moist air for a few hours produces a rust which may endure for centuries or a projectile force which launches a cannonball into space produces a motion which would continue forever unless some other force counteracted it Between the two examples which we have here given there is a difference worth pointing out In the former in which the phenomenon produced is a substance and not a motion of a substance since the rust remains forever and unaltered unless some new cause supervenes we may speak of the contact of air a hundred years ago as even the proximate cause of the rust which has existed from that time until now But when the effect is motion which is itself a change we must use a different language The permanency of the effect is now only the permanency of a series of changes The second foot or inch or mile of motion is not the mere prolonged duration of the first foot or inch or mile but another fact which succeeds and which may in some respects be very unlike the former since it carries the body through a different region of space Now the original projectile force which set the body moving is the remote cause of all its motion however long continued but the proximate cause of no motion except that which took place at the first instant The motion at any subsequent instant is proximately caused by the motion which took place at the instant preceding It is on that and not on the original moving cause that the motion at any given moment depends For suppose that the body passes through some resisting medium which partially counteracts the effect of the original impulse and retards the motion this counteraction it need scarcely here be repeated is as strict an example of obedience to the law of the impulse as if the body had gone on moving with its original velocity but the motion which results is different being now a compound of the effects of two causes acting in contrary directions instead of the single effect of one cause Now what cause does the body obey in its subsequent motion The original cause of motion or the actual motion at the preceding instant The latter for when the object issues from the resisting medium it continues moving not with its original but with its retarded velocity The motion having once been diminished all that which follows is diminished The effect changes because the cause which it really obeys the proximate cause the real cause in fact has changed This principle is recognized by mathematicians when they enumerate among the causes by which the motion of a body is at any instant determined the force generated by the previous motion an expression which would be absurd if taken to imply that this force was an intermediate link between the cause and the effect but which really means only the previous motion itself considered as a cause of further motion We must therefore if we would speak with perfect precision consider each link in the succession of motions as the effect of the link preceding it But if for the convenience of discourse we speak of the whole series as one effect it must be as an effect produced by the original impelling force a permanent effect produced by an instantaneous cause and possessing the property of selfperpetuation Let us now suppose that the original agent or cause instead of being instantaneous is permanent Whatever effect has been produced up to a given time would unless prevented by the intervention of some new cause subsist permanently even if the cause were to perish Since however the cause does not perish but continues to exist and to operate it must go on producing more and more of the effect and instead of a uniform effect we have a progressive series of effects arising from the accumulated influence of a permanent cause Thus the contact of iron with the atmosphere causes a portion of it to rust and if the cause ceased the effect already produced would be permanent but no further effect would be added If however the cause namely exposure to moist air continues more and more of the iron becomes rusted until all which is exposed is converted into a red powder when one of the conditions of the production of rust namely the presence of unoxidized iron has ceased and the effect can not any longer be produced Again the earth causes bodies to fall toward it that is the existence of the earth at a given instant causes an unsupported body to move toward it at the succeeding instant and if the earth were annihilated as much of the effect as is already produced would continue the object would go on moving in the same direction with its acquired velocity until intercepted by some body or deflected by some other force The earth however not being annihilated goes on producing in the second instant an effect similar and of equal amount with the first which two effects being added together there results an accelerated velocity and this operation being repeated at each successive instant the mere permanence of the cause though without increase gives rise to a constant progressive increase of the effect so long as all the conditions negative and positive of the production of that effect continue to be realized It is obvious that this state of things is merely a case of the Composition of Causes A cause which continues in action must on a strict analysis be considered as a number of causes exactly similar successively introduced and producing by their combination the sum of the effects which they would severally produce if they acted singly The progressive rusting of the iron is in strictness the sum of the effects of many particles of air acting in succession upon corresponding particles of iron The continued action of the earth upon a falling body is equivalent to a series of forces applied in successive instants each tending to produce a certain constant quantity of motion and the motion at each instant is the sum of the effects of the new force applied at the preceding instant and the motion already acquired In each instant a fresh effect of which gravity is the proximate cause is added to the effect of which it was the remote cause or to express the same thing in another manner the effect produced by the earth’s influence at the instant last elapsed is added to the sum of the effects of which the remote causes were the influences exerted by the earth at all the previous instants since the motion began The case therefore comes under the principle of a concurrence of causes producing an effect equal to the sum of their separate effects But as the causes come into play not all at once but successively and as the effect at each instant is the sum of the effects of those causes only which have come into action up to that instant the result assumes the form of an ascending series a succession of sums each greater than that which preceded it and we have thus a progressive effect from the continued action of a cause Since the continuance of the cause influences the effect only by adding to its quantity and since the addition takes place according to a fixed law equal quantities in equal times the result is capable of being computed on mathematical principles In fact this case being that of infinitesimal increments is precisely the case which the differential calculus was invented to meet The questions what effect will result from the continual addition of a given cause to itself and what amount of the cause being continually added to itself will produce a given amount of the effect are evidently mathematical questions and to be treated therefore deductively If as we have seen cases of the Composition of Causes are seldom adapted for any other than deductive investigation this is especially true in the case now examined the continual composition of a cause with its own previous effects since such a case is peculiarly amenable to the deductive method while the undistinguishable manner in which the effects are blended with one another and with the causes must make the treatment of such an instance experimentally still more chimerical than in any other case We shall next advert to a rather more intricate operation of the same principle namely when the cause does not merely continue in action but undergoes during the same time a progressive change in those of its circumstances which contribute to determine the effect In this case as in the former the total effect goes on accumulating by the continual addition of a fresh effect to that already produced but it is no longer by the addition of equal quantities in equal times the quantities added are unequal and even the quality may now be different If the change in the state of the permanent cause be progressive the effect will go through a double series of changes arising partly from the accumulated action of the cause and partly from the changes in its action The effect is still a progressive effect produced however not by the mere continuance of a cause but by its continuance and its progressiveness combined A familiar example is afforded by the increase of the temperature as summer advances that is as the sun draws nearer to a vertical position and remains a greater number of hours above the horizon This instance exemplifies in a very interesting manner the twofold operation on the effect arising from the continuance of the cause and from its progressive change When once the sun has come near enough to the zenith and remains above the horizon long enough to give more warmth during one diurnal rotation than the counteracting cause the earth’s radiation can carry off the mere continuance of the cause would progressively increase the effect even if the sun came no nearer and the days grew no longer but in addition to this a change takes place in the accidents of the cause its series of diurnal positions tending to increase the quantity of the effect When the summer solstice has passed the progressive change in the cause begins to take place the reverse way but for some time the accumulating effect of the mere continuance of the cause exceeds the effect of the changes in it and the temperature continues to increase Again the motion of a planet is a progressive effect produced by causes at once permanent and progressive The orbit of a planet is determined omitting perturbations by two causes first the action of the central body a permanent cause which alternately increases and diminishes as the planet draws nearer to or goes farther from its perihelion and which acts at every point in a different direction and secondly the tendency of the planet to continue moving in the direction and with the velocity which it has already acquired This force also grows greater as the planet draws nearer to its perihelion because as it does so its velocity increases and less as it recedes from its perihelion and this force as well as the other acts at each point in a different direction because at every point the action of the central force by deflecting the planet from its previous direction alters the line in which it tends to continue moving The motion at each instant is determined by the amount and direction of the motion and the amount and direction of the sun’s action at the previous instant and if we speak of the entire revolution of the planet as one phenomenon which as it is periodical and similar to itself we often find it convenient to do that phenomenon is the progressive effect of two permanent and progressive causes the central force and the acquired motion Those causes happening to be progressive in the particular way which is called periodical the effect necessarily is so too because the quantities to be added together returning in a regular order the same sums must also regularly return This example is worthy of consideration also in another respect Though the causes themselves are permanent and independent of all conditions known to us the changes which take place in the quantities and relations of the causes are actually caused by the periodical changes in the effects The causes as they exist at any moment having produced a certain motion that motion becoming itself a cause reacts upon the causes and produces a change in them By altering the distance and direction of the central body relatively to the planet and the direction and quantity of the force in the direction of the tangent it alters the elements which determine the motion at the next succeeding instant This change renders the next motion somewhat different and this difference by a fresh reaction upon the causes renders the next motion again different and so on The original state of the causes might have been such that this series of actions modified by reactions would not have been periodical The sun’s action and the original impelling force might have been in such a ratio to one another that the reaction of the effect would have been such as to alter the causes more and more without ever bringing them back to what they were at any former time The planet would then have moved in a parabola or an hyperbola curves not returning into themselves The quantities of the two forces were however originally such that the successive reactions of the effect bring back the causes after a certain time to what they were before and from that time all the variations continued to recur again and again in the same periodical order and must so continue while the causes subsist and are not counteracted In all cases of progressive effects whether arising from the accumulation of unchanging or of changing elements there is a uniformity of succession not merely between the cause and the effect but between the first stages of the effect and its subsequent stages That a body in vacuo falls sixteen feet in the first second fortyeight in the second and so on in the ratio of the odd numbers is as much a uniform sequence as that when the supports are removed the body falls The sequence of spring and summer is as regular and invariable as that of the approach of the sun and spring but we do not consider spring to be the cause of summer it is evident that both are successive effects of the heat received from the sun and that considered merely in itself spring might continue forever without having the slightest tendency to produce summer As we have so often remarked not the conditional but the unconditional invariable antecedent is termed the cause That which would not be followed by the effect unless something else had preceded and which if that something else had preceded would not have been required is not the cause however invaluable the sequence may in fact be It is in this way that most of those uniformities of succession are generated which are not cases of causation When a phenomenon goes on increasing or periodically increases and diminishes or goes through any continued and unceasing process of variation reducible to a uniform rule or law of succession we do not on this account presume that any two successive terms of the series are cause and effect We presume the contrary we expect to find that the whole series originates either from the continued action of fixed causes or from causes which go through a corresponding process of continuous change A tree grows from half an inch high to a hundred feet and some trees will generally grow to that height unless prevented by some counteracting cause But we do not call the seedling the cause of the fullgrown tree the invariable antecedent it certainly is and we know very imperfectly on what other antecedents the sequence is contingent but we are convinced that it is contingent on something because the homogeneousness of the antecedent with the consequent the close resemblance of the seedling to the tree in all respects except magnitude and the graduality of the growth so exactly resembling the progressively accumulating effect produced by the long action of some one cause leave no possibility of doubting that the seedling and the tree are two terms in a series of that description the first term of which is yet to seek The conclusion is further confirmed by this that we are able to prove by strict induction the dependence of the growth of the tree and even of the continuance of its existence upon the continued repetition of certain processes of nutrition the rise of the sap the absorptions and exhalations by the leaves etc and the same experiments would probably prove to us that the growth of the tree is the accumulated sum of the effects of these continued processes were we not for want of sufficiently microscopic eyes unable to observe correctly and in detail what those effects are This supposition by no means requires that the effect should not during its progress undergo many modifications besides those of quantity or that it should not sometimes appear to undergo a very marked change of character This may be either because the unknown cause consists of several component elements or agents whose effects accumulating according to different laws are compounded in different proportions at different periods in the existence of the organized being or because at certain points in its progress fresh causes or agencies come in or are evolved which intermix their laws with those of the prime agent Scientific inquirers give the name of Empirical Laws to those uniformities which observation or experiment has shown to exist but on which they hesitate to rely in cases varying much from those which have been actually observed for want of seeing any reason why such a law should exist It is implied therefore in the notion of an empirical law that it is not an ultimate law that if true at all its truth is capable of being and requires to be accounted for It is a derivative law the derivation of which is not yet known To state the explanation the why of the empirical law would be to state the laws from which it is derived the ultimate causes on which it is contingent And if we knew these we should also know what are its limits under what conditions it would cease to be fulfilled The periodical return of eclipses as originally ascertained by the persevering observation of the early Eastern astronomers was an empirical law until the general laws of the celestial motions had accounted for it The following are empirical laws still waiting to be resolved into the simpler laws from which they are derived the local laws of the flux and reflux of the tides in different places the succession of certain kinds of weather to certain appearances of sky the apparent exceptions to the almost universal truth that bodies expand by increase of temperature the law that breeds both animal and vegetable are improved by crossing that gases have a strong tendency to permeate animal membranes that substances containing a very high proportion of nitrogen such as hydrocyanic acid and morphia are powerful poisons that when different metals are fused together the alloy is harder than the various elements that the number of atoms of acid required to neutralize one atom of any base is equal to the number of atoms of oxygen in the base that the solubility of substances in one another depends at least in some degree on the similarity of their elements An empirical law then is an observed uniformity presumed to be resolvable into simpler laws but not yet resolved into them The ascertainment of the empirical laws of phenomena often precedes by a long interval the explanation of those laws by the Deductive Method and the verification of a deduction usually consists in the comparison of its results with empirical laws previously ascertained From a limited number of ultimate laws of causation there are necessarily generated a vast number of derivative uniformities both of succession and coexistence Some are laws of succession or of coexistence between different effects of the same cause of these we had examples in the last chapter Some are laws of succession between effects and their remote causes resolvable into the laws which connect each with the intermediate link Thirdly when causes act together and compound their effects the laws of those causes generate the fundamental law of the effect namely that it depends on the coexistence of those causes And finally the order of succession or of coexistence which obtains among effects necessarily depends on their causes If they are effects of the same cause it depends on the laws of that cause if on different causes it depends on the laws of those causes severally and on the circumstances which determine their coexistence If we inquire further when and how the causes will coexist that again depends on their causes and we may thus trace back the phenomena higher and higher until the different series of effects meet in a point and the whole is shown to have depended ultimately on some common cause or until instead of converging to one point they terminate in different points and the order of the effects is proved to have arisen from the collocation of some of the primeval causes or natural agents For example the order of succession and of coexistence among the heavenly motions which is expressed by Kepler’s laws is derived from the coexistence of two primeval causes the sun and the original impulse or projectile force belonging to each planet Kepler’s laws are resolved into the laws of these causes and the fact of their coexistence Derivative laws therefore do not depend solely on the ultimate laws into which they are resolvable they mostly depend on those ultimate laws and an ultimate fact namely the mode of coexistence of some of the component elements of the universe The ultimate laws of causation might be the same as at present and yet the derivative laws completely different if the causes coexisted in different proportions or with any difference in those of their relations by which the effects are influenced If for example the sun’s attraction and the original projectile force had existed in some other ratio to one another than they did and we know of no reason why this should not have been the case the derivative laws of the heavenly motions might have been quite different from what they are The proportions which exist happen to be such as to produce regular elliptical motions any other proportions would have produced different ellipses or circular or parabolic or hyperbolic motions but still regular ones because the effects of each of the agents accumulate according to a uniform law and two regular series of quantities when their corresponding terms are added must produce a regular series of some sort whatever the quantities themselves are Now this lastmentioned element in the resolution of a derivative law the element which is not a law of causation but a collocation of causes can not itself be reduced to any law There is as formerly remarked no uniformity no norma principle or rule perceivable in the distribution of the primeval natural agents through the universe The different substances composing the earth the powers that pervade the universe stand in no constant relation to one another One substance is more abundant than others one power acts through a larger extent of space than others without any pervading analogy that we can discover We not only do not know of any reason why the sun’s attraction and the force in the direction of the tangent coexist in the exact proportion they do but we can trace no coincidence between it and the proportions in which any other elementary powers in the universe are intermingled The utmost disorder is apparent in the combination of the causes which is consistent with the most regular order in their effects for when each agent carries on its own operations according to a uniform law even the most capricious combination of agencies will generate a regularity of some sort as we see in the kaleidoscope where any casual arrangement of coloured bits of glass produces by the laws of reflection a beautiful regularity in the effect In the above considerations lies the justification of the limited degree of reliance which scientific inquirers are accustomed to place in empirical laws A derivative law which results wholly from the operation of some one cause will be as universally true as the laws of the cause itself that is it will always be true except where some one of those effects of the cause on which the derivative law depends is defeated by a counteracting cause But when the derivative law results not from different effects of one cause but from effects of several causes we can not be certain that it will be true under any variation in the mode of coexistence of those causes or of the primitive natural agents on which the causes ultimately depend The proposition that coalbeds rest on certain descriptions of strata exclusively though true on the earth so far as our observation has reached can not be extended to the moon or the other planets supposing coal to exist there because we can not be assured that the original constitution of any other planet was such as to produce the different depositions in the same order as in our globe The derivative law in this case depends not solely on laws but on a collocation and collocations can not be reduced to any law Now it is the very nature of a derivative law which has not yet been resolved into its elements in other words an empirical law that we do not know whether it results from the different effects of one cause or from effects of different causes We can not tell whether it depends wholly on laws or partly on laws and partly on a collocation If it depends on a collocation it will be true in all the cases in which that particular collocation exists But since we are entirely ignorant in case of its depending on a collocation what the collocation is we are not safe in extending the law beyond the limits of time and place in which we have actual experience of its truth Since within those limits the law has always been found true we have evidence that the collocations whatever they are on which it depends do really exist within those limits But knowing of no rule or principle to which the collocations themselves conform we can not conclude that because a collocation is proved to exist within certain limits of place or time it will exist beyond those limits Empirical laws therefore can only be received as true within the limits of time and place in which they have been found true by observation and not merely the limits of time and place but of time place and circumstance for since it is the very meaning of an empirical law that we do not know the ultimate laws of causation on which it is dependent we can not foresee without actual trial in what manner or to what extent the introduction of any new circumstance may affect it But how are we to know that a uniformity ascertained by experience is only an empirical law Since by the supposition we have not been able to resolve it into any other laws how do we know that it is not an ultimate law of causation I answer that no generalization amounts to more than an empirical law when the only proof on which it rests is that of the Method of Agreement For it has been seen that by that method alone we never can arrive at causes The utmost that the Method of Agreement can do is to ascertain the whole of the circumstances common to all cases in which a phenomenon is produced and this aggregate includes not only the cause of the phenomenon but all phenomena with which it is connected by any derivative uniformity whether as being collateral effects of the same cause or effects of any other cause which in all the instances we have been able to observe coexisted with it The method affords no means of determining which of these uniformities are laws of causation and which are merely derivative laws resulting from those laws of causation and from the collocation of the causes None of them therefore can be received in any other character than that of derivative laws the derivation of which has not been traced in other words empirical laws in which light all results obtained by the Method of Agreement and therefore almost all truths obtained by simple observation without experiment must be considered until either confirmed by the Method of Difference or explained deductively in other words accounted for a priori These empirical laws may be of greater or less authority according as there is reason to presume that they are resolvable into laws only or into laws and collocations together The sequences which we observe in the production and subsequent life of an animal or a vegetable resting on the Method of Agreement only are mere empirical laws but though the antecedents in those sequences may not be the causes of the consequents both the one and the other are doubtless in the main successive stages of a progressive effect originating in a common cause and therefore independent of collocations The uniformities on the other hand in the order of superposition of strata on the earth are empirical laws of a much weaker kind since they not only are not laws of causation but there is no reason to believe that they depend on any common cause all appearances are in favour of their depending on the particular collocation of natural agents which at some time or other existed on our globe and from which no inference can be drawn as to the collocation which exists or has existed in any other portion of the universe Our definition of an empirical law including not only those uniformities which are not known to be laws of causation but also those which are provided there be reason to presume that they are not ultimate laws this is the proper place to consider by what signs we may judge that even if an observed uniformity be a law of causation it is not an ultimate but a derivative law The first sign is if between the antecedent a and the consequent b there be evidence of some intermediate link some phenomenon of which we can surmise the existence though from the imperfection of our senses or of our instruments we are unable to ascertain its precise nature and laws If there be such a phenomenon which may be denoted by the letter x it follows that even if a be the cause of b it is but the remote cause and that the law a causes b is resolvable into at least two laws a causes x and x causes b This is a very frequent case since the operations of nature mostly take place on so minute a scale that many of the successive steps are either imperceptible or very indistinctly perceived Take for example the laws of the chemical composition of substances as that hydrogen and oxygen being combined water is produced All we see of the process is that the two gases being mixed in certain proportions and heat or electricity being applied an explosion takes place the gases disappear and water remains There is no doubt about the law or about its being a law of causation But between the antecedent the gases in a state of mechanical mixture heated or electrified and the consequent the production of water there must be an intermediate process which we do not see For if we take any portion whatever of the water and subject it to analysis we find that it always contains hydrogen and oxygen nay the very same proportions of them namely twothirds in volume of hydrogen and onethird oxygen This is true of a single drop it is true of the minutest portion which our instruments are capable of appreciating Since then the smallest perceptible portion of the water contains both those substances portions of hydrogen and oxygen smaller than the smallest perceptible must have come together in every such minute portion of space must have come closer together than when the gases were in a state of mechanical mixture since to mention no other reasons the water occupies far less space than the gases Now as we can not see this contact or close approach of the minute particles we can not observe with what circumstances it is attended or according to what laws it produces its effects The production of water that is of the sensible phenomena which characterize the compound may be a very remote effect of those laws There may be innumerable intervening links and we are sure that there must be some Having full proof that corpuscular action of some kind takes place previous to any of the great transformations in the sensible properties of substances we can have no doubt that the laws of chemical action as at present known are not ultimate but derivative laws however ignorant we may be and even though we should forever remain ignorant of the nature of the laws of corpuscular action from which they are derived In like manner all the processes of vegetative life whether in the vegetable properly so called or in the animal body are corpuscular processes Nutrition is the addition of particles to one another sometimes merely replacing other particles separated and excreted sometimes occasioning an increase of bulk or weight so gradual that only after a long continuance does it become perceptible Various organs by means of peculiar vessels secrete from the blood fluids the component particles of which must have been in the blood but which differ from it most widely both in mechanical properties and in chemical composition Here then are abundance of unknown links to be filled up and there can be no doubt that the laws of the phenomena of vegetative or organic life are derivative laws dependent on properties of the corpuscles and of those elementary tissues which are comparatively simple combinations of corpuscles The first sign then from which a law of causation though hitherto unresolved may be inferred to be a derivative law is any indication of the existence of an intermediate link or links between the antecedent and the consequent The second is when the antecedent is an extremely complex phenomenon and its effects therefore probably in part at least compounded of the effects of its different elements since we know that the case in which the effect of the whole is not made up of the effects of its parts is exceptional the Composition of Causes being by far the more ordinary case We will illustrate this by two examples in one of which the antecedent is the sum of many homogeneous in the other of heterogeneous parts The weight of a body is made up of the weights of its minute particles a truth which astronomers express in its most general terms when they say that bodies at equal distances gravitate to one another in proportion to their quantity of matter All true propositions therefore which can be made concerning gravity are derivative laws the ultimate law into which they are all resolvable being that every particle of matter attracts every other As our second example we may take any of the sequences observed in meteorology for instance a diminution of the pressure of the atmosphere indicated by a fall of the barometer is followed by rain The antecedent is here a complex phenomenon made up of heterogeneous elements the column of the atmosphere over any particular place consisting of two parts a column of air and a column of aqueous vapor mixed with it and the change in the two together manifested by a fall of the barometer and followed by rain must be either a change in one of these or in the other or in both We might then even in the absence of any other evidence form a reasonable presumption from the invariable presence of both these elements in the antecedent that the sequence is probably not an ultimate law but a result of the laws of the two different agents a presumption only to be destroyed when we had made ourselves so well acquainted with the laws of both as to be able to affirm that those laws could not by themselves produce the observed result There are but few known cases of succession from very complex antecedents which have not either been actually accounted for from simpler laws or inferred with great probability from the ascertained existence of intermediate links of causation not yet understood to be capable of being so accounted for It is therefore highly probable that all sequences from complex antecedents are thus resolvable and that ultimate laws are in all cases comparatively simple If there were not the other reasons already mentioned for believing that the laws of organized nature are resolvable into simpler laws it would be almost a sufficient reason that the antecedents in most of the sequences are so very complex In the preceding discussion we have recognized two kinds of empirical laws those known to be laws of causation but presumed to be resolvable into simpler laws and those not known to be laws of causation at all Both these kinds of laws agree in the demand which they make for being explained by deduction and agree in being the appropriate means of verifying such deduction since they represent the experience with which the result of the deduction must be compared They agree further in this that until explained and connected with the ultimate laws from which they result they have not attained the highest degree of certainty of which laws are susceptible It has been shown on a former occasion that laws of causation which are derivative and compounded of simpler laws are not only as the nature of the case implies less general but even less certain than the simpler laws from which they result not in the same degree to be relied on as universally true The inferiority of evidence however which attaches to this class of laws is trifling compared with that which is inherent in uniformities not known to be laws of causation at all So long as these are unresolved we can not tell on how many collocations as well as laws their truth may be dependent we can never therefore extend them with any confidence to cases in which we have not assured ourselves by trial that the necessary collocation of causes whatever it may be exists It is to this class of laws alone that the property which philosophers usually consider as characteristic of empirical laws belongs in all its strictness the property of being unfit to be relied on beyond the limits of time place and circumstance in which the observations have been made These are empirical laws in a more emphatic sense and when I employ that term except where the context manifestly indicates the reverse I shall generally mean to designate those uniformities only whether of succession or of coexistence which are not known to be laws of causation Considering then as empirical laws only those observed uniformities respecting which the question whether they are laws of causation must remain undecided until they can be explained deductively or until some means are found of applying the Method of Difference to the case it has been shown in the preceding chapter that until a uniformity can in one or the other of these modes be taken out of the class of empirical laws and brought either into that of laws of causation or of the demonstrated results of laws of causation it can not with any assurance be pronounced true beyond the local and other limits within which it has been found so by actual observation It remains to consider how we are to assure ourselves of its truth even within those limits after what quantity of experience a generalization which rests solely on the Method of Agreement can be considered sufficiently established even as an empirical law In a former chapter when treating of the Methods of Direct Induction we expressly reserved this question and the time is now come for endeavouring to solve it We found that the Method of Agreement has the defect of not proving causation and can therefore only be employed for the ascertainment of empirical laws But we also found that besides this deficiency it labours under a characteristic imperfection tending to render uncertain even such conclusions as it is in itself adapted to prove This imperfection arises from Plurality of Causes Although two or more cases in which the phenomenon a has been met with may have no common antecedent except A this does not prove that there is any connection between a and A since a may have many causes and may have been produced in these different instances not by any thing which the instances had in common but by some of those elements in them which were different We nevertheless observed that in proportion to the multiplication of instances pointing to A as the antecedent the characteristic uncertainty of the method diminishes and the existence of a law of connection between A and a more nearly approaches to certainty It is now to be determined after what amount of experience this certainty may be deemed to be practically attained and the connection between A and a may be received as an empirical law This question may be otherwise stated in more familiar terms After how many and what sort of instances may it be concluded that an observed coincidence between two phenomena is not the effect of chance It is of the utmost importance for understanding the logic of induction that we should form a distinct conception of what is meant by chance and how the phenomena which common language ascribes to that abstraction are really produced Chance is usually spoken of in direct antithesis to law whatever it is supposed can not be ascribed to any law is attributed to chance It is however certain that whatever happens is the result of some law is an effect of causes and could have been predicted from a knowledge of the existence of those causes and from their laws If I turn up a particular card that is a consequence of its place in the pack Its place in the pack was a consequence of the manner in which the cards were shuffled or of the order in which they were played in the last game which again were effects of prior causes At every stage if we had possessed an accurate knowledge of the causes in existence it would have been abstractedly possible to foretell the effect An event occurring by chance may be better described as a coincidence from which we have no ground to infer a uniformity the occurrence of a phenomenon in certain circumstances without our having reason on that account to infer that it will happen again in those circumstances This however when looked closely into implies that the enumeration of the circumstances is not complete Whatever the fact be since it has occurred once we may be sure that if all the same circumstances were repeated it would occur again and not only if all but there is some particular portion of those circumstances on which the phenomenon is invariably consequent With most of them however it is not connected in any permanent manner its conjunction with those is said to be the effect of chance to be merely casual Facts casually conjoined are separately the effects of causes and therefore of laws but of different causes and causes not connected by any law It is incorrect then to say that any phenomenon is produced by chance but we may say that two or more phenomena are conjoined by chance that they coexist or succeed one another only by chance meaning that they are in no way related through causation that they are neither cause and effect nor effects of the same cause nor effects of causes between which there subsists any law of coexistence nor even effects of the same collocation of primeval causes If the same casual coincidence never occurred a second time we should have an easy test for distinguishing such from the coincidences which are the results of a law As long as the phenomena had been found together only once so long unless we knew some more general laws from which the coincidence might have resulted we could not distinguish it from a casual one but if it occurred twice we should know that the phenomena so conjoined must be in some way connected through their causes There is however no such test A coincidence may occur again and again and yet be only casual Nay it would be inconsistent with what we know of the order of nature to doubt that every casual coincidence will sooner or later be repeated as long as the phenomena between which it occurred do not cease to exist or to be reproduced The recurrence therefore of the same coincidence more than once or even its frequent recurrence does not prove that it is an instance of any law does not prove that it is not casual or in common language the effect of chance And yet when a coincidence can not be deduced from known laws nor proved by experiment to be itself a case of causation the frequency of its occurrence is the only evidence from which we can infer that it is the result of a law Not however its absolute frequency The question is not whether the coincidence occurs often or seldom in the ordinary sense of those terms but whether it occurs more often than chance will account for more often than might rationally be expected if the coincidence were casual We have to decide therefore what degree of frequency in a coincidence chance will account for and to this there can be no general answer We can only state the principle by which the answer must be determined the answer itself will be different in every different case Suppose that one of the phenomena A exists always and the other phenomenon B only occasionally it follows that every instance of B will be an instance of its coincidence with A and yet the coincidence will be merely casual not the result of any connection between them The fixed stars have been constantly in existence since the beginning of human experience and all phenomena that have come under human observation have in every single instance coexisted with them yet this coincidence though equally invariable with that which exists between any of those phenomena and its own cause does not prove that the stars are its cause nor that they are in anywise connected with it As strong a case of coincidence therefore as can possibly exist and a much stronger one in point of mere frequency than most of those which prove laws does not here prove a law why because since the stars exist always they must coexist with every other phenomenon whether connected with them by causation or not The uniformity great though it be is no greater than would occur on the supposition that no such connection exists On the other hand suppose that we were inquiring whether there be any connection between rain and any particular wind Rain we know occasionally occurs with every wind therefore the connection if it exists can not be an actual law but still rain may be connected with some particular wind through causation that is though they can not be always effects of the same cause for if so they would regularly coexist there may be some causes common to the two so that in so far as either is produced by those common causes they will from the laws of the causes be found to coexist How then shall we ascertain this The obvious answer is by observing whether rain occurs with one wind more frequently than with any other That however is not enough for perhaps that one wind blows more frequently than any other so that its blowing more frequently in rainy weather is no more than would happen although it had no connection with the causes of rain provided it were not connected with causes adverse to rain In England westerly winds blow during about twice as great a portion of the year as easterly If therefore it rains only twice as often with a westerly as with an easterly wind we have no reason to infer that any law of nature is concerned in the coincidence If it rains more than twice as often we may be sure that some law is concerned either there is some cause in nature which in this climate tends to produce both rain and a westerly wind or a westerly wind has itself some tendency to produce rain But if it rains less than twice as often we may draw a directly opposite inference the one instead of being a cause or connected with causes of the other must be connected with causes adverse to it or with the absence of some cause which produces it and though it may still rain much oftener with a westerly wind than with an easterly so far would this be from proving any connection between the phenomena that the connection proved would be between rain and an easterly wind to which in mere frequency of coincidence it is less allied Here then are two examples in one the greatest possible frequency of coincidence with no instance whatever to the contrary does not prove that there is any law in the other a much less frequency of coincidence even when noncoincidence is still more frequent does prove that there is a law In both cases the principle is the same In both we consider the positive frequency of the phenomena themselves and how great frequency of coincidence that must of itself bring about without supposing any connection between them provided there be no repugnance provided neither be connected with any cause tending to frustrate the other If we find a greater frequency of coincidence than this we conclude that there is some connection if a less frequency that there is some repugnance In the former case we conclude that one of the phenomena can under some circumstances cause the other or that there exists something capable of causing them both in the latter that one of them or some cause which produces one of them is capable of counteracting the production of the other We have thus to deduct from the observed frequency of coincidence as much as may be the effect of chance that is of the mere frequency of the phenomena themselves and if any thing remains what does remain is the residual fact which proves the existence of a law The frequency of the phenomena can only be ascertained within definite limits of space and time depending as it does on the quantity and distribution of the primeval natural agents of which we can know nothing beyond the boundaries of human observation since no law no regularity can be traced in it enabling us to infer the unknown from the known But for the present purpose this is no disadvantage the question being confined within the same limits as the data The coincidences occurred in certain places and times and within those we can estimate the frequency with which such coincidences would be produced by chance If then we find from observation that A exists in one case out of every two and B in one case out of every three then if there be neither connection nor repugnance between them or between any of their causes the instances in which A and B will both exist that is to say will coexist will be one case in every six For A exists in three cases out of six and B existing in one case out of every three without regard to the presence or absence of A will exist in one case out of those three There will therefore be of the whole number of cases two in which A exists without B one case of B without A two in which neither B nor A exists and one case out of six in which they both exist If then in point of fact, they are found to coexist oftener than in one case out of six and consequently A does not exist without B so often as twice in three times nor B without A so often as once in every twice there is some cause in existence which tends to produce a conjunction between A and B Generalizing the result we may say that if A occurs in a larger proportion of the cases where B is than of the cases where B is not then will B also occur in a larger proportion of the cases where A is than of the cases where A is not and there is some connection through causation between A and B If we could ascend to the causes of the two phenomena we should find at some stage either proximate or remote some cause or causes common to both and if we could ascertain what these are we could frame a generalization which would be true without restriction of place or time but until we can do so the fact of a connection between the two phenomena remains an empirical law Having considered in what manner it may be determined whether any given conjunction of phenomena is casual or the result of some law to complete the theory of chance it is necessary that we should now consider those effects which are partly the result of chance and partly of law or, in other words, in which the effects of casual conjunctions of causes are habitually blended in one result with the effects of a constant cause This is a case of Composition of Causes and the peculiarity of it is that instead of two or more causes intermixing their effects in a regular manner with those of one another we have now one constant cause producing an effect which is successively modified by a series of variable causes Thus as summer advances the approach of the sun to a vertical position tends to produce a constant increase of temperature but with this effect of a constant cause there are blended the effects of many variable causes winds clouds evaporation electric agencies and the like so that the temperature of any given day depends in part on these fleeting causes and only in part on the constant cause If the effect of the constant cause is always accompanied and disguised by effects of variable causes it is impossible to ascertain the law of the constant cause in the ordinary manner by separating it from all other causes and observing it apart Hence arises the necessity of an additional rule of experimental inquiry When the action of a cause A is liable to be interfered with not steadily by the same cause or causes but by different causes at different times and when these are so frequent or so indeterminate that we can not possibly exclude all of them from any experiment though we may vary them our resource is to endeavour to ascertain what is the effect of all the variable causes taken together In order to do this we make as many trials as possible preserving A invariable The results of these different trials will naturally be different since the indeterminate modifying causes are different in each if then we do not find these results to be progressive but on the contrary to oscillate about a certain point one experiment giving a result a little greater another a little less one a result tending a little more in one direction another a little more in the contrary direction while the average or middle point does not vary but different sets of experiments taken in as great a variety of circumstances as possible yield the same mean provided only they be sufficiently numerous then that mean or average result is the part in each experiment which is due to the cause A and is the effect which would have been obtained if A could have acted alone the variable remainder is the effect of chance that is of causes the coexistence of which with the cause A was merely casual The test of the sufficiency of the induction in this case is when any increase of the number of trials from which the average is struck does not materially alter the average This kind of elimination in which we do not eliminate any one assignable cause but the multitude of floating unassignable ones may be termed the Elimination of Chance We afford an example of it when we repeat an experiment in order by taking the mean of different results to get rid of the effects of the unavoidable errors of each individual experiment When there is no permanent cause such as would produce a tendency to error peculiarly in one direction we are warranted by experience in assuming that the errors on one side will in a certain number of experiments about balance the errors on the contrary side We therefore repeat the experiment until any change which is produced in the average of the whole by further repetition falls within limits of error consistent with the degree of accuracy required by the purpose we have in view In the supposition hitherto made the effect of the constant cause A has been assumed to form so great and conspicuous a part of the general result that its existence never could be a matter of uncertainty and the object of the eliminating process was only to ascertain how much is attributable to that cause what is its exact law Cases however occur in which the effect of a constant cause is so small compared with that of some of the changeable causes with which it is liable to be casually conjoined that of itself it escapes notice and the very existence of any effect arising from a constant cause is first learned by the process which in general serves only for ascertaining the quantity of that effect This case of induction may be characterized as follows A given effect is known to be chiefly and not known not to be wholly determined by changeable causes If it be wholly so produced then if the aggregate be taken of a sufficient number of instances the effects of these different causes will cancel one another If therefore we do not find this to be the case but on the contrary after such a number of trials has been made that no further increase alters the average result we find that average to be not zero but some other quantity about which though small in comparison with the total effect the effect nevertheless oscillates and which is the middle point in its oscillation we may conclude this to be the effect of some constant cause which cause by some of the methods already treated of we may hope to detect This may be called the discovery of a residual phenomenon by eliminating the effects of chance It is in this manner for example that loaded dice may be discovered Of course no dice are so clumsily loaded that they must always throw certain numbers otherwise the fraud would be instantly detected The loading a constant cause mingles with the changeable causes which determine what cast will be thrown in each individual instance If the dice were not loaded and the throw were left to depend entirely on the changeable causes these in a sufficient number of instances would balance one another and there would be no preponderant number of throws of any one kind If therefore after such a number of trials that no further increase of their number has any material effect upon the average we find a preponderance in favour of a particular throw we may conclude with assurance that there is some constant cause acting in favour of that throw or, in other words, that the dice are not fair and the exact amount of the unfairness In a similar manner what is called the diurnal variation of the barometer which is very small compared with the variations arising from the irregular changes in the state of the atmosphere was discovered by comparing the average height of the barometer at different hours of the day When this comparison was made it was found that there was a small difference which on the average was constant however the absolute quantities might vary and which difference therefore must be the effect of a constant cause This cause was afterward ascertained deductively to be the rarefaction of the air occasioned by the increase of temperature as the day advances After these general remarks on the nature of chance we are prepared to consider in what manner assurance may be obtained that a conjunction between two phenomena which has been observed a certain number of times is not casual but a result of causation and to be received therefore as one of the uniformities of nature though until accounted for a priori only as an empirical law We will suppose the strongest case namely that the phenomenon B has never been observed except in conjunction with A Even then the probability that they are connected is not measured by the total number of instances in which they have been found together but by the excess of that number above the number due to the absolutely frequency of A If for example A exists always and therefore coexists with every thing no number of instances of its coexistence with B would prove a connection as in our example of the fixed stars If A be a fact of such common occurrence that it may be presumed to be present in half of all the cases that occur and therefore in half the cases in which B occurs it is only the proportional excess above half that is to be reckoned as evidence toward proving a connection between A and B In addition to the question What is the number of coincidences which on an average of a great multitude of trials may be expected to arise from chance alone there is also another question namely Of what extent of deviation from that average is the occurrence credible from chance alone in some number of instances smaller than that required for striking a fair average It is not only to be considered what is the general result of the chances in the long run but also what are the extreme limits of variation from the general result which may occasionally be expected as the result of some smaller number of instances The consideration of the latter question and any consideration of the former beyond that already given to it belong to what mathematicians term the doctrine of chances or in a phrase of greater pretension the Theory of Probabilities Probability says Laplace has reference partly to our ignorance partly to our knowledge We know that among three or more events one and only one must happen but there is nothing leading us to believe that any one of them will happen rather than the others In this state of indecision it is impossible for us to pronounce with certainty on their occurrence It is however probable that any one of these events selected at pleasure will not take place because we perceive several cases all equally possible which exclude its occurrence and only one which favors it The theory of chances consists in reducing all events of the same kind to a certain number of cases equally possible that is such that we are equally undecided as to their existence and in determining the number of these cases which are favourable to the event of which the probability is sought The ratio of that number to the number of all the possible cases is the measure of the probability which is thus a fraction having for its numerator the number of cases favourable to the event and for its denominator the number of all the cases which are possible To a calculation of chances then according to Laplace two things are necessary we must know that of several events some one will certainly happen and no more than one and we must not know nor have any reason to expect that it will be one of these events rather than another It has been contended that these are not the only requisites and that Laplace has overlooked in the general theoretical statement a necessary part of the foundation of the doctrine of chances To be able it has been said to pronounce two events equally probable it is not enough that we should know that one or the other must happen and should have no grounds for conjecturing which Experience must have shown that the two events are of equally frequent occurrence Why in tossing up a halfpenny do we reckon it equally probable that we shall throw cross or pile Because we know that in any great number of throws cross and pile are thrown about equally often and that the more throws we make the more nearly the equality is perfect We may know this if we please by actual experiment or by the daily experience which life affords of events of the same general character or deductively from the effect of mechanical laws on a symmetrical body acted upon by forces varying indefinitely in quantity and direction We may know it in short either by specific experience or on the evidence of our general knowledge of nature But in one way or the other we must know it to justify us in calling the two events equally probable and if we knew it not we should proceed as much at haphazard in staking equal sums on the result as in laying odds This view of the subject was taken in the first edition of the present work but I have since become convinced that the theory of chances as conceived by Laplace and by mathematicians generally has not the fundamental fallacy which I had ascribed to it We must remember that the probability of an event is not a quality of the event itself but a mere name for the degree of ground which we or some one else have for expecting it The probability of an event to one person is a different thing from the probability of the same event to another or to the same person after he has acquired additional evidence The probability to me that an individual of whom I know nothing but his name will die within the year is totally altered by my being told the next minute that he is in the last stage of a consumption Yet this makes no difference in the event itself nor in any of the causes on which it depends Every event is in itself certain not probable if we knew all we should either know positively that it will happen or positively that it will not But its probability to us means the degree of expectation of its occurrence which we are warranted in entertaining by our present evidence Bearing this in mind I think it must be admitted that even when we have no knowledge whatever to guide our expectations except the knowledge that what happens must be some one of a certain number of possibilities we may still reasonably judge that one supposition is more probable to us than another supposition and if we have any interest at stake we shall best provide for it by acting conformably to that judgment Suppose that we are required to take a ball from a box of which we only know that it contains balls both black and white and none of any other colour We know that the ball we select will be either a black or a white ball but we have no ground for expecting black rather than white or white rather than black In that case if we are obliged to make a choice and to stake something on one or the other supposition it will as a question of prudence be perfectly indifferent which and we shall act precisely as we should have acted if we had known beforehand that the box contained an equal number of black and white balls But though our conduct would be the same it would not be founded on any surmise that the balls were in fact thus equally divided for we might on the contrary know by authentic information that the box contained ninetynine balls of one colour and only one of the other still if we are not told which colour has only one and which has ninetynine the drawing of a white and of a black ball will be equally probable to us We shall have no reason for staking any thing on the one event rather than on the other the option between the two will be a matter of indifference in other words it will be an even chance But let it now be supposed that instead of two there are three colours white black and red and that we are entirely ignorant of the proportion in which they are mingled We should then have no reason for expecting one more than another and if obliged to bet should venture our stake on red white or black with equal indifference But should we be indifferent whether we betted for or against some one colour as for instance white Surely not From the very fact that black and red are each of them separately equally probable to us with white the two together must be twice as probable We should in this case expect not white rather than white and so much rather that we would lay two to one upon it It is true there might for aught we knew be more white balls than black and red together and if so our bet would if we knew more be seen to be a disadvantageous one But so also for aught we knew might there be more red balls than black and white or more black balls than white and red and in such case the effect of additional knowledge would be to prove to us that our bet was more advantageous than we had supposed it to be There is in the existing state of our knowledge a rational probability of two to one against white a probability fit to be made a basis of conduct No reasonable person would lay an even wager in favour of white against black and red though against black alone or red alone he might do so without imprudence The common theory therefore of the calculation of chances appears to be tenable Even when we know nothing except the number of the possible and mutually excluding contingencies and are entirely ignorant of their comparative frequency we may have grounds and grounds numerically appreciable for acting on one supposition rather than on another and this is the meaning of Probability The principle however on which the reasoning proceeds is sufficiently evident It is the obvious one that when the cases which exist are shared among several kinds it is impossible that each of those kinds should be a majority of the whole on the contrary there must be a majority against each kind except one at most and if any kind has more than its share in proportion to the total number the others collectively must have less Granting this axiom and assuming that we have no ground for selecting any one kind as more likely than the rest to surpass the average proportion it follows that we can not rationally presume this of any which we should do if we were to bet in favour of it receiving less odds than in the ratio of the number of the other kinds Even therefore in this extreme case of the calculation of probabilities which does not rest on special experience at all the logical ground of the process is our knowledge such knowledge as we then have of the laws governing the frequency of occurrence of the different cases but in this case the knowledge is limited to that which being universal and axiomatic does not require reference to specific experience or to any considerations arising out of the special nature of the problem under discussion Except however in such cases as games of chance where the very purpose in view requires ignorance instead of knowledge I can conceive no case in which we ought to be satisfied with such an estimate of chances as this an estimate founded on the absolute minimum of knowledge respecting the subject It is plain that in the case of the coloured balls a very slight ground of surmise that the white balls were really more numerous than either of the other colours would suffice to vitiate the whole of the calculations made in our previous state of indifference It would place us in that position of more advanced knowledge in which the probabilities to us would be different from what they were before and in estimating these new probabilities we should have to proceed on a totally different set of data furnished no longer by mere counting of possible suppositions but by specific knowledge of facts Such data it should always be our endeavour to obtain and in all inquiries unless on subjects equally beyond the range of our means of knowledge and our practical uses they may be obtained if not good at least better than none at all It is obvious too that even when the probabilities are derived from observation and experiment a very slight improvement in the data by better observations or by taking into fuller consideration the special circumstances of the case is of more use than the most elaborate application of the calculus to probabilities founded on the data in their previous state of inferiority The neglect of this obvious reflection has given rise to misapplications of the calculus of probabilities which have made it the real opprobrium of mathematics It is sufficient to refer to the applications made of it to the credibility of witnesses and to the correctness of the verdicts of juries In regard to the first common sense would dictate that it is impossible to strike a general average of the veracity and other qualifications for true testimony of mankind or of any class of them and even if it were possible the employment of it for such a purpose implies a misapprehension of the use of averages which serve indeed to protect those whose interest is at stake against mistaking the general result of large masses of instances but are of extremely small value as grounds of expectation in any one individual instance unless the case be one of those in which the great majority of individual instances do not differ much from the average In the case of a witness persons of common sense would draw their conclusions from the degree of consistency of his statements his conduct under crossexamination and the relation of the case itself to his interests his partialities and his mental capacity instead of applying so rude a standard even if it were capable of being verified as the ratio between the number of true and the number of erroneous statements which he may be supposed to make in the course of his life Again on the subject of juries or other tribunals some mathematicians have set out from the proposition that the judgment of any one judge or juryman is at least in some small degree more likely to be right than wrong and have concluded that the chance of a number of persons concurring in a wrong verdict is diminished the more the number is increased so that if the judges are only made sufficiently numerous the correctness of the judgment may be reduced almost to certainty I say nothing of the disregard shown to the effect produced on the moral position of the judges by multiplying their numbers the virtual destruction of their individual responsibility and weakening of the application of their minds to the subject I remark only the fallacy of reasoning from a wide average to cases necessarily differing greatly from any average It may be true that taking all causes one with another the opinion of any one of the judges would be oftener right than wrong but the argument forgets that in all but the more simple cases in all cases in which it is really of much consequence what the tribunal is the proposition might probably be reversed besides which the cause of error whether arising from the intricacy of the case or from some common prejudice or mental infirmity if it acted upon one judge would be extremely likely to affect all the others in the same manner or at least a majority and thus render a wrong instead of a right decision more probable the more the number was increased These are but samples of the errors frequently committed by men who having made themselves familiar with the difficult formulae which algebra affords for the estimation of chances under suppositions of a complex character like better to employ those formulae in computing what are the probabilities to a person half informed about a case than to look out for means of being better informed Before applying the doctrine of chances to any scientific purpose the foundation must be laid for an evaluation of the chances by possessing ourselves of the utmost attainable amount of positive knowledge The knowledge required is that of the comparative frequency with which the different events in fact occur For the purposes therefore of the present work it is allowable to suppose that conclusions respecting the probability of a fact of a particular kind rest on our knowledge of the proportion between the cases in which facts of that kind occur and those in which they do not occur this knowledge being either derived from specific experiment or deduced from our knowledge of the causes in operation which tend to produce compared with those which tend to prevent the fact in question Such calculation of chances is grounded on an induction and to render the calculation legitimate the induction must be a valid one It is not less an induction though it does not prove that the event occurs in all cases of a given description but only that out of a given number of such cases it occurs in about so many The fraction which mathematicians use to designate the probability of an event is the ratio of these two numbers the ascertained proportion between the number of cases in which the event occurs and the sum of all the cases those in which it occurs and in which it does not occur taken together In playing at cross and pile the description of cases concerned are throws and the probability of cross is onehalf because if we throw often enough cross is thrown about once in every two throws In the cast of a die the probability of ace is onesixth not simply because there are six possible throws of which ace is one and because we do not know any reason why one should turn up rather than another though I have admitted the validity of this ground in default of a better but because we do actually know either by reasoning or by experience that in a hundred or a million of throws ace is thrown in about onesixth of that number or once in six times I say either by reasoning or by experience meaning specific experience But in estimating probabilities it is not a matter of indifference from which of these two sources we derive our assurance The probability of events as calculated from their mere frequency in past experience affords a less secure basis for practical guidance than their probability as deduced from an equally accurate knowledge of the frequency of occurrence of their causes The generalization that an event occurs in ten out of every hundred cases of a given description is as real an induction as if the generalization were that it occurs in all cases But when we arrive at the conclusion by merely counting instances in actual experience and comparing the number of cases in which A has been present with the number in which it has been absent the evidence is only that of the Method of Agreement and the conclusion amounts only to an empirical law We can make a step beyond this when we can ascend to the causes on which the occurrence of A or its nonoccurrence will depend and form an estimate of the comparative frequency of the causes favourable and of those unfavourable to the occurrence These are data of a higher order by which the empirical law derived from a mere numerical comparison of affirmative and negative instances will be either corrected or confirmed and in either case we shall obtain a more correct measure of probability than is given by that numerical comparison It has been well remarked that in the kind of examples by which the doctrine of chances is usually illustrated that of balls in a box the estimate of probabilities is supported by reasons of causation stronger than specific experience What is the reason that in a box where there are nine black balls and one white we expect to draw a black ball nine times as much in other words nine times as often frequency being the gauge of intensity in expectation as a white Obviously because the local conditions are nine times as favourable because the hand may alight in nine places and get a black ball while it can only alight in one place and find a white ball just for the same reason that we do not expect to succeed in finding a friend in a crowd the conditions in order that we and he should come together being many and difficult This of course would not hold to the same extent were the white balls of smaller size than the black neither would the probability remain the same the larger ball would be much more likely to meet the hand It is in fact evident that when once causation is admitted as a universal law our expectation of events can only be rationally grounded on that law To a person who recognizes that every event depends on causes a thing’s having happened once is a reason for expecting it to happen again only because proving that there exists or is liable to exist a cause adequate to produce it The frequency of the particular event apart from all surmise respecting its cause can give rise to no other induction than that per enumerationem simplicem and the precarious inferences derived from this are superseded and disappear from the field as soon as the principle of causation makes its appearance there Notwithstanding however the abstract superiority of an estimate of probability grounded on causes it is a fact that in almost all cases in which chances admit of estimation sufficiently precise to render their numerical appreciation of any practical value the numerical data are not drawn from knowledge of the causes but from experience of the events themselves The probabilities of life at different ages or in different climates the probabilities of recovery from a particular disease the chances of the birth of male or female offspring the chances of the destruction of houses or other property by fire the chances of the loss of a ship in a particular voyage are deduced from bills of mortality returns from hospitals registers of births of shipwrecks etc that is from the observed frequency not of the causes but of the effects The reason is that in all these classes of facts the causes are either not amenable to direct observation at all or not with the requisite precision and we have no means of judging of their frequency except from the empirical law afforded by the frequency of the effects The inference does not the less depend on causation alone We reason from an effect to a similar effect by passing through the cause If the actuary of an insurance office infers from his tables that among a hundred persons now living of a particular age five on the average will attain the age of seventy his inference is legitimate not for the simple reason that this is the proportion who have lived till seventy in times past but because the fact of their having so lived shows that this is the proportion existing at that place and time between the causes which prolong life to the age of seventy and those tending to bring it to an earlier close From the preceding principles it is easy to deduce the demonstration of that theorem of the doctrine of probabilities which is the foundation of its application to inquiries for ascertaining the occurrence of a given event or the reality of an individual fact The signs or evidences by which a fact is usually proved are some of its consequences and the inquiry hinges upon determining what cause is most likely to have produced a given effect The theorem applicable to such investigations is the Sixth Principle in Laplace’s Essai Philosophique sur les Probabilits which is described by him as the fundamental principle of that branch of the Analysis of Chances which consists in ascending from events to their causes Given an effect to be accounted for and there being several causes which might have produced it but of the presence of which in the particular case nothing is known the probability that the effect was produced by any one of these causes is as the antecedent probability of the cause multiplied by the probability that the cause if it existed would have produced the given effect Let M be the effect and A B two causes by either of which it might have been produced To find the probability that it was produced by the one and not by the other ascertain which of the two is most likely to have existed and which of them if it did exist was most likely to produce the effect M the probability sought is a compound of these two probabilities Let the causes be both alike in the second respect either A or B when it exists being supposed equally likely or equally certain to produce M but let A be in itself twice as likely as B to exist that is twice as frequent a phenomenon Then it is twice as likely to have existed in this case and to have been the cause which produced M For since A exists in nature twice as often as B in any 300 cases in which one or other existed A has existed 200 times and B 100 But either A or B must have existed wherever M is produced therefore in 300 times that M is produced A was the producing cause 200 times B only 100 that is in the ratio of 2 to 1 Thus then if the causes are alike in their capacity of producing the effect the probability as to which actually produced it is in the ratio of their antecedent probabilities Reversing the last hypothesis let us suppose that the causes are equally frequent equally likely to have existed but not equally likely if they did exist to produce M that in three times in which A occurs it produces that effect twice while B in three times produces it only once Since the two causes are equally frequent in their occurrence in every six times that either one or the other exists A exists three times and B three times A of its three times produces M in two B of its three times produces M in one Thus in the whole six times M is only produced thrice but of that thrice it is produced twice by A once only by B Consequently when the antecedent probabilities of the causes are equal the chances that the effect was produced by them are in the ratio of the probabilities that if they did exist they would produce the effect The third case that in which the causes are unlike in both respects is solved by what has preceded For when a quantity depends on two other quantities in such a manner that while either of them remains constant it is proportional to the other it must necessarily be proportional to the product of the two quantities the product being the only function of the two which obeys that law of variation Therefore the probability that M was produced by either cause is as the antecedent probability of the cause multiplied by the probability that if it existed it would produce M Which was to be demonstrated Or we may prove the third case as we proved the first and second Let A be twice as frequent as B and let them also be unequally likely when they exist to produce M let A produce it twice in four times B thrice in four times The antecedent probability of A is to that of B as 2 to 1 the probabilities of their producing M are as 2 to 3 the product of these ratios is the ratio of 4 to 3 and this will be the ratio of the probabilities that A or B was the producing cause in the given instance For since A is twice as frequent as B out of twelve cases in which one or other exists A exists in 8 and B in 4 But of its eight cases A by the supposition produces M in only 4 while B of its four cases produces M in 3 M therefore is only produced at all in seven of the twelve cases but in four of these it is produced by A in three by B hence the probabilities of its being produced by A and by B are as 4 to 3 and are expressed by the fractions 47 and 37 Which was to be demonstrated It remains to examine the bearing of the doctrine of chances on the peculiar problem which occupied us in the preceding chapter namely how to distinguish coincidences which are casual from those which are the result of law from those in which the facts which accompany or follow one another are somehow connected through causation The doctrine of chances affords means by which if we knew the average number of coincidences to be looked for between two phenomena connected only casually we could determine how often any given deviation from that average will occur by chance If the probability of any casual coincidence considered in itself be 1m the probability that the same coincidence will be repeated n times in succession is 1mn For example in one throw of a die the probability of ace being 16 the probability of throwing ace twice in succession will be 1 divided by the square of 6 or 136 For ace is thrown at the first throw once in six or six in thirtysix times and of those six the die being cast again ace will be thrown but once being altogether once in thirtysix times The chance of the same cast three times successively is by a similar reasoning 163 or 1216 that is the event will happen on a large average only once in two hundred and sixteen throws We have thus a rule by which to estimate the probability that any given series of coincidences arises from chance provided we can measure correctly the probability of a single coincidence If we can obtain an equally precise expression for the probability that the same series of coincidences arises from causation we should only have to compare the numbers This however can rarely be done Let us see what degree of approximation can practically be made to the necessary precision The question falls within Laplace’s sixth principle just demonstrated The given fact that is to say the series of coincidences may have originated either in a casual conjunction of causes or in a law of nature The probabilities therefore that the fact originated in these two modes are as their antecedent probabilities multiplied by the probabilities that if they existed they would produce the effect But the particular combination of chances if it occurred or the law of nature if real would certainly produce the series of coincidences The probabilities therefore that the coincidences are produced by the two causes in question are as the antecedent probabilities of the causes One of these the antecedent probability of the combination of mere chances which would produce the given result is an appreciable quantity The antecedent probability of the other supposition may be susceptible of a more or less exact estimation according to the nature of the case In some cases the coincidence supposing it to be the result of causation at all must be the result of a known cause as the succession of aces if not accidental must arise from the loading of the die In such cases we may be able to form a conjecture as to the antecedent probability of such a circumstance from the characters of the parties concerned or other such evidence but it would be impossible to estimate that probability with any thing like numerical precision The counterprobability however that of the accidental origin of the coincidence dwindling so rapidly as it does at each new trial the stage is soon reached at which the chance of unfairness in the die however small in itself must be greater than that of a casual coincidence and on this ground a practical decision can generally be come to without much hesitation if there be the power of repeating the experiment When however the coincidence is one which can not be accounted for by any known cause and the connection between the two phenomena if produced by causation must be the result of some law of nature hitherto unknown which is the case we had in view in the last chapter then though the probability of a casual coincidence may be capable of appreciation that of the countersupposition the existence of an undiscovered law of nature is clearly unsusceptible of even an approximate valuation In order to have the data which such a case would require it would be necessary to know what proportion of all the individual sequences or coexistences occurring in nature are the result of law and what proportion are mere casual coincidences It being evident that we can not form any plausible conjecture as to this proportion much less appreciate it numerically we can not attempt any precise estimation of the comparitive probabilities But of this we are sure that the detection of an unknown law of nature of some previously unrecognized constancy of conjunction among phenomena is no uncommon event If therefore the number of instances in which a coincidence is observed over and above that which would arise on the average from the mere concurrence of chances be such that so great an amount of coincidences from accident alone would be an extremely uncommon event we have reason to conclude that the coincidence is the effect of causation and may be received subject to correction from further experience as an empirical law Further than this in point of precision we can not go nor in most cases is greater precision required for the solution of any practical doubt We have had frequent occasion to notice the inferior generality of derivative laws compared with the ultimate laws from which they are derived This inferiority which affects not only the extent of the propositions themselves but their degree of certainty within that extent is most conspicuous in the uniformities of coexistence and sequence obtaining between effects which depend ultimately on different primeval causes Such uniformities will only obtain where there exists the same collocation of those primeval causes If the collocation varies though the laws themselves remain the same a totally different set of derivative uniformities may and generally will be the result Even where the derivative uniformity is between different effects of the same cause it will by no means obtain as universally as the law of the cause itself If a and b accompany or succeed one another as effects of the cause A it by no means follows that A is the only cause which can produce them or that if there be another cause as B capable of producing a it must produce b likewise The conjunction therefore of a and b perhaps does not hold universally but only in the instances in which a arises from A When it is produced by a cause other than A a and b may be dissevered Day for example is always in our experience followed by night but day is not the cause of night both are successive effects of a common cause the periodical passage of the spectator into and out of the earth’s shadow consequent on the earth’s rotation and on the illuminating property of the sun If therefore day is ever produced by a different cause or set of causes from this day will not or at least may not be followed by night On the sun’s own surface for instance this may be the case Finally even when the derivative uniformity is itself a law of causation resulting from the combination of several causes it is not altogether independent of collocations If a cause supervenes capable of wholly or partially counteracting the effect of any one of the conjoined causes the effect will no longer conform to the derivative law While therefore each ultimate law is only liable to frustration from one set of counteracting causes the derivative law is liable to it from several Now the possibility of the occurrence of counteracting causes which do not arise from any of the conditions involved in the law itself depends on the original collocations It is true that as we formerly remarked laws of causation whether ultimate or derivative are in most cases fulfilled even when counteracted the cause produces its effect though that effect is destroyed by something else That the effect may be frustrated is therefore no objection to the universality of laws of causation But it is fatal to the universality of the sequences or coexistences of effects which compose the greater part of the derivative laws flowing from laws of causation When from the law of a certain combination of causes there results a certain order in the effects as from the combination of a single sun with the rotation of an opaque body round its axis there results on the whole surface of that opaque body an alternation of day and night then if we suppose one of the combined causes counteracted the rotation stopped the sun extinguished or a second sun superadded the truth of that particular law of causation is in no way affected it is still true that one sun shining on an opaque revolving body will alternately produce day and night but since the sun no longer does shine on such a body the derivative uniformity the succession of day and night on the given planet is no longer true Those derivative uniformities therefore which are not laws of causation are except in the rare case of their depending on one cause alone not on a combination of causes always more or less contingent on collocations and are hence subject to the characteristic infirmity of empirical laws that of being admissible only where the collocations are known by experience to be such as are requisite for the truth of the law that is only within the conditions of time and place confirmed by actual observation This principle when stated in general terms seems clear and indisputable yet many of the ordinary judgments of mankind the propriety of which is not questioned have at least the semblance of being inconsistent with it On what grounds it may be asked do we expect that the sun will rise tomorrow Tomorrow is beyond the limits of time comprehended in our observations They have extended over some thousands of years past but they do not include the future Yet we infer with confidence that the sun will rise tomorrow and nobody doubts that we are entitled to do so Let us consider what is the warrant for this confidence In the example in question we know the causes on which the derivative uniformity depends They are the sun giving out light the earth in a state of rotation and intercepting light The induction which shows these to be the real causes and not merely prior effects of a common cause being complete the only circumstances which could defeat the derivative law are such as would destroy or counteract one or other of the combined causes While the causes exist and are not counteracted the effect will continue If they exist and are not counteracted tomorrow the sun will rise tomorrow Since the causes namely the sun and the earth the one in the state of giving out light the other in a state of rotation will exist until something destroys them all depends on the probabilities of their destruction or of their counteraction We know by observation omitting the inferential proofs of an existence for thousands of ages anterior that these phenomena have continued for say five thousand years Within that time there has existed no cause sufficient to diminish them appreciably nor which has counteracted their effect in any appreciable degree The chance therefore that the sun may not rise tomorrow amounts to the chance that some cause which has not manifested itself in the smallest degree during five thousand years will exist tomorrow in such intensity as to destroy the sun or the earth the sun’s light or the earth’s rotation or to produce an immense disturbance in the effect resulting from those causes Now if such a cause will exist tomorrow or at any future time some cause proximate or remote of that cause must exist now and must have existed during the whole of the five thousand years If therefore the sun do not rise tomorrow it will be because some cause has existed the effects of which though during five thousand years they have not amounted to a perceptible quantity will in one day become overwhelming Since this cause has not been recognized during such an interval of time by observers stationed on our earth it must if it be a single agent be either one whose effects develop themselves gradually and very slowly or one which existed in regions beyond our observation and is now on the point of arriving in our part of the universe Now all causes which we have experience of act according to laws incompatible with the supposition that their effects after accumulating so slowly as to be imperceptible for five thousand years should start into immensity in a single day No mathematical law of proportion between an effect and the quantity or relations of its cause could produce such contradictory results The sudden development of an effect of which there was no previous trace always arises from the coming together of several distinct causes not previously conjoined but if such sudden conjunction is destined to take place the causes or their causes must have existed during the entire five thousand years and their not having once come together during that period shows how rare that particular combination is We have therefore the warrant of a rigid induction for considering it probable in a degree undistinguishable from certainty that the known conditions requisite for the sun’s rising will exist tomorrow But this extension of derivative laws not causative beyond the limits of observation can only be to adjacent cases If instead of tomorrow we had said this day twenty thousand years the inductions would have been any thing but conclusive That a cause which in opposition to very powerful causes produced no perceptible effect during five thousand years should produce a very considerable one by the end of twenty thousand has nothing in it which is not in conformity with our experience of causes We know many agents the effect of which in a short period does not amount to a perceptible quantity but by accumulating for a much longer period becomes considerable Besides looking at the immense multitude of the heavenly bodies their vast distances and the rapidity of the motion of such of them as are known to move it is a supposition not at all contradictory to experience that some body may be in motion toward us or we toward it within the limits of whose influence we have not come during five thousand years but which in twenty thousand more may be producing effects upon us of the most extraordinary kind Or the fact which is capable of preventing sunrise may be not the cumulative effect of one cause but some new combination of causes and the chances favourable to that combination though they have not produced it once in five thousand years may produce it once in twenty thousand So that the inductions which authorize us to expect future events grow weaker and weaker the further we look into the future and at length become inappreciable We have considered the probabilities of the sun’s rising tomorrow as derived from the real laws that is from the laws of the causes on which that uniformity is dependent Let us now consider how the matter would have stood if the uniformity had been known only as an empirical law if we had not been aware that the sun’s light and the earth’s rotation or the sun’s motion were the causes on which the periodical occurrence of daylight depends We could have extended this empirical law to cases adjacent in time though not to so great a distance of time as we can now Having evidence that the effects had remained unaltered and been punctually conjoined for five thousand years we could infer that the unknown causes on which the conjunction is dependent had existed undiminished and uncounteracted during the same period The same conclusions therefore would follow as in the preceding case except that we should only know that during five thousand years nothing had occurred to defeat perceptibly this particular effect while when we know the causes we have the additional assurance that during that interval no such change has been noticeable in the causes themselves as by any degree of multiplication or length of continuance could defeat the effect To this must be added that when we know the causes we may be able to judge whether there exists any known cause capable of counteracting them while as long as they are unknown we can not be sure but that if we did know them we could predict their destruction from causes actually in existence A bedridden savage who had never seen the cataract of Niagara but who lived within hearing of it might imagine that the sound he heard would endure forever but if he knew it to be the effect of a rush of waters over a barrier of rock which is progressively wearing away he would know that within a number of ages which may be calculated it will be heard no more In proportion therefore to our ignorance of the causes on which the empirical law depends we can be less assured that it will continue to hold good and the further we look into futurity the less improbable is it that some one of the causes whose coexistence gives rise to the derivative uniformity may be destroyed or counteracted With every prolongation of time the chances multiply of such an event that is to say its nonoccurrence hitherto becomes a less guarantee of its not occurring within the given time If then it is only to cases which in point of time are adjacent or nearly adjacent to those which we have actually observed that any derivative law not of causation can be extended with an assurance equivalent to certainty much more is this true of a merely empirical law Happily for the purposes of life it is to such cases alone that we can almost ever have occasion to extend them In respect of place it might seem that a merely empirical law could not be extended even to adjacent cases that we could have no assurance of its being true in any place where it has not been specially observed The past duration of a cause is a guarantee for its future existence unless something occurs to destroy it but the existence of a cause in one or any number of places is no guarantee for its existence in any other place since there is no uniformity in the collocations of primeval causes When therefore an empirical law is extended beyond the local limits within which it has been found true by observation the cases to which it is thus extended must be such as are presumably within the influence of the same individual agents If we discover a new planet within the known bounds of the solar system or even beyond those bounds but indicating its connection with the system by revolving round the sun we may conclude with great probability that it revolves on its axis For all the known planets do so and this uniformity points to some common cause antecedent to the first records of astronomical observation and though the nature of this cause can only be matter of conjecture yet if it be as is not unlikely and as Laplace’s theory supposes not merely the same kind of cause but the same individual cause such as an impulse given to all the bodies at once that cause acting at the extreme points of the space occupied by the sun and planets is likely unless defeated by some counteracting cause to have acted at every intermediate point and probably somewhat beyond and therefore acted in all probability upon the supposed newlydiscovered planet When therefore effects which are always found conjoined can be traced with any probability to an identical and not merely a similar origin we may with the same probability extend the empirical law of their conjunction to all places within the extreme local boundaries within which the fact has been observed subject to the possibility of counteracting causes in some portion of the field Still more confidently may we do so when the law is not merely empirical when the phenomena which we find conjoined are effects of ascertained causes from the laws of which the conjunction of their effects is deducible In that case we may both extend the derivative uniformity over a larger space and with less abatement for the chance of counteracting causes The first because instead of the local boundaries of our observation of the fact itself we may include the extreme boundaries of the ascertained influence of its causes Thus the succession of day and night we know holds true of all the bodies of the solar system except the sun itself but we know this only because we are acquainted with the causes If we were not we could not extend the proposition beyond the orbits of the earth and moon at both extremities of which we have the evidence of observation for its truth With respect to the probability of counteracting causes it has been seen that this calls for a greater abatement of confidence in proportion to our ignorance of the causes on which the phenomena depend On both accounts therefore a derivative law which we know how to resolve is susceptible of a greater extension to cases adjacent in place than a merely empirical law The word Analogy as the name of a mode of reasoning is generally taken for some kind of argument supposed to be of an inductive nature but not amounting to a complete induction There is no word however which is used more loosely or in a greater variety of senses than Analogy It sometimes stands for arguments which may be examples of the most rigorous induction Archbishop Whately for instance following Ferguson and other writers defines Analogy conformably to its primitive acceptation that which was given to it by mathematicians Resemblance of Relations In this sense when a country which has sent out colonies is termed the mother country the expression is analogical signifying that the colonies of a country stand in the same relation to her in which children stand to their parents And if any inference be drawn from this resemblance of relations as for instance that obedience or affection is due from colonies to the mother country this is called reasoning by analogy Or if it be argued that a nation is most beneficially governed by an assembly elected by the people from the admitted fact that other associations for a common purpose such as jointstock companies are best managed by a committee chosen by the parties interested this too is an argument from analogy in the preceding sense because its foundation is not that a nation is like a jointstock company or Parliament like a board of directors but that Parliament stands in the same relation to the nation in which a board of directors stands to a jointstock company Now in an argument of this nature there is no inherent inferiority of conclusiveness Like other arguments from resemblance it may amount to nothing or it may be a perfect and conclusive induction The circumstance in which the two cases resemble may be capable of being shown to be the material circumstance to be that on which all the consequences necessary to be taken into account in the particular discussion depend In the example last given the resemblance is one of relation the fundamentum relationis being the management by a few persons of affairs in which a much greater number are interested along with them Now some may contend that this circumstance which is common to the two cases and the various consequences which follow from it have the chief share in determining all the effects which make up what we term good or bad administration If they can establish this their argument has the force of a rigorous induction if they can not they are said to have failed in proving the analogy between the two cases a mode of speech which implies that when the analogy can be proved the argument founded on it can not be resisted It is on the whole more usual however to extend the name of analogical evidence to arguments from any sort of resemblance provided they do not amount to a complete induction without peculiarly distinguishing resemblance of relations Analogical reasoning in this sense may be reduced to the following formula Two things resemble each other in one or more respects a certain proposition is true of the one therefore it is true of the other But we have nothing here by which to discriminate analogy from induction since this type will serve for all reasoning from experience In the strictest induction equally with the faintest analogy we conclude because A resembles B in one or more properties that it does so in a certain other property The difference is that in the case of a complete induction it has been previously shown by due comparison of instances that there is an invariable conjunction between the former property or properties and the latter property but in what is called analogical reasoning no such conjunction has been made out There have been no opportunities of putting in practice the Method of Difference or even the Method of Agreement but we conclude and that is all which the argument of analogy amounts to that a fact m known to be true of A is more likely to be true of B if B agrees with A in some of its properties even though no connection is known to exist between m and those properties than if no resemblance at all could be traced between B and any other thing known to possess the attribute m To this argument it is of course requisite that the properties common to A with B shall be merely not known to be connected with m they must not be properties known to be unconnected with it If either by processes of elimination or by deduction from previous knowledge of the laws of the properties in question it can be concluded that they have nothing to do with m the argument of analogy is put out of court The supposition must be that m is an effect really dependent on some property of A but we know not on which We can not point out any of the properties of A which is the cause of m or united with it by any law After rejecting all which we know to have nothing to do with it there remain several between which we are unable to decide of which remaining properties B possesses one or more This accordingly we consider as affording grounds of more or less strength for concluding by analogy that B possesses the attribute m There can be no doubt that every such resemblance which can be pointed out between B and A affords some degree of probability beyond what would otherwise exist in favour of the conclusion drawn from it If B resembled A in all its ultimate properties its possessing the attribute m would be a certainty not a probability and every resemblance which can be shown to exist between them places it by so much the nearer to that point If the resemblance be in an ultimate property there will be resemblance in all the derivative properties dependent on that ultimate property and of these m may be one If the resemblance be in a derivative property there is reason to expect resemblance in the ultimate property on which it depends and in the other derivative properties dependent on the same ultimate property Every resemblance which can be shown to exist affords ground for expecting an indefinite number of other resemblances the particular resemblance sought will therefore be oftener found among things thus known to resemble than among things between which we know of no resemblance For example I might infer that there are probably inhabitants in the moon because there are inhabitants on the earth in the sea and in the air and this is the evidence of analogy The circumstance of having inhabitants is here assumed not to be an ultimate property but as is reasonable to suppose a consequence of other properties and depending therefore in the case of the earth on some of its properties as a portion of the universe but on which of those properties we know not Now the moon resembles the earth in being a solid opaque nearly spherical substance appearing to contain or to have contained active volcanoes receiving heat and light from the sun in about the same quantity as our earth revolving on its axis composed of materials which gravitate and obeying all the various laws resulting from that property And I think no one will deny that if this were all that was known of the moon the existence of inhabitants in that luminary would derive from these various resemblances to the earth a greater degree of probability than it would otherwise have though the amount of the augmentation it would be useless to attempt to estimate If however every resemblance proved between B and A in any point not known to be immaterial with respect to m forms some additional reason for presuming that B has the attribute m it is clear contra that every dissimilarity which can be proved between them furnishes a counterprobability of the same nature on the other side It is not indeed unusual that different ultimate properties should in some particular instances produce the same derivative property but on the whole it is certain that things which differ in their ultimate properties will differ at least as much in the aggregate of their derivative properties and that the differences which are unknown will on the average of cases bear some proportion to those which are known There will therefore be a competition between the known points of agreement and the known points of difference in A and B and according as the one or the other may be deemed to preponderate the probability derived from analogy will be for or against B’s having the property m The moon for instance agrees with the earth in the circumstances already mentioned but differs in being smaller in having its surface more unequal and apparently volcanic throughout in having at least on the side next the earth no atmosphere sufficient to refract light no clouds and it is therefore concluded no water These differences considered merely as such might perhaps balance the resemblances so that analogy would afford no presumption either way But considering that some of the circumstances which are wanting on the moon are among those which on the earth are found to be indispensable conditions of animal life we may conclude that if that phenomenon does exist in the moon or at all events on the nearer side it must be as an effect of causes totally different from those on which it depends here as a consequence therefore of the moon’s differences from the earth not of the points of agreement Viewed in this light all the resemblances which exist become presumptions against not in favour of the moon’s being inhabited Since life can not exist there in the manner in which it exists here the greater the resemblance of the lunar world to the terrestrial in other respects the less reason we have to believe that it can contain life There are however other bodies in our system between which and the earth there is a much closer resemblance which possess an atmosphere clouds consequently water or some fluid analogous to it and even give strong indications of snow in their polar regions while the cold or heat though differing greatly on the average from ours is in some parts at least of those planets possibly not more extreme than in some regions of our own which are habitable To balance these agreements the ascertained differences are chiefly in the average light and heat velocity of rotation density of material intensity of gravity and similar circumstances of a secondary kind With regard to these planets therefore the argument of analogy gives a decided preponderance in favour of their resembling the earth in any of its derivative properties such as that of having inhabitants though when we consider how immeasurably multitudinous are those of their properties which we are entirely ignorant of compared with the few which we know we can attach but trifling weight to any considerations of resemblance in which the known elements bear so inconsiderable a proportion to the unknown Besides the competition between analogy and diversity there may be a competition of conflicting analogies The new case may be similar in some of its circumstances to cases in which the fact m exists but in others to cases in which it is known not to exist Amber has some properties in common with vegetable others with mineral products A painting of unknown origin may resemble in certain of its characters known works of a particular master but in others it may as strikingly resemble those of some other painter A vase may bear some analogy to works of Grecian and some to those of Etruscan or Egyptian art We are of course supposing that it does not possess any quality which has been ascertained by a sufficient induction to be a conclusive mark either of the one or of the other Since the value of an analogical argument inferring one resemblance from other resemblances without any antecedent evidence of a connection between them depends on the extent of ascertained resemblance compared first with the amount of ascertained difference and next with the extent of the unexplored region of unascertained properties it follows that where the resemblance is very great the ascertained difference very small and our knowledge of the subjectmatter tolerably extensive the argument from analogy may approach in strength very near to a valid induction If after much observation of B we find that it agrees with A in nine out of ten of its known properties we may conclude with a probability of nine to one that it will possess any given derivative property of A If we discover for example an unknown animal or plant resembling closely some known one in the greater number of the properties we observe in it but differing in some few we may reasonably expect to find in the unobserved remainder of its properties a general agreement with those of the former but also a difference corresponding proportionately to the amount of observed diversity It thus appears that the conclusions derived from analogy are only of any considerable value when the case to which we reason is an adjacent case adjacent not as before in place or time but in circumstances In the case of effects of which the causes are imperfectly or not at all known when consequently the observed order of their occurrence amounts only to an empirical law it often happens that the conditions which have coexisted whenever the effect was observed have been very numerous Now if a new case presents itself in which all these conditions do not exist but the far greater part of them do some one or a few only being wanting the inference that the effect will occur notwithstanding this deficiency of complete resemblance to the cases in which it has been observed may though of the nature of analogy possess a high degree of probability It is hardly necessary to add that however considerable this probability may be no competent inquirer into nature will rest satisfied with it when a complete induction is attainable but will consider the analogy as a mere guidepost pointing out the direction in which more rigorous investigations should be prosecuted It is in this last respect that considerations of analogy have the highest scientific value The cases in which analogical evidence affords in itself any very high degree of probability are as we have observed only those in which the resemblance is very close and extensive but there is no analogy however faint which may not be of the utmost value in suggesting experiments or observations that may lead to more positive conclusions When the agents and their effects are out of the reach of further observation and experiment as in the speculations already alluded to respecting the moon and planets such slight probabilities are no more than an interesting theme for the pleasant exercise of imagination but any suspicion however slight that sets an ingenious person at work to contrive an experiment or affords a reason for trying one experiment rather than another may be of the greatest benefit to science On this ground though I can not accept as positive truths any of those scientific hypotheses which are unsusceptible of being ultimately brought to the test of actual induction such for instance as the two theories of light the emission theory of the last century and the undulatory theory which predominates in the present I am yet unable to agree with those who consider such hypotheses to be worthy of entire disregard As is well said by Hartley and concurred in by a thinker in general so diametrically opposed to Hartley’s opinions as Dugald Stewart any hypothesis which has so much plausibility as to explain a considerable number of facts helps us to digest these facts in proper order to bring new ones to light and make experimenta crucis for the sake of future inquirers If an hypothesis both explains known facts and has led to the prediction of others previously unknown and since verified by experience the laws of the phenomenon which is the subject of inquiry must bear at least a great similarity to those of the class of phenomena to which the hypothesis assimilates it and since the analogy which extends so far may probably extend further nothing is more likely to suggest experiments tending to throw light upon the real properties of the phenomenon than the following out such an hypothesis But to this end it is by no means necessary that the hypothesis be mistaken for a scientific truth On the contrary that illusion is in this respect as in every other an impediment to the progress of real knowledge by leading inquirers to restrict themselves arbitrarily to the particular hypothesis which is most accredited at the time instead of looking out for every class of phenomena between the laws of which and those of the given phenomenon any analogy exists and trying all such experiments as may tend to the discovery of ulterior analogies pointing in the same direction We have now completed our review of the logical processes by which the laws or uniformities of the sequence of phenomena and those uniformities in their coexistence which depend on the laws of their sequence are ascertained or tested As we recognized in the commencement and have been enabled to see more clearly in the progress of the investigation the basis of all these logical operations is the law of causation The validity of all the Inductive Methods depends on the assumption that every event or the beginning of every phenomenon must have some cause some antecedent on the existence of which it is invariably and unconditionally consequent In the Method of Agreement this is obvious that method avowedly proceeding on the supposition that we have found the true cause as soon as we have negatived every other The assertion is equally true of the Method of Difference That method authorizes us to infer a general law from two instances one in which A exists together with a multitude of other circumstances and B follows another in which A being removed and all other circumstances remaining the same B is prevented What however does this prove It proves that B in the particular instance can not have had any other cause than A but to conclude from this that A was the cause or that A will on other occasions be followed by B is only allowable on the assumption that B must have some cause that among its antecedents in any single instance in which it occurs there must be one which has the capacity of producing it at other times This being admitted it is seen that in the case in question that antecedent can be no other than A but that if it be no other than A it must be A is not proved by these instances at least but taken for granted There is no need to spend time in proving that the same thing is true of the other Inductive Methods The universality of the law of causation is assumed in them all But is this assumption warranted Doubtless it may be said most phenomena are connected as effects with some antecedent or cause that is are never produced unless some assignable fact has preceded them but the very circumstance that complicated processes of induction are sometimes necessary shows that cases exist in which this regular order of succession is not apparent to our unaided apprehension If then the processes which bring these cases within the same category with the rest require that we should assume the universality of the very law which they do not at first sight appear to exemplify is not this a petitio principii Can we prove a proposition by an argument which takes it for granted And if not so proved on what evidence does it rest For this difficulty which I have purposely stated in the strongest terms it will admit of the school of metaphysicians who have long predominated in this country find a ready salvo They affirm that the universality of causation is a truth which we can not help believing that the belief in it is an instinct one of the laws of our believing faculty As the proof of this they say and they have nothing else to say that every body does believe it and they number it among the propositions rather numerous in their catalogue which may be logically argued against and perhaps can not be logically proved but which are of higher authority than logic and so essentially inherent in the human mind that even he who denies them in speculation shows by his habitual practice that his arguments make no impression upon himself Into the merits of this question considered as one of psychology it would be foreign to my purpose to enter here but I must protest against adducing as evidence of the truth of a fact in external nature the disposition however strong or however general of the human mind to believe it Belief is not proof and does not dispense with the necessity of proof I am aware that to ask for evidence of a proposition which we are supposed to believe instinctively is to expose one’s self to the charge of rejecting the authority of the human faculties which of course no one can consistently do since the human faculties are all which any one has to judge by and inasmuch as the meaning of the word evidence is supposed to be something which when laid before the mind induces it to believe to demand evidence when the belief is insured by the mind’s own laws is supposed to be appealing to the intellect against the intellect But this I apprehend is a misunderstanding of the nature of evidence By evidence is not meant any thing and every thing which produces belief There are many things which generate belief besides evidence A mere strong association of ideas often causes a belief so intense as to be unshakable by experience or argument Evidence is not that which the mind does or must yield to but that which it ought to yield to namely that by yielding to which its belief is kept conformable to fact There is no appeal from the human faculties generally but there is an appeal from one human faculty to another from the judging faculty to those which take cognizance of fact the faculties of sense and consciousness The legitimacy of this appeal is admitted whenever it is allowed that our judgments ought to be conformable to fact To say that belief suffices for its own justification is making opinion the test of opinion it is denying the existence of any outward standard the conformity of an opinion to which constitutes its truth We call one mode of forming opinions right and another wrong because the one does and the other does not tend to make the opinion agree with the fact to make people believe what really is and expect what really will be Now a mere disposition to believe even if supposed instinctive is no guarantee for the truth of the thing believed If indeed the belief ever amounted to an irresistible necessity there would then be no use in appealing from it because there would be no possibility of altering it But even then the truth of the belief would not follow it would only follow that mankind were under a permanent necessity of believing what might possibly not be true in other words that a case might occur in which our senses or consciousness if they could be appealed to might testify one thing and our reason believe another But in fact there is no such permanent necessity There is no proposition of which it can be asserted that every human mind must eternally and irrevocably believe it Many of the propositions of which this is most confidently stated great numbers of human beings have disbelieved The things which it has been supposed that nobody could possibly help believing are innumerable but no two generations would make out the same catalogue of them One age or nation believes implicitly what to another seems incredible and inconceivable one individual has not a vestige of a belief which another deems to be absolutely inherent in humanity There is not one of these supposed instinctive beliefs which is really inevitable It is in the power of every one to cultivate habits of thought which make him independent of them The habit of philosophical analysis of which it is the surest effect to enable the mind to command instead of being commanded by the laws of the merely passive part of its own nature by showing to us that things are not necessarily connected in fact because their ideas are connected in our minds is able to loosen innumerable associations which reign despotically over the undisciplined or earlyprejudiced mind And this habit is not without power even over those associations which the school of which I have been speaking regard as connate and instinctive I am convinced that any one accustomed to abstraction and analysis who will fairly exert his faculties for the purpose will when his imagination has once learned to entertain the notion find no difficulty in conceiving that in some one for instance of the many firmaments into which sidereal astronomy now divides the universe events may succeed one another at random without any fixed law nor can any thing in our experience or in our mental nature constitute a sufficient or indeed any reason for believing that this is nowhere the case Were we to suppose what it is perfectly possible to imagine that the present order of the universe were brought to an end and that a chaos succeeded in which there was no fixed succession of events and the past gave no assurance of the future if a human being were miraculously kept alive to witness this change he surely would soon cease to believe in any uniformity the uniformity itself no longer existing If this be admitted the belief in uniformity either is not an instinct or it is an instinct conquerable like all other instincts by acquired knowledge But there is no need to speculate on what might be when we have positive and certain knowledge of what has been It is not true as a matter of fact that mankind have always believed that all the successions of events were uniform and according to fixed laws The Greek philosophers not even excepting Aristotle recognized Chance and Spontaneity and as among the agents in nature in other words they believed that to that extent there was no guarantee that the past had been similar to itself or that the future would resemble the past Even now a full half of the philosophical world including the very same metaphysicians who contend most for the instinctive character of the belief in uniformity consider one important class of phenomena volitions to be an exception to the uniformity and not governed by a fixed law As was observed in a former place the belief we entertain in the universality throughout nature of the law of cause and effect, is itself an instance of induction and by no means one of the earliest which any of us or which mankind in general can have made We arrive at this universal law by generalization from many laws of inferior generality We should never have had the notion of causation in the philosophical meaning of the term as a condition of all phenomena unless many cases of causation or in other words, many partial uniformities of sequence had previously become familiar The more obvious of the particular uniformities suggest and give evidence of the general uniformity and the general uniformity once established enables us to prove the remainder of the particular uniformities of which it is made up As however all rigorous processes of induction presuppose the general uniformity our knowledge of the particular uniformities from which it was first inferred was not of course derived from rigorous induction but from the loose and uncertain mode of induction per enumerationem simplicem and the law of universal causation being collected from results so obtained can not itself rest on any better foundation It would seem therefore that induction per enumerationem simplicem not only is not necessarily an illicit logical process but is in reality the only kind of induction possible since the more elaborate process depends for its validity on a law itself obtained in that inartificial mode Is there not then an inconsistency in contrasting the looseness of one method with the rigidity of another when that other is indebted to the looser method for its own foundation The inconsistency however is only apparent Assuredly if induction by simple enumeration were an invalid process no process grounded on it could be valid just as no reliance could be placed on telescopes if we could not trust our eyes But though a valid process it is a fallible one and fallible in very different degrees if therefore we can substitute for the more fallible forms of the process an operation grounded on the same process in a less fallible form we shall have effected a very material improvement And this is what scientific induction does A mode of concluding from experience must be pronounced untrustworthy when subsequent experience refuses to confirm it According to this criterion induction by simple enumeration in other words generalization of an observed fact from the mere absence of any known instance to the contrary affords in general a precarious and unsafe ground of assurance for such generalizations are incessantly discovered on further experience to be false Still however it affords some assurance sufficient in many cases for the ordinary guidance of conduct It would be absurd to say that the generalizations arrived at by mankind in the outset of their experience such as these food nourishes fire burns water drowns were unworthy of reliance There is a scale of trustworthiness in the results of the original unscientific induction and on this diversity as observed in the fourth chapter of the present book depend the rules for the improvement of the process The improvement consists in correcting one of these inartificial generalizations by means of another As has been already pointed out this is all that art can do To test a generalization by showing that it either follows from or conflicts with some stronger induction some generalization resting on a broader foundation of experience is the beginning and end of the logic of induction Now the precariousness of the method of simple enumeration is in an inverse ratio to the largeness of the generalization The process is delusive and insufficient exactly in proportion as the subjectmatter of the observation is special and limited in extent As the sphere widens this unscientific method becomes less and less liable to mislead and the most universal class of truths the law of causation for instance and the principles of number and of geometry are duly and satisfactorily proved by that method alone nor are they susceptible of any other proof With respect to the whole class of generalizations of which we have recently treated the uniformities which depend on causation the truth of the remark just made follows by obvious inference from the principles laid down in the preceding chapters When a fact has been observed a certain number of times to be true and is not in any instance known to be false if we at once affirm that fact as a universal truth or law of nature without either testing it by any of the four methods of induction or deducing it from other known laws we shall in general err grossly but we are perfectly justified in affirming it as an empirical law true within certain limits of time place and circumstance provided the number of coincidences be greater than can with any probability be ascribed to chance The reason for not extending it beyond those limits is that the fact of its holding true within them may be a consequence of collocations which can not be concluded to exist in one place because they exist in another or may be dependent on the accidental absence of counteracting agencies which any variation of time or the smallest change of circumstances may possibly bring into play If we suppose then the subjectmatter of any generalization to be so widely diffused that there is no time no place and no combination of circumstances but must afford an example either of its truth or of its falsity and if it be never found otherwise than true its truth can not be contingent on any collocations unless such as exist at all times and places nor can it be frustrated by any counteracting agencies unless by such as never actually occur It is therefore an empirical law coextensive with all human experience at which point the distinction between empirical laws and laws of nature vanishes and the proposition takes its place among the most firmly established as well as largest truths accessible to science Now the most extensive in its subjectmatter of all generalizations which experience warrants respecting the sequences and coexistences of phenomena is the law of causation It stands at the head of all observed uniformities in point of universality and therefore if the preceding observations are correct in point of certainty And if we consider not what mankind would have been justified in believing in the infancy of their knowledge but what may rationally be believed in its present more advanced state we shall find ourselves warranted in considering this fundamental law though itself obtained by induction from particular laws of causation as not less certain but on the contrary more so than any of those from which it was drawn It adds to them as much proof as it receives from them For there is probably no one even of the best established laws of causation which is not sometimes counteracted and to which therefore apparent exceptions do not present themselves which would have necessarily and justly shaken the confidence of mankind in the universality of those laws if inductive processes founded on the universal law had not enabled us to refer those exceptions to the agency of counteracting causes and thereby reconcile them with the law with which they apparently conflict Errors moreover may have slipped into the statement of any one of the special laws through inattention to some material circumstance and instead of the true proposition another may have been enunciated false as a universal law though leading in all cases hitherto observed to the same result To the law of causation on the contrary we not only do not know of any exception but the exceptions which limit or apparently invalidate the special laws are so far from contradicting the universal one that they confirm it since in all cases which are sufficiently open to our observation we are able to trace the difference of result either to the absence of a cause which had been present in ordinary cases or to the presence of one which had been absent The law of cause and effect, being thus certain is capable of imparting its certainty to all other inductive propositions which can be deduced from it and the narrower inductions may be regarded as receiving their ultimate sanction from that law since there is no one of them which is not rendered more certain than it was before when we are able to connect it with that larger induction and to show that it can not be denied consistently with the law that every thing which begins to exist has a cause And hence we are justified in the seeming inconsistency of holding induction by simple enumeration to be good for proving this general truth the foundation of scientific induction and yet refusing to rely on it for any of the narrower inductions I fully admit that if the law of causation were unknown generalization in the more obvious cases of uniformity in phenomena would nevertheless be possible and though in all cases more or less precarious and in some extremely so would suffice to constitute a certain measure of probability but what the amount of this probability might be we are dispensed from estimating since it never could amount to the degree of assurance which the proposition acquires when by the application to it of the Four Methods the supposition of its falsity is shown to be inconsistent with the Law of Causation We are therefore logically entitled and by the necessities of scientific induction required to disregard the probabilities derived from the early rude method of generalizing and to consider no minor generalization as proved except so far as the law of causation confirms it nor probable except so far as it may reasonably be expected to be so confirmed The assertion that our inductive processes assume the law of causation while the law of causation is itself a case of induction is a paradox only on the old theory of reasoning which supposes the universal truth or major premise in a ratiocination to be the real proof of the particular truths which are ostensibly inferred from it According to the doctrine maintained in the present treatise the major premise is not the proof of the conclusion but is itself proved along with the conclusion from the same evidence All men are mortal is not the proof that Lord Palmerston is mortal but our past experience of mortality authorizes us to infer both the general truth and the particular fact and the one with exactly the same degree of assurance as the other The mortality of Lord Palmerston is not an inference from the mortality of all men but from the experience which proves the mortality of all men and is a correct inference from experience if that general truth is so too This relation between our general beliefs and their particular applications holds equally true in the more comprehensive case which we are now discussing Any new fact of causation inferred by induction is rightly inferred if no other objection can be made to the inference than can be made to the general truth that every event has a cause The utmost certainty which can be given to a conclusion arrived at in the way of inference stops at this point When we have ascertained that the particular conclusion must stand or fall with the general uniformity of the laws of nature that it is liable to no doubt except the doubt whether every event has a cause we have done all that can be done for it The strongest assurance we can obtain of any theory respecting the cause of a given phenomenon is that the phenomenon has either that cause or none The latter supposition might have been an admissible one in a very early period of our study of nature But we have been able to perceive that in the stage which mankind have now reached the generalization which gives the Law of Universal Causation has grown into a stronger and better induction one deserving of greater reliance than any of the subordinate generalizations We may even I think go a step further than this and regard the certainty of that great induction as not merely comparative but for all practical purposes complete The considerations which as I apprehend give at the present day to the proof of the law of uniformity of succession as true of all phenomena without exception this character of completeness and conclusiveness are the following First that we now know it directly to be true of far the greatest number of phenomena that there are none of which we know it not to be true the utmost that can be said being that of some we can not positively from direct evidence affirm its truth while phenomenon after phenomenon as they become better known to us are constantly passing from the latter class into the former and in all cases in which that transition has not yet taken place the absence of direct proof is accounted for by the rarity or the obscurity of the phenomena our deficient means of observing them or the logical difficulties arising from the complication of the circumstances in which they occur insomuch that notwithstanding as rigid a dependence on given conditions as exists in the case of any other phenomenon it was not likely that we should be better acquainted with those conditions than we are Besides this first class of considerations there is a second which still further corroborates the conclusion Although there are phenomena the production and changes of which elude all our attempts to reduce them universally to any ascertained law yet in every such case the phenomenon or the objects concerned in it are found in some instances to obey the known laws of nature The wind for example is the type of uncertainty and caprice yet we find it in some cases obeying with as much constancy as any phenomenon in nature the law of the tendency of fluids to distribute themselves so as to equalize the pressure on every side of each of their particles as in the case of the tradewinds and the monsoons Lightning might once have been supposed to obey no laws but since it has been ascertained to be identical with electricity we know that the very same phenomenon in some of its manifestations is implicitly obedient to the action of fixed causes I do not believe that there is now one object or event in all our experience of nature within the bounds of the solar system at least which has not either been ascertained by direct observation to follow laws of its own or been proved to be closely similar to objects and events which in more familiar manifestations or on a more limited scale follow strict laws our inability to trace the same laws on a larger scale and in the more recondite instances being accounted for by the number and complication of the modifying causes or by their inaccessibility to observation The progress of experience therefore has dissipated the doubt which must have rested on the universality of the law of causation while there were phenomena which seemed to be sui generis not subject to the same laws with any other class of phenomena and not as yet ascertained to have peculiar laws of their own This great generalization however might reasonably have been as it in fact was acted on as a probability of the highest order before there were sufficient grounds for receiving it as a certainty In matters of evidence as in all other human things we neither require nor can attain the absolute We must hold even our strongest convictions with an opening left in our minds for the reception of facts which contradict them and only when we have taken this precaution have we earned the right to act upon our convictions with complete confidence when no such contradiction appears Whatever has been found true in innumerable instances and never found to be false after due examination in any we are safe in acting on as universal provisionally until an undoubted exception appears provided the nature of the case be such that a real exception could scarcely have escaped notice When every phenomenon that we ever knew sufficiently well to be able to answer the question had a cause on which it was invariably consequent it was more rational to suppose that our inability to assign the causes of other phenomena arose from our ignorance than that there were phenomena which were uncaused and which happened to be exactly those which we had hitherto had no sufficient opportunity of studying It must at the same time be remarked that the reasons for this reliance do not hold in circumstances unknown to us and beyond the possible range of our experience In distant parts of the stellar regions where the phenomena may be entirely unlike those with which we are acquainted it would be folly to affirm confidently that this general law prevails any more than those special ones which we have found to hold universally on our own planet The uniformity in the succession of events otherwise called the law of causation must be received not as a law of the universe but of that portion of it only which is within the range of our means of sure observation with a reasonable degree of extension to adjacent cases To extend it further is to make a supposition without evidence and to which in the absence of any ground from experience for estimating its degree of probability it would be idle to attempt to assign any The order of the occurrence of phenomena in time is either successive or simultaneous the uniformities therefore which obtain in their occurrence are either uniformities of succession or of coexistence Uniformities of succession are all comprehended under the law of causation and its consequences Every phenomenon has a cause which it invariably follows and from this are derived other invariable sequences among the successive stages of the same effect as well as between the effects resulting from causes which invariably succeed one another In the same manner with these derivative uniformities of succession a great variety of uniformities of coexistence also take their rise Coordinate effects of the same cause naturally coexist with one another High water at any point on the earth’s surface and high water at the point diametrically opposite to it are effects uniformly simultaneous resulting from the direction in which the combined attractions of the sun and moon act upon the waters of the ocean An eclipse of the sun to us and an eclipse of the earth to a spectator situated in the moon are in like manner phenomena invariably coexistent and their coexistence can equally be deduced from the laws of their production It is an obvious question therefore whether all the uniformities of coexistence among phenomena may not be accounted for in this manner And it can not be doubted that between phenomena which are themselves effects the coexistences must necessarily depend on the causes of those phenomena If they are effects immediately or remotely of the same cause they can not coexist except by virtue of some laws or properties of that cause if they are effects of different causes they can not coexist unless it be because their causes coexist and the uniformity of coexistence if such there be between the effects proves that those particular causes within the limits of our observation have uniformly been coexistent But these same considerations compel us to recognize that there must be one class of coexistences which can not depend on causation the coexistences between the ultimate properties of things those properties which are the causes of all phenomena but are not themselves caused by any phenomenon and a cause for which could only be sought by ascending to the origin of all things Yet among these ultimate properties there are not only coexistences but uniformities of coexistence General propositions may be and are formed which assert that whenever certain properties are found certain others are found along with them We perceive an object say for instance water We recognize it to be water of course by certain of its properties Having recognized it we are able to affirm of it innumerable other properties which we could not do unless it were a general truth a law or uniformity in nature that the set of properties by which we identify the substance as water always have those other properties conjoined with them In a former place it has been explained in some detail what is meant by the Kinds of objects those classes which differ from one another not by a limited and definite but by an indefinite and unknown number of distinctions To this we have now to add that every proposition by which any thing is asserted of a Kind affirms a uniformity of coexistence Since we know nothing of Kinds but their properties the Kind to us is the set of properties by which it is identified and which must of course be sufficient to distinguish it from every other kind In affirming any thing therefore of a Kind we are affirming something to be uniformly coexistent with the properties by which the kind is recognized and that is the sole meaning of the assertion Among the uniformities of coexistence which exist in nature may hence be numbered all the properties of Kinds The whole of these however are not independent of causation but only a portion of them Some are ultimate properties others derivative of some no cause can be assigned but others are manifestly dependent on causes Thus pure oxygen gas is a Kind and one of its most unequivocal properties is its gaseous form this property however has for its cause the presence of a certain quantity of latent heat and if that heat could be taken away as has been done from so many gases in Faraday’s experiments the gaseous form would doubtless disappear together with numerous other properties which depend on or are caused by that property In regard to all substances which are chemical compounds and which therefore may be regarded as products of the juxtaposition of substances different in Kind from themselves there is considerable reason to presume that the specific properties of the compound are consequent as effects on some of the properties of the elements though little progress has yet been made in tracing any invariable relation between the latter and the former Still more strongly will a similar presumption exist when the object itself as in the case of organized beings is no primeval agent but an effect which depends on a cause or causes for its very existence The Kinds therefore which are called in chemistry simple substances or elementary natural agents are the only ones any of whose properties can with certainty be considered ultimate and of these the ultimate properties are probably much more numerous than we at present recognize since every successful instance of the resolution of the properties of their compounds into simpler laws generally leads to the recognition of properties in the elements distinct from any previously known The resolution of the laws of the heavenly motions established the previously unknown ultimate property of a mutual attraction between all bodies the resolution so far as it has yet proceeded of the laws of crystallization of chemical composition electricity magnetism etc points to various polarities ultimately inherent in the particles of which bodies are composed the comparative atomic weights of different kinds of bodies were ascertained by resolving into more general laws the uniformities observed in the proportions in which substances combine with one another and so forth Thus although every resolution of a complex uniformity into simpler and more elementary laws has an apparent tendency to diminish the number of the ultimate properties and really does remove many properties from the list yet since the result of this simplifying process is to trace up an ever greater variety of different effects to the same agents the further we advance in this direction the greater number of distinct properties we are forced to recognize in one and the same object the coexistences of which properties must accordingly be ranked among the ultimate generalities of nature There are therefore only two kinds of propositions which assert uniformity of coexistence between properties Either the properties depend on causes or they do not If they do the proposition which affirms them to be coexistent is a derivative law of coexistence between effects and until resolved into the laws of causation on which it depends is an empirical law and to be tried by the principles of induction to which such laws are amenable If on the other hand the properties do not depend on causes but are ultimate properties then if it be true that they invariably coexist they must all be ultimate properties of one and the same Kind and it is of these only that the coexistences can be classed as a peculiar sort of laws of nature When we affirm that all crows are black or that all negroes have woolly hair we assert a uniformity of coexistence We assert that the property of blackness or of having woolly hair invariably coexists with the properties which in common language or in the scientific classification that we adopt are taken to constitute the class crow or the class negro Now supposing blackness to be an ultimate property of black objects or woolly hair an ultimate property of the animals which possess it supposing that these properties are not results of causation are not connected with antecedent phenomena by any law then if all crows are black and all negroes have woolly hair these must be ultimate properties of the kind crow or negro or of some kind which includes them If on the contrary blackness or woolly hair be an effect depending on causes these general propositions are manifestly empirical laws and all that has already been said respecting that class of generalizations may be applied without modification to these Now we have seen that in the case of all compounds of all things in short except the elementary substances and primary powers of nature the presumption is that the properties do really depend upon causes and it is impossible in any case whatever to be certain that they do not We therefore should not be safe in claiming for any generalization respecting the coexistence of properties a degree of certainty to which if the properties should happen to be the result of causes it would have no claim A generalization respecting coexistence or, in other words, respecting the properties of kinds may be an ultimate truth but it may also be merely a derivative one and since if so it is one of those derivative laws which are neither laws of causation nor have been resolved into the laws of causation on which they depend it can possess no higher degree of evidence than belongs to an empirical law This conclusion will be confirmed by the consideration of one great deficiency which precludes the application to the ultimate uniformities of coexistence of a system of rigorous scientific induction such as the uniformities in the succession of phenomena have been found to admit of The basis of such a system is wanting there is no general axiom standing in the same relation to the uniformities of coexistence as the law of causation does to those of succession The Methods of Induction applicable to the ascertainment of causes and effects are grounded on the principle that every thing which has a beginning must have some cause or other that among the circumstances which actually existed at the time of its commencement there is certainly some one combination on which the effect in question is unconditionally consequent and on the repetition of which it would certainly again recur But in an inquiry whether some kind as crow universally possesses a certain property as blackness there is no room for any assumption analogous to this We have no previous certainty that the property must have something which constantly coexists with it must have an invariable coexistent in the same manner as an event must have an invariable antecedent When we feel pain we must be in some circumstances under which if exactly repeated we should always feel pain But when we are conscious of blackness it does not follow that there is something else present of which blackness is a constant accompaniment There is therefore no room for elimination no method of Agreement or Difference or of Concomitant Variations which is but a modification either of the Method of Agreement or of the Method of Difference We can not conclude that the blackness we see in crows must be an invariable property of crows merely because there is nothing else present of which it can be an invariable property We therefore inquire into the truth of a proposition like All crows are black under the same disadvantage as if in our inquiries into causation we were compelled to let in as one of the possibilities that the effect may in that particular instance have arisen without any cause at all To overlook this grand distinction was as it seems to me the capital error in Bacon’s view of inductive philosophy The principle of elimination that great logical instrument which he had the immense merit of first bringing into general use he deemed applicable in the same sense and in as unqualified a manner to the investigation of the coexistences as to that of the successions of phenomena He seems to have thought that as every event has a cause or invariable antecedent so every property of an object has an invariable coexistent which he called its form and the examples he chiefly selected for the application and illustration of his method were inquiries into such forms attempts to determine in what else all those objects resembled which agreed in some one general property as hardness or softness dryness or moistness heat or coldness Such inquiries could lead to no result The objects seldom have any such circumstances in common They usually agree in the one point inquired into and in nothing else A great proportion of the properties which so far as we can conjecture are the likeliest to be really ultimate would seem to be inherently properties of many different kinds of things not allied in any other respect And as for the properties which being effects of causes we are able to give some account of they have generally nothing to do with the ultimate resemblances or diversities in the objects themselves but depend on some outward circumstances under the influence of which any objects whatever are capable of manifesting those properties as is emphatically the case with those favourite subjects of Bacon’s scientific inquiries hotness and coldness as well as with hardness and softness solidity and fluidity and many other conspicuous qualities In the absence then of any universal law of coexistence similar to the universal law of causation which regulates sequence we are thrown back upon the unscientific induction of the ancients per enumerationem simplicem ubi non reperitur instantia contradictoria The reason we have for believing that all crows are black is simply that we have seen and heard of many black crows and never one of any other colour It remains to be considered how far this evidence can reach and how we are to measure its strength in any given case It sometimes happens that a mere change in the mode of verbally enunciating a question though nothing is really added to the meaning expressed is of itself a considerable step toward its solution This I think happens in the present instance The degree of certainty of any generalization which rests on no other evidence than the agreement so far as it goes of all past observation is but another phrase for the degree of improbability that an exception if any existed could have hitherto remained unobserved The reason for believing that all crows are black is measured by the improbability that crows of any other colour should have existed to the present time without our being aware of it Let us state the question in this last mode and consider what is implied in the supposition that there may be crows which are not black and under what conditions we can be justified in regarding this as incredible If there really exist crows which are not black one of two things must be the fact Either the circumstance of blackness in all crows hitherto observed must be as it were an accident not connected with any distinction of Kind or if it be a property of Kind the crows which are not black must be a new Kind a Kind hitherto overlooked though coming under the same general description by which crows have hitherto been characterized The first supposition would be proved true if we were to discover casually a white crow among black ones or if it were found that black crows sometimes turn white The second would be shown to be the fact if in Australia or Central Africa a species or a race of white or gray crows were found to exist The former of these suppositions necessarily implies that the colour is an effect of causation If blackness in the crows in which it has been observed be not a property of Kind but can be present or absent without any difference generally in the properties of the object then it is not an ultimate fact in the individuals themselves but is certainly dependent on a cause There are no doubt many properties which vary from individual to individual of the same Kind even the same infima species or lowest Kind Some flowers may be either white or red without differing in any other respect But these properties are not ultimate they depend on causes So far as the properties of a thing belong to its own nature and do not arise from some cause extrinsic to it they are always the same in the same Kind Take for instance all simple substances and elementary powers the only things of which we are certain that some at least of their properties are really ultimate Color is generally esteemed the most variable of all properties yet we do not find that sulphur is sometimes yellow and sometimes white or that it varies in colour at all except so far as colour is the effect of some extrinsic cause as of the sort of light thrown upon it the mechanical arrangement of the particles as after fusion etc We do not find that iron is sometimes fluid and sometimes solid at the same temperature gold sometimes malleable and sometimes brittle that hydrogen will sometimes combine with oxygen and sometimes not or the like If from simple substances we pass to any of their definite compounds as water lime or sulphuric acid there is the same constancy in their properties When properties vary from individual to individual it is either in the case of miscellaneous aggregations such as atmospheric air or rock composed of heterogeneous substances and not constituting or belonging to any real Kind or it is in the case of organic beings In them indeed there is variability in a high degree Animals of the same species and race human beings of the same age sex and country will be most different for example in face and figure But organized beings from the extreme complication of the laws by which they are regulated being more eminently modifiable that is liable to be influenced by a greater number and variety of causes than any other phenomena whatever having also themselves had a beginning and therefore a cause there is reason to believe that none of their properties are ultimate but all of them derivative and produced by causation And the presumption is confirmed by the fact that the properties which vary from one individual to another also generally vary more or less at different times in the same individual which variation like any other event supposes a cause and implies consequently that the properties are not independent of causation If therefore blackness be merely accidental in crows and capable of varying while the Kind remains the same its presence or absence is doubtless no ultimate fact but the effect of some unknown cause and in that case the universality of the experience that all crows are black is sufficient proof of a common cause and establishes the generalization as an empirical law Since there are innumerable instances in the affirmative and hitherto none at all in the negative the causes on which the property depends must exist everywhere in the limits of the observations which have been made and the proposition may be received as universal within those limits and with the allowable degree of extension to adjacent cases If in the second place the property in the instances in which it has been observed is not an effect of causation it is a property of Kind and in that case the generalization can only be set aside by the discovery of a new Kind of crow That however a peculiar Kind not hitherto discovered should exist in nature is a supposition so often realized that it can not be considered at all improbable We have nothing to authorize us in attempting to limit the Kinds of things which exist in nature The only unlikelihood would be that a new Kind should be discovered in localities which there was previously reason to believe had been thoroughly explored and even this improbability depends on the degree of conspicuousness of the difference between the newlydiscovered Kind and all others since new kinds of minerals plants and even animals previously overlooked or confounded with known species are still continually detected in the most frequented situations On this second ground therefore as well as on the first the observed uniformity of coexistence can only hold good as an empirical law within the limits not only of actual observation but of an observation as accurate as the nature of the case required And hence it is that as remarked in an early chapter of the present book we so often give up generalizations of this class at the first summons If any credible witness stated that he had seen a white crow under circumstances which made it not incredible that it should have escaped notice previously we should give full credence to the statement It appears then that the uniformities which obtain in the coexistence of phenomena those which we have reason to consider as ultimate no less than those which arise from the laws of causes yet undetected are entitled to reception only as empirical laws are not to be presumed true except within the limits of time place and circumstance in which the observations were made or except in cases strictly adjacent We have seen in the last chapter that there is a point of generality at which empirical laws become as certain as laws of nature or rather at which there is no longer any distinction between empirical laws and laws of nature As empirical laws approach this point in other words as they rise in their degree of generality they become more certain their universality may be more strongly relied on For in the first place if they are results of causation which even in the class of uniformities treated of in the present chapter we never can be certain that they are not the more general they are the greater is proved to be the space over which the necessary collocations prevail and within which no causes exist capable of counteracting the unknown causes on which the empirical law depends To say that any thing is an invariable property of some very limited class of objects is to say that it invariably accompanies some very numerous and complex group of distinguishing properties which if causation be at all concerned in the matter argues a combination of many causes and therefore a great liability to counteraction while the comparatively narrow range of the observations renders it impossible to predict to what extent unknown counteracting causes may be distributed throughout nature But when a generalization has been found to hold good of a very large proportion of all things whatever it is already proved that nearly all the causes which exist in nature have no power over it that very few changes in the combination of causes can affect it since the greater number of possible combinations must have already existed in some one or other of the instances in which it has been found true If therefore any empirical law is a result of causation the more general it is the more it may be depended on And even if it be no result of causation but an ultimate coexistence the more general it is the greater amount of experience it is derived from and the greater therefore is the probability that if exceptions had existed some would already have presented themselves For these reasons it requires much more evidence to establish an exception to one of the more general empirical laws than to the more special ones We should not have any difficulty in believing that there might be a new Kind of crow or a new kind of bird resembling a crow in the properties hitherto considered distinctive of that Kind But it would require stronger proof to convince us of the existence of a Kind of crow having properties at variance with any generally recognized universal property of birds and a still higher degree if the properties conflict with any recognized universal property of animals And this is conformable to the mode of judgment recommended by the common sense and general practice of mankind who are more incredulous as to any novelties in nature according to the degree of generality of the experience which these novelties seem to contradict It is conceivable that the alleged properties might conflict with some recognized universal property of all matter In that case their improbability would be at the highest but would not even then amount to incredibility There are only two known properties common to all matter in other words there is but one known uniformity of coexistence of properties coextensive with all physical nature namely that whatever opposes resistance to movement gravitates or as Professor Bain expresses it Inertia and Gravity are coexistent through all matter and proportionate in their amount These properties as he truly says are not mutually implicated from neither of them could we on grounds of causation presume the other But for this very reason we are never certain that a Kind may not be discovered possessing one of the properties without the other The hypothetical ether if it exists may be such a Kind Our senses can not recognize in it either resistance or gravity but if the reality of a resisting medium should eventually be proved by alteration for example in the times of revolution of periodic comets combined with the evidences afforded by the phenomena of light and heat it would be rash to conclude from this alone without other proofs that it must gravitate For even the greater generalizations which embrace comprehensive Kinds containing under them a great number and variety of infimae species are only empirical laws resting on induction by simple enumeration merely and not on any process of elimination a process wholly inapplicable to this sort of case Such generalizations therefore ought to be grounded on an examination of all the infimae species comprehended in them and not of a portion only We can not conclude where causation is not concerned because a proposition is true of a number of things resembling one another only in being animals that it is therefore true of all animals If indeed any thing be true of species which differ more from one another than either differs from a third especially if that third species occupies in most of its known properties a position between the two former there is some probability that the same thing will also be true of that intermediate species for it is often though by no means universally found that there is a sort of parallelism in the properties of different Kinds and that their degree of unlikeness in one respect bears some proportion to their unlikeness in others We see this parallelism in the properties of the different metals in those of sulphur phosphorus and carbon of chlorine iodine and bromine in the natural orders of plants and animals etc But there are innumerable anomalies and exceptions to this sort of conformity if indeed the conformity itself be any thing but an anomaly and an exception in nature Universal propositions therefore respecting the properties of superior Kinds unless grounded on proved or presumed connection by causation ought not to be hazarded except after separately examining every known subkind included in the larger Kind And even then such generalizations must be held in readiness to be given up on the occurrence of some new anomaly which when the uniformity is not derived from causation can never even in the case of the most general of these empirical laws be considered very improbable Thus all the universal propositions which it has been attempted to lay down respecting simple substances or concerning any of the classes which have been formed among simple substances and the attempt has been often made have with the progress of experience either faded into inanity or been proved to be erroneous and each Kind of simple substance remains with its own collection of properties apart from the rest saving a certain parallelism with a few other Kinds the most similar to itself In organized beings indeed there are abundance of propositions ascertained to be universally true of superior genera to many of which the discovery hereafter of any exceptions must be regarded as extremely improbable But these as already observed are we have every reason to believe properties dependent on causation Uniformities of coexistence then not only when they are consequences of laws of succession but also when they are ultimate truths must be ranked for the purpose of logic among empirical laws and are amenable in every respect to the same rules with those unresolved uniformities which are known to be dependent on causation
In our inquiries into the nature of the inductive process we must not confine our notice to such generalizations from experience as profess to be universally true There is a class of inductive truths avowedly not universal in which it is not pretended that the predicate is always true of the subject but the value of which as generalizations is nevertheless extremely great An important portion of the field of inductive knowledge does not consist of universal truths but of approximations to such truths and when a conclusion is said to rest on probable evidence the premises it is drawn from are usually generalizations of this sort As every certain inference respecting a particular case implies that there is ground for a general proposition of the form every A is B so does every probable inference suppose that there is ground for a proposition of the form Most A are B and the degree of probability of the inference in an average case will depend on the proportion between the number of instances existing in nature which accord with the generalization and the number of those which conflict with it Propositions in the form Most A are B are of a very different degree of importance in science and in the practice of life To the scientific inquirer they are valuable chiefly as materials for and steps toward universal truths The discovery of these is the proper end of science its work is not done if it stops at the proposition that a majority of A are B without circumscribing that majority by some common character fitted to distinguish them from the minority Independently of the inferior precision of such imperfect generalizations and the inferior assurance with which they can be applied to individual cases it is plain that compared with exact generalizations they are almost useless as means of discovering ulterior truths by way of deduction We may it is true by combining the proposition Most A are B with a universal proposition Every B is C arrive at the conclusion that Most A are C But when a second proposition of the approximate kind is introduced or even when there is but one if that one be the major premise nothing can in general be positively concluded When the major is Most B are D then even if the minor be Every A is B we can not infer that most A are D or with any certainty that even some A are D Though the majority of the class B have the attribute signified by D the whole of the subclass A may belong to the minority Though so little use can be made in science of approximate generalizations except as a stage on the road to something better for practical guidance they are often all we have to rely on Even when science has really determined the universal laws of any phenomenon not only are those laws generally too much encumbered with conditions to be adapted for everyday use but the cases which present themselves in life are too complicated and our decisions require to be taken too rapidly to admit of waiting till the existence of a phenomenon can be proved by what have been scientifically ascertained to be universal marks of it To be indecisive and reluctant to act because we have not evidence of a perfectly conclusive character to act on is a defect sometimes incident to scientific minds but which wherever it exists renders them unfit for practical emergencies If we would succeed in action we must judge by indications which though they do not generally mislead us sometimes do and must make up as far as possible for the incomplete conclusiveness of any one indication by obtaining others to corroborate it The principles of induction applicable to approximate generalization are therefore a not less important subject of inquiry than the rules for the investigation of universal truths and might reasonably be expected to detain us almost as long were it not that these principles are mere corollaries from those which have been already treated of There are two sorts of cases in which we are forced to guide ourselves by generalizations of the imperfect form Most A are B The first is when we have no others when we have not been able to carry our investigation of the laws of the phenomena any further as in the following propositions Most darkeyed persons have dark hair Most springs contain mineral substances Most stratified formations contain fossils The importance of this class of generalizations is not very great for though it frequently happens that we see no reason why that which is true of most individuals of a class is not true of the remainder nor are able to bring the former under any general description which can distinguish them from the latter yet if we are willing to be satisfied with propositions of a less degree of generality and to break down the class A into subclasses we may generally obtain a collection of propositions exactly true We do not know why most wood is lighter than water nor can we point out any general property which discriminates wood that is lighter than water from that which is heavier But we know exactly what species are the one and what the other And if we meet with a specimen not conformable to any known species the only case in which our previous knowledge affords no other guidance than the approximate generalization we can generally make a specific experiment which is a surer resource It often happens however that the proposition Most A are B is not the ultimatum of our scientific attainments though the knowledge we possess beyond it can not conveniently be brought to bear upon the particular instance We may know well enough what circumstances distinguish the portion of A which has the attribute B from the portion which has it not but may have no means or may not have time to examine whether those characteristic circumstances exist or not in the individual case This is the situation we are generally in when the inquiry is of the kind called moral that is of the kind which has in view to predict human actions To enable us to affirm any thing universally concerning the actions of classes of human beings the classification must be grounded on the circumstances of their mental culture and habits which in an individual case are seldom exactly known and classes grounded on these distinctions would never precisely accord with those into which mankind are divided for social purposes All propositions which can be framed respecting the actions of human beings as ordinarily classified or as classified according to any kind of outward indications are merely approximate We can only say Most persons of a particular age profession country or rank in society have such and such qualities or Most persons when placed in certain circumstances act in such and such a way Not that we do not often know well enough on what causes the qualities depend or what sort of persons they are who act in that particular way but we have seldom the means of knowing whether any individual person has been under the influence of those causes or is a person of that particular sort We could replace the approximate generalizations by propositions universally true but these would hardly ever be capable of being applied to practice We should be sure of our majors but we should not be able to get minors to fit we are forced therefore to draw our conclusions from coarser and more fallible indications Proceeding now to consider what is to be regarded as sufficient evidence of an approximate generalization we can have no difficulty in at once recognizing that when admissible at all it is admissible only as an empirical law Propositions of the form Every A is B are not necessarily laws of causation or ultimate uniformities of coexistence propositions like Most A are B can not be so Propositions hitherto found true in every observed instance may yet be no necessary consequence of laws of causation or of ultimate uniformities and unless they are so may for aught we know be false beyond the limits of actual observation still more evidently must this be the case with propositions which are only true in a mere majority of the observed instances There is some difference however in the degree of certainty of the proposition Most A are B according as that approximate generalization composes the whole of our knowledge of the subject or not Suppose first that the former is the case We know only that most A are B not why they are so nor in what respect those which are differ from those which are not How then did we learn that most A are B Precisely in the manner in which we should have learned had such happened to be the fact that all A are B We collected a number of instances sufficient to eliminate chance and having done so compared the number of instances in the affirmative with the number in the negative The result like other unresolved derivative laws can be relied on solely within the limits not only of place and time but also of circumstance under which its truth has been actually observed for as we are supposed to be ignorant of the causes which make the proposition true we can not tell in what manner any new circumstance might perhaps affect it The proposition Most judges are inaccessible to bribes would probably be found true of Englishmen Frenchmen Germans North Americans and so forth but if on this evidence alone we extended the assertion to Orientals we should step beyond the limits not only of place but of circumstance within which the fact had been observed and should let in possibilities of the absence of the determining causes or the presence of counteracting ones which might be fatal to the approximate generalization In the case where the approximate proposition is not the ultimatum of our scientific knowledge but only the most available form of it for practical guidance where we know not only that most A have the attribute B but also the causes of B or some properties by which the portion of A which has that attribute is distinguished from the portion which has it not we are rather more favorably situated than in the preceding case For we have now a double mode of ascertaining whether it be true that most A are B the direct mode as before and an indirect one that of examining whether the proposition admits of being deduced from the known cause or from any known criterion of B Let the question for example be whether most Scotchmen can read We may not have observed or received the testimony of others respecting a sufficient number and variety of Scotchmen to ascertain this fact but when we consider that the cause of being able to read is the having been taught it another mode of determining the question presents itself namely by inquiring whether most Scotchmen have been sent to schools where reading is effectually taught Of these two modes sometimes one and sometimes the other is the more available In some cases the frequency of the effect is the more accessible to that extensive and varied observation which is indispensable to the establishment of an empirical law at other times the frequency of the causes or of some collateral indications It commonly happens that neither is susceptible of so satisfactory an induction as could be desired and that the grounds on which the conclusion is received are compounded of both Thus a person may believe that most Scotchmen can read because so far as his information extends most Scotchmen have been sent to school and most Scotch schools teach reading effectually and also because most of the Scotchmen whom he has known or heard of could read though neither of these two sets of observations may by itself fulfill the necessary conditions of extent and variety Although the approximate generalization may in most cases be indispensable for our guidance even when we know the cause or some certain mark of the attribute predicated it needs hardly be observed that we may always replace the uncertain indication by a certain one in any case in which we can actually recognize the existence of the cause or mark For example an assertion is made by a witness and the question is whether to believe it If we do not look to any of the individual circumstances of the case we have nothing to direct us but the approximate generalization that truth is more common than falsehood or, in other words, that most persons on most occasions speak truth But if we consider in what circumstances the cases where truth is spoken differ from those in which it is not we find for instance the following the witness’s being an honest person or not his being an accurate observer or not his having an interest to serve in the matter or not Now not only may we be able to obtain other approximate generalizations respecting the degree of frequency of these various possibilities but we may know which of them is positively realized in the individual case That the witness has or has not an interest to serve we perhaps know directly and the other two points indirectly by means of marks as for example from his conduct on some former occasion or from his reputation which though a very uncertain mark affords an approximate generalization as for instance Most persons who are believed to be honest by those with whom they have had frequent dealings are really so which approaches nearer to a universal truth than the approximate general proposition with which we set out viz Most persons on most occasions speak truth As it seems unnecessary to dwell further on the question of the evidence of approximate generalizations we shall proceed to a not less important topic that of the cautions to be observed in arguing from these incompletely universal propositions to particular cases So far as regards the direct application of an approximate generalization to an individual instance this question presents no difficulty If the proposition Most A are B has been established by a sufficient induction as an empirical law we may conclude that any particular A is B with a probability proportioned to the preponderance of the number of affirmative instances over the number of exceptions If it has been found practicable to attain numerical precision in the data a corresponding degree of precision may be given to the evaluation of the chances of error in the conclusion If it can be established as an empirical law that nine out of every ten A are B there will be one chance in ten of error in assuming that any A not individually known to us is a B but this of course holds only within the limits of time place and circumstance embraced in the observations and therefore can not be counted on for any subclass or variety of A or for A in any set of external circumstances which were not included in the average It must be added that we can guide ourselves by the proposition Nine out of every ten A are B only in cases of which we know nothing except that they fall within the class A For if we know of any particular instances i not only that it falls under A but to what species or variety of A it belongs we shall generally err in applying to i the average struck for the whole genus from which the average corresponding to that species alone would in all probability materially differ And so if i instead of being a particular sort of instance is an instance known to be under the influence of a particular set of circumstances the presumption drawn from the numerical proportions in the whole genus would probably in such a case only mislead A general average should only be applied to cases which are neither known nor can be presumed to be other than average cases Such averages therefore are commonly of little use for the practical guidance of any affairs but those which concern large numbers Tables of the chances of life are useful to insurance offices but they go a very little way toward informing any one of the chances of his own life or any other life in which he is interested since almost every life is either better or worse than the average Such averages can only be considered as supplying the first term in a series of approximations the subsequent terms proceeding on an appreciation of the circumstances belonging to the particular case From the application of a single approximate generalization to individual cases we proceed to the application of two or more of them together to the same case When a judgment applied to an individual instance is grounded on two approximate generalizations taken in conjunction the propositions may cooperate toward the result in two different ways In the one each proposition is separately applicable to the case in hand and our object in combining them is to give to the conclusion in that particular case the double probability arising from the two propositions separately This may be called joining two probabilities by way of Addition and the result is a probability greater than either The other mode is when only one of the propositions is directly applicable to the case the second being only applicable to it by virtue of the application of the first This is joining two probabilities by way of Ratiocination or Deduction the result of which is a less probability than either The type of the first argument is Most A are B most C are B this thing is both an A and a C therefore it is probably a B The type of the second is Most A are B most C are A this is a C therefore it is probably an A therefore it is probably a B The first is exemplified when we prove a fact by the testimony of two unconnected witnesses the second when we adduce only the testimony of one witness that he has heard the thing asserted by another Or again in the first mode it may be argued that the accused committed the crime because he concealed himself and because his clothes were stained with blood in the second that he committed it because he washed or destroyed his clothes which is supposed to render it probable that they were stained with blood Instead of only two links as in these instances we may suppose chains of any length A chain of the former kind was termed by Bentham a selfcorroborative chain of evidence the second a selfinfirmative chain When approximate generalizations are joined by way of addition we may deduce from the theory of probabilities laid down in a former chapter in what manner each of them adds to the probability of a conclusion which has the warrant of them all If on an average two of every three As are Bs and three of every four Cs are Bs the probability that something which is both an A and a C is a B will be more than two in three or than three in four Of every twelve things which are As all except four are Bs by the supposition and if the whole twelve and consequently those four have the characters of C likewise three of these will be Bs on that ground Therefore out of twelve which are both As and Cs eleven are Bs To state the argument in another way a thing which is both an A and a C but which is not a B is found in only one of three sections of the class A and in only one of four sections of the class C but this fourth of C being spread over the whole of A indiscriminately only onethird part of it or onetwelfth of the whole number belongs to the third section of A therefore a thing which is not a B occurs only once among twelve things which are both As and Cs The argument would in the language of the doctrine of chances be thus expressed the chance that an A is not a B is 13 the chance that a C is not a B is 14 hence if the thing be both an A and a C the chance is 13 of 14 112 In this computation it is of course supposed that the probabilities arising from A and C are independent of each other There must not be any such connection between A and C that when a thing belongs to the one class it will therefore belong to the other or even have a greater chance of doing so Otherwise the notBs which are Cs may be most or even all of them identical with the notBs which are As in which last case the probability arising from A and C together will be no greater than that arising from A alone When approximate generalizations are joined together in the other mode that of deduction the degree of probability of the inference instead of increasing diminishes at each step From two such premises as Most A are B Most B are C we can not with certainty conclude that even a single A is C for the whole of the portion of A which in any way falls under B may perhaps be comprised in the exceptional part of it Still the two propositions in question afford an appreciable probability that any given A is C provided the average on which the second proposition is grounded was taken fairly with reference to the first provided the proposition Most B are C was arrived at in a manner leaving no suspicion that the probability arising from it is otherwise than fairly distributed over the section of B which belongs to A For though the instances which are A may be all in the minority they may also be all in the majority and the one possibility is to be set against the other On the whole the probability arising from the two propositions taken together will be correctly measured by the probability arising from the one abated in the ratio of that arising from the other If nine out of ten Swedes have light hair and eight out of nine inhabitants of Stockholm are Swedes the probability arising from these two propositions that any given inhabitant of Stockholm is lighthaired will amount to eight in ten though it is rigorously possible that the whole Swedish population of Stockholm might belong to that tenth section of the people of Sweden who are an exception to the rest If the premises are known to be true not of a bare majority but of nearly the whole of their respective subjects we may go on joining one such proposition to another for several steps before we reach a conclusion not presumably true even of a majority The error of the conclusion will amount to the aggregate of the errors of all the premises Let the proposition most A are B be true of nine in ten Most B are C of eight in nine then not only will one A in ten not be C because not B but even of the ninetenths which are B only eightninths will be C that is the cases of A which are C will be only 89 of 910 or fourfifths Let us now add Most C are D and suppose this to be true of seven cases out of eight the proportion of A which is D will be only 78 of 89 of 910 or 710 Thus the probability progressively dwindles The experience however on which our approximate generalizations are grounded has so rarely been subjected to or admits of accurate numerical estimation that we can not in general apply any measurement to the diminution of probability which takes place at each illation but must be content with remembering that it does diminish at every step and that unless the premises approach very nearly indeed to being universally true the conclusion after a very few steps is worth nothing A hearsay of a hearsay or an argument from presumptive evidence depending not on immediate marks but on marks of marks is worthless at a very few removes from the first stage There are however two cases in which reasonings depending on approximate generalizations may be carried to any length we please with as much assurance and are as strictly scientific as if they were composed of universal laws of nature But these cases are exceptions of the sort which are currently said to prove the rule The approximate generalizations are as suitable in the cases in question for purposes of ratiocination as if they were complete generalizations because they are capable of being transformed into complete generalizations exactly equivalent First If the approximate generalization is of the class in which our reason for stopping at the approximation is not the impossibility but only the inconvenience of going further if we are cognizant of the character which distinguishes the cases that accord with the generalization from those which are exceptions to it we may then substitute for the approximate proposition a universal proposition with a proviso The proposition Most persons who have uncontrolled power employ it ill is a generalization of this class and may be transformed into the following All persons who have uncontrolled power employ it ill provided they are not persons of unusual strength of judgment and rectitude of purpose The proposition carrying the hypothesis or proviso with it may then be dealt with no longer as an approximate but as a universal proposition and to whatever number of steps the reasoning may reach the hypothesis being carried forward to the conclusion will exactly indicate how far that conclusion is from being applicable universally If in the course of the argument other approximate generalizations are introduced each of them being in like manner expressed as a universal proposition with a condition annexed the sum of all the conditions will appear at the end as the sum of all the errors which affect the conclusion Thus to the proposition last cited let us add the following All absolute monarchs have uncontrolled power unless their position is such that they need the active support of their subjects as was the case with Queen Elizabeth Frederick of Prussia and others Combining these two propositions we can deduce from them a universal conclusion which will be subject to both the hypotheses in the premises All absolute monarchs employ their power ill unless their position makes them need the active support of their subjects or unless they are persons of unusual strength of judgment and rectitude of purpose It is of no consequence how rapidly the errors in our premises accumulate if we are able in this manner to record each error and keep an account of the aggregate as it swells up Secondly there is a case in which approximate propositions even without our taking note of the conditions under which they are not true of individual cases are yet for the purposes of science universal ones namely in the inquiries which relate to the properties not of individuals but of multitudes The principal of these is the science of politics or of human society This science is principally concerned with the actions not of solitary individuals but of masses with the fortunes not of single persons but of communities For the statesman therefore it is generally enough to know that most persons act or are acted upon in a particular way since his speculations and his practical arrangements refer almost exclusively to cases in which the whole community or some large portion of it is acted upon at once and in which therefore what is done or felt by most persons determines the result produced by or upon the body at large He can get on well enough with approximate generalizations on human nature since what is true approximately of all individuals is true absolutely of all masses And even when the operations of individual men have a part to play in his deductions as when he is reasoning of kings or other single rulers still as he is providing for indefinite duration involving an indefinite succession of such individuals he must in general both reason and act as if what is true of most persons were true of all The two kinds of considerations above adduced are a sufficient refutation of the popular error that speculations on society and government as resting on merely probable evidence must be inferior in certainty and scientific accuracy to the conclusions of what are called the exact sciences and less to be relied on in practice There are reasons enough why the moral sciences must remain inferior to at least the more perfect of the physical why the laws of their more complicated phenomena can not be so completely deciphered nor the phenomena predicted with the same degree of assurance But though we can not attain to so many truths there is no reason that those we can attain should deserve less reliance or have less of a scientific character Of this topic however I shall treat more systematically in the concluding Book to which place any further consideration of it must be deferred In the First Book we found that all the assertions which can be conveyed by language express some one or more of five different things Existence Order in Place Order in Time Causation and Resemblance Of these Causation in our view of the subject not being fundamentally different from Order in Time the five species of possible assertions are reduced to four The propositions which affirm Order in Time in either of its two modes Coexistence and Succession have formed thus far the subject of the present Book And we have now concluded the exposition so far as it falls within the limits assigned to this work of the nature of the evidence on which these propositions rest and the processes of investigation by which they are ascertained and proved There remain three classes of facts Existence Order in Place and Resemblance in regard to which the same questions are now to be resolved Regarding the first of these very little needs be said Existence in general is a subject not for our science but for metaphysics To determine what things can be recognized as really existing independently of our own sensible or other impressions and in what meaning the term is in that case predicated of them belongs to the consideration of Things in themselves from which throughout this work we have as much as possible kept aloof Existence so far as Logic is concerned about it has reference only to phenomena to actual or possible states of external or internal consciousness in ourselves or others Feelings of sensitive beings or possibilities of having such feelings are the only things the existence of which can be a subject of logical induction because the only things of which the existence in individual cases can be a subject of experience It is true that a thing is said by us to exist even when it is absent and therefore is not and can not be perceived But even then its existence is to us only another word for our conviction that we should perceive it on a certain supposition namely if we were in the needful circumstances of time and place and endowed with the needful perfection of organs My belief that the Emperor of China exists is simply my belief that if I were transported to the imperial palace or some other locality in Pekin I should see him My belief that Julius Caesar existed is my belief that I should have seen him if I had been present in the field of Pharsalia or in the senatehouse at Rome When I believe that stars exist beyond the utmost range of my vision though assisted by the most powerful telescopes yet invented my belief philosophically expressed is that with still better telescopes if such existed I could see them or that they may be perceived by beings less remote from them in space or whose capacities of perception are superior to mine The existence therefore of a phenomenon is but another word for its being perceived or for the inferred possibility of perceiving it When the phenomenon is within the range of present observation by present observation we assure ourselves of its existence when it is beyond that range and is therefore said to be absent we infer its existence from marks or evidences But what can these evidences be Other phenomena ascertained by induction to be connected with the given phenomenon either in the way of succession or of coexistence The simple existence therefore of an individual phenomenon when not directly perceived is inferred from some inductive law of succession or coexistence and is consequently not amenable to any peculiar inductive principles We prove the existence of a thing by proving that it is connected by succession or coexistence with some known thing With respect to general propositions of this class that is which affirm the bare fact of existence they have a peculiarity which renders the logical treatment of them a very easy matter they are generalizations which are sufficiently proved by a single instance That ghosts or unicorns or seaserpents exist would be fully established if it could be ascertained positively that such things had been even once seen Whatever has once happened is capable of happening again the only question relates to the conditions under which it happens So far therefore as relates to simple existence the Inductive Logic has no knots to untie And we may proceed to the remaining two of the great classes into which facts have been divided Resemblance and Order in Place Resemblance and its opposite except in the case in which they assume the names of Equality and Inequality are seldom regarded as subjects of science they are supposed to be perceived by simple apprehension by merely applying our senses or directing our attention to the two objects at once or in immediate succession And this simultaneous or virtually simultaneous application of our faculties to the two things which are to be compared does necessarily constitute the ultimate appeal wherever such application is practicable But in most cases it is not practicable the objects can not be brought so close together that the feeling of their resemblance at least a complete feeling of it directly arises in the mind We can only compare each of them with some third object capable of being transported from one to the other And besides even when the objects can be brought into immediate juxtaposition their resemblance or difference is but imperfectly known to us unless we have compared them minutely part by part Until this has been done things in reality very dissimilar often appear undistinguishably alike Two lines of very unequal length will appear about equal when lying in different directions but place them parallel with their farther extremities even and if we look at the nearer extremities their inequality becomes a matter of direct perception To ascertain whether and in what two phenomena resemble or differ is not always therefore so easy a thing as it might at first appear When the two can not be brought into juxtaposition or not so that the observer is able to compare their several parts in detail he must employ the indirect means of reasoning and general propositions When we can not bring two straight lines together to determine whether they are equal we do it by the physical aid of a footrule applied first to one and then to the other and the logical aid of the general proposition or formula Things which are equal to the same thing are equal to one another The comparison of two things through the intervention of a third thing when their direct comparison is impossible is the appropriate scientific process for ascertaining resemblances and dissimilarities and is the sum total of what Logic has to teach on the subject An undue extension of this remark induced Locke to consider reasoning itself as nothing but the comparison of two ideas through the medium of a third and knowledge as the perception of the agreement or disagreement of two ideas doctrines which the Condillac school blindly adopted without the qualifications and distinctions with which they were studiously guarded by their illustrious author Where indeed the agreement or disagreement otherwise called resemblance or dissimilarity of any two things is the very matter to be determined as is the case particularly in the sciences of quantity and extension there the process by which a solution if not attainable by direct perception must be indirectly sought consists in comparing these two things through the medium of a third But this is far from being true of all inquiries The knowledge that bodies fall to the ground is not a perception of agreement or disagreement but of a series of physical occurrences a succession of sensations Locke’s definitions of knowledge and of reasoning required to be limited to our knowledge of and reasoning about resemblances Nor even when thus restricted are the propositions strictly correct since the comparison is not made as he represents between the ideas of the two phenomena but between the phenomena themselves This mistake has been pointed out in an earlier part of our inquiry and we traced it to an imperfect conception of what takes place in mathematics where very often the comparison is really made between the ideas without any appeal to the outward senses only however because in mathematics a comparison of the ideas is strictly equivalent to a comparison of the phenomena themselves Where as in the case of numbers lines and figures our idea of an object is a complete picture of the object so far as respects the matter in hand we can of course learn from the picture whatever could be learned from the object itself by mere contemplation of it as it exists at the particular instant when the picture is taken No mere contemplation of gunpowder would ever teach us that a spark would make it explode nor consequently would the contemplation of the idea of gunpowder do so but the mere contemplation of a straight line shows that it can not enclose a space accordingly the contemplation of the idea of it will show the same What takes place in mathematics is thus no argument that the comparison is between the ideas only It is always either indirectly or directly a comparison of the phenomena In cases in which we can not bring the phenomena to the test of direct inspection at all or not in a manner sufficiently precise but must judge of their resemblance by inference from other resemblances or dissimilarities more accessible to observation we of course require as in all cases of ratiocination generalizations or formulae applicable to the subject We must reason from laws of nature from the uniformities which are observable in the fact of likeness or unlikeness Of these laws or uniformities the most comprehensive are those supplied by mathematics the axioms relating to equality inequality and proportionality and the various theorems thereon founded And these are the only Laws of Resemblance which require to be or which can be treated apart It is true there are innumerable other theorems which affirm resemblances among phenomena as that the angle of the reflection of light is equal to its angle of incidence equality being merely exact resemblance in magnitude Again that the heavenly bodies describe equal areas in equal times and that their periods of revolution are proportional another species of resemblance to the sesquiplicate powers of their distances from the centre of force These and similar propositions affirm resemblances of the same nature with those asserted in the theorems of mathematics but the distinction is that the propositions of mathematics are true of all phenomena whatever or at least without distinction of origin while the truths in question are affirmed only of special phenomena which originate in a certain way and the equalities proportionalities or other resemblances which exist between such phenomena must necessarily be either derived from or identical with the law of their origin the law of causation on which they depend The equality of the areas described in equal times by the planets is derived from the laws of the causes and until its derivation was shown it was an empirical law The equality of the angles of reflection and incidence is identical with the law of the cause for the cause is the incidence of a ray of light upon a reflecting surface and the equality in question is the very law according to which that cause produces its effects This class therefore of the uniformities of resemblance between phenomena are inseparable in fact and in thought from the laws of the production of those phenomena and the principles of induction applicable to them are no other than those of which we have treated in the preceding chapters of this Book It is otherwise with the truths of mathematics The laws of equality and inequality between spaces or between numbers have no connection with laws of causation That the angle of reflection is equal to the angle of incidence is a statement of the mode of action of a particular cause but that when two straight lines intersect each other the opposite angles are equal is true of all such lines and angles by whatever cause produced That the squares of the periodic times of the planets are proportional to the cubes of their distances from the sun is a uniformity derived from the laws of the causes or forces which produce the planetary motions but that the square of any number is four times the square of half the number is true independently of any cause The only laws of resemblance therefore which we are called upon to consider independently of causation belong to the province of mathematics The same thing is evident with respect to the only one remaining of our five categories Order in Place The order in place of the effects of a cause is like every thing else belonging to the effects a consequence of the laws of that cause The order in place or as we have termed it the collocation of the primeval causes is as well as their resemblance in each instance an ultimate fact in which no laws or uniformities are traceable The only remaining general propositions respecting order in place and the only ones which have nothing to do with causation are some of the truths of geometry laws through which we are able from the order in place of certain points lines or spaces to infer the order in place of others which are connected with the former in some known mode quite independently of the particular nature of those points lines or spaces in any other respect than position or magnitude as well as independently of the physical cause from which in any particular case they happen to derive their origin It thus appears that mathematics is the only department of science into the methods of which it still remains to inquire And there is the less necessity that this inquiry should occupy us long as we have already in the Second Book made considerable progress in it We there remarked that the directly inductive truths of mathematics are few in number consisting of the axioms together with certain propositions concerning existence tacitly involved in most of the socalled definitions And we gave what appeared conclusive reasons for affirming that these original premises from which the remaining truths of the science are deduced are notwithstanding all appearances to the contrary results of observation and experience founded in short on the evidence of the senses That things equal to the same thing are equal to one another and that two straight lines which have once intersected one another continue to diverge are inductive truths resting indeed like the law of universal causation only on induction per enumerationem simplicem on the fact that they have been perpetually perceived to be true and never once found to be false But as we have seen in a recent chapter that this evidence in the case of a law so completely universal as the law of causation amounts to the fullest proof so is this even more evidently true of the general propositions to which we are now adverting because as a perception of their truth in any individual case whatever requires only the simple act of looking at the objects in a proper position there never could have been in their case what for a long period there were in the case of the law of causation instances which were apparently though not really exceptions to them Their infallible truth was recognized from the very dawn of speculation and as their extreme familiarity made it impossible for the mind to conceive the objects under any other law they were and still are generally considered as truths recognized by their own evidence or by instinct There is something which seems to require explanation in the fact that the immense multitude of truths a multitude still as far from being exhausted as ever comprised in the mathematical sciences can be elicited from so small a number of elementary laws One sees not at first how it is that there can be room for such an infinite variety of true propositions on subjects apparently so limited To begin with the science of number The elementary or ultimate truths of this science are the common axioms concerning equality namely Things which are equal to the same thing are equal to one another and Equals added to equals make equal sums no other axioms are required together with the definitions of the various numbers Like other socalled definitions these are composed of two things the explanation of a name and the assertion of a fact of which the latter alone can form a first principle or premise of a science The fact asserted in the definition of a number is a physical fact Each of the numbers two three four etc denotes physical phenomena and connotes a physical property of those phenomena Two for instance denotes all pairs of things and twelve all dozens of things connoting what makes them pairs or dozens and that which makes them so is something physical since it can not be denied that two apples are physically distinguishable from three apples two horses from one horse and so forth that they are a different visible and tangible phenomenon I am not undertaking to say what the difference is it is enough that there is a difference of which the senses can take cognizance And although a hundred and two horses are not so easily distinguished from a hundred and three as two horses are from three though in most positions the senses do not perceive any difference yet they may be so placed that a difference will be perceptible or else we should never have distinguished them and given them different names Weight is confessedly a physical property of things yet small differences between great weights are as imperceptible to the senses in most situations as small differences between great numbers and are only put in evidence by placing the two objects in a peculiar position namely in the opposite scales of a delicate balance What then is that which is connoted by a name of number Of course some property belonging to the agglomeration of things which we call by the name and that property is the characteristic manner in which the agglomeration is made up of and may be separated into parts I will endeavour to make this more intelligible by a few explanations When we call a collection of objects two three or four they are not two three or four in the abstract they are two three or four things of some particular kind pebbles horses inches pounds’ weight What the name of number connotes is the manner in which single objects of the given kind must be put together in order to produce that particular aggregate If the aggregate be of pebbles and we call it two the name implies that to compose the aggregate one pebble must be joined to one pebble If we call it three one and one and one pebble must be brought together to produce it or else one pebble must be joined to an aggregate of the kind called two already existing The aggregate which we call four has a still greater number of characteristic modes of formation One and one and one and one pebble may be brought together or two aggregates of the kind called two may be united or one pebble may be added to an aggregate of the kind called three Every succeeding number in the ascending series may be formed by the junction of smaller numbers in a progressively greater variety of ways Even limiting the parts to two the number may be formed and consequently may be divided in as many different ways as there are numbers smaller than itself and if we admit of threes fours etc in a still greater variety Other modes of arriving at the same aggregate present themselves not by the union of smaller but by the dismemberment of larger aggregates Thus three pebbles may be formed by taking away one pebble from an aggregate of four two pebbles by an equal division of a similar aggregate and so on Every arithmetical proposition every statement of the result of an arithmetical operation is a statement of one of the modes of formation of a given number It affirms that a certain aggregate might have been formed by putting together certain other aggregates or by withdrawing certain portions of some aggregate and that by consequence we might reproduce those aggregates from it by reversing the process Thus when we say that the cube of 12 is 1728 what we affirm is this that if having a sufficient number of pebbles or of any other objects we put them together into the particular sort of parcels or aggregates called twelves and put together these twelves again into similar collections and finally make up twelve of these largest parcels the aggregate thus formed will be such a one as we call 1728 namely that which to take the most familiar of its modes of formation may be made by joining the parcel called a thousand pebbles the parcel called seven hundred pebbles the parcel called twenty pebbles and the parcel called eight pebbles The converse proposition that the cube root of 1728 is 12 asserts that this large aggregate may again be decomposed into the twelve twelves of twelves of pebbles which it consists of The modes of formation of any number are innumerable but when we know one mode of formation of each all the rest may be determined deductively If we know that a is formed from b and c b from a and e c from d and f and so forth until we have included all the numbers of any scale we choose to select taking care that for each number the mode of formation be really a distinct one not bringing us round again to the former numbers but introducing a new number we have a set of propositions from which we may reason to all the other modes of formation of those numbers from one another Having established a chain of inductive truths connecting together all the numbers of the scale we can ascertain the formation of any one of those numbers from any other by merely traveling from one to the other along the chain Suppose that we know only the following modes of formation 642 473 752 594 We could determine how 6 may be formed from 9 For 642732523294232 It may therefore be formed by taking away 4 and 3 and adding 2 and 2 If we know besides that 224 we obtain 6 from 9 in a simpler mode by merely taking away 3 It is sufficient therefore to select one of the various modes of formation of each number as a means of ascertaining all the rest And since things which are uniform and therefore simple are most easily received and retained by the understanding there is an obvious advantage in selecting a mode of formation which shall be alike for all in fixing the connotation of names of number on one uniform principle The mode in which our existing numerical nomenclature is contrived possesses this advantage with the additional one that it happily conveys to the mind two of the modes of formation of every number Each number is considered as formed by the addition of a unit to the number next below it in magnitude and this mode of formation is conveyed by the place which it occupies in the series And each is also considered as formed by the addition of a number of units less than ten and a number of aggregates each equal to one of the successive powers of ten and this mode of its formation is expressed by its spoken name and by its numerical character What renders arithmetic the type of a deductive science is the fortunate applicability to it of a law so comprehensive as The sums of equals are equals or to express the same principle in less familiar but more characteristic language Whatever is made up of parts is made up of the parts of those parts This truth obvious to the senses in all cases which can be fairly referred to their decision and so general as to be coextensive with nature itself being true of all sorts of phenomena for all admit of being numbered must be considered an inductive truth or law of nature of the highest order And every arithmetical operation is an application of this law or of other laws capable of being deduced from it This is our warrant for all calculations We believe that five and two are equal to seven on the evidence of this inductive law combined with the definitions of those numbers We arrive at that conclusion as all know who remember how they first learned it by adding a single unit at a time 5 16 therefore 511617 and again 211 therefore 525117 Innumerable as are the true propositions which can be formed concerning particular numbers no adequate conception could be gained from these alone of the extent of the truths composing the science of number Such propositions as we have spoken of are the least general of all numerical truths It is true that even these are coextensive with all nature the properties of the number four are true of all objects that are divisible into four equal parts and all objects are either actually or ideally so divisible But the propositions which compose the science of algebra are true not of a particular number but of all numbers not of all things under the condition of being divided in a particular way but of all things under the condition of being divided in any way of being designated by a number at all Since it is impossible for different numbers to have any of their modes of formation completely in common it is a kind of paradox to say that all propositions which can be made concerning numbers relate to their modes of formation from other numbers and yet that there are propositions which are true of all numbers But this very paradox leads to the real principle of generalization concerning the properties of numbers Two different numbers can not be formed in the same manner from the same numbers but they may be formed in the same manner from different numbers as nine is formed from three by multiplying it into itself and sixteen is formed from four by the same process Thus there arises a classification of modes of formation or in the language commonly used by mathematicians a classification of Functions Any number considered as formed from any other number is called a function of it and there are as many kinds of functions as there are modes of formation The simple functions are by no means numerous most functions being formed by the combination of several of the operations which form simple functions or by successive repetitions of some one of those operations The simple functions of any number x are all reducible to the following forms xa xa ax xa log x to the base a and the same expressions varied by putting x for a and a for x wherever that substitution would alter the value to which perhaps ought to be added sin x and arc sinx All other functions of x are formed by putting some one or more of the simple functions in the place of x or a and subjecting them to the same elementary operations In order to carry on general reasonings on the subject of Functions we require a nomenclature enabling us to express any two numbers by names which without specifying what particular numbers they are shall show what function each is of the other or, in other words, shall put in evidence their mode of formation from one another The system of general language called algebraical notation does this The expressions a and a23a denote the one any number the other the number formed from it in a particular manner The expressions a b n and abn denote any three numbers and a fourth which is formed from them in a certain mode The following may be stated as the general problem of the algebraical calculus F being a certain function of a given number to find what function F will be of any function of that number For example a binomial a b is a function of its two parts a and b and the parts are in their turn functions of a b now a bn is a certain function of the binomial what function will this be of a and b the two parts The answer to this question is the binomial theorem The formula a bn an n1 an1 b nn112 an2 b2 etc shows in what manner the number which is formed by multiplying a b into itself n times might be formed without that process directly from a b and n And of this nature are all the theorems of the science of number They assert the identity of the result of different modes of formation They affirm that some mode of formation from x and some mode of formation from a certain function of x produce the same number Such as above described is the aim and end of the calculus As for its processes every one knows that they are simply deductive In demonstrating an algebraical theorem or in resolving an equation we travel from the datum to the quaesitum by pure ratiocination in which the only premises introduced besides the original hypotheses are the fundamental axioms already mentioned that things equal to the same thing are equal to one another and that the sums of equal things are equal At each step in the demonstration or in the calculation we apply one or other of these truths or truths deducible from them as that the differences products etc of equal numbers are equal It would be inconsistent with the scale of this work and not necessary to its design to carry the analysis of the truths and processes of algebra any further which is also the less needful as the task has been to a very great extent performed by other writers Peacock’s Algebra and Dr Whewell’s Doctrine of Limits are full of instruction on the subject The profound treatises of a truly philosophical mathematician Professor De Morgan should be studied by every one who desires to comprehend the evidence of mathematical truths and the meaning of the obscurer processes of the calculus and the speculations of M Comte in his Cours de Philosophie Positive on the philosophy of the higher branches of mathematics are among the many valuable gifts for which philosophy is indebted to that eminent thinker If the extreme generality and remoteness not so much from sense as from the visual and tactual imagination of the laws of number renders it a somewhat difficult effort of abstraction to conceive those laws as being in reality physical truths obtained by observation the same difficulty does not exist with regard to the laws of extension The facts of which those laws are expressions are of a kind peculiarly accessible to the senses and suggesting eminently distinct images to the fancy That geometry is a strictly physical science would doubtless have been recognized in all ages had it not been for the illusions produced by two circumstances One of these is the characteristic property already noticed of the facts of geometry that they may be collected from our ideas or mental pictures of objects as effectually as from the objects themselves The other is the demonstrative character of geometrical truths which was at one time supposed to constitute a radical distinction between them and physical truths the latter as resting on merely probable evidence being deemed essentially uncertain and unprecise The advance of knowledge has however made it manifest that physical science in its better understood branches is quite as demonstrative as geometry The task of deducing its details from a few comparatively simple principles is found to be any thing but the impossibility it was once supposed to be and the notion of the superior certainty of geometry is an illusion arising from the ancient prejudice which in that science mistakes the ideal data from which we reason for a peculiar class of realities while the corresponding ideal data of any deductive physical science are recognized as what they really are hypotheses Every theorem in geometry is a law of external nature and might have been ascertained by generalizing from observation and experiment which in this case resolve themselves into comparison and measurement But it was found practicable and being practicable was desirable to deduce these truths by ratiocination from a small number of general laws of nature the certainty and universality of which are obvious to the most careless observer and which compose the first principles and ultimate premises of the science Among these general laws must be included the same two which we have noticed as ultimate principles of the Science of Number also and which are applicable to every description of quantity viz The sums of equals are equal and Things which are equal to the same thing are equal to one another the latter of which may be expressed in a manner more suggestive of the inexhaustible multitude of its consequences by the following terms Whatever is equal to any one of a number of equal magnitudes is equal to any other of them To these two must be added in geometry a third law of equality namely that lines surfaces or solid spaces which can be so applied to one another as to coincide are equal Some writers have asserted that this law of nature is a mere verbal definition that the expression equal magnitudes means nothing but magnitudes which can be so applied to one another as to coincide But in this opinion I can not agree The equality of two geometrical magnitudes can not differ fundamentally in its nature from the equality of two weights two degrees of heat or two portions of duration to none of which would this definition of equality be suitable None of these things can be so applied to one another as to coincide yet we perfectly understand what we mean when we call them equal Things are equal in magnitude as things are equal in weight when they are felt to be exactly similar in respect of the attribute in which we compare them and the application of the objects to each other in the one case like the balancing them with a pair of scales in the other is but a mode of bringing them into a position in which our senses can recognize deficiencies of exact resemblance that would otherwise escape our notice Along with these three general principles or axioms the remainder of the premises of geometry consists of the socalled definitions that is to say propositions asserting the real existence of the various objects therein designated together with some one property of each In some cases more than one property is commonly assumed but in no case is more than one necessary It is assumed that there are such things in nature as straight lines and that any two of them setting out from the same point diverge more and more without limit This assumption which includes and goes beyond Euclid’s axiom that two straight lines can not enclose a space is as indispensable in geometry and as evident resting on as simple familiar and universal observation as any of the other axioms It is also assumed that straight lines diverge from one another in different degrees in other words that there are such things as angles and that they are capable of being equal or unequal It is assumed that there is such a thing as a circle and that all its radii are equal such things as ellipses and that the sums of the focal distances are equal for every point in an ellipse such things as parallel lines and that those lines are everywhere equally distant It is a matter of more than curiosity to consider to what peculiarity of the physical truths which are the subject of geometry it is owing that they can all be deduced from so small a number of original premises why it is that we can set out from only one characteristic property of each kind of phenomenon and with that and two or three general truths relating to equality can travel from mark to mark until we obtain a vast body of derivative truths to all appearance extremely unlike those elementary ones The explanation of this remarkable fact seems to lie in the following circumstances In the first place all questions of position and figure may be resolved into questions of magnitude The position and figure of any object are determined by determining the position of a sufficient number of points in it and the position of any point may be determined by the magnitude of three rectangular coordinates that is of the perpendiculars drawn from the point to three planes at right angles to one another arbitrarily selected By this transformation of all questions of quality into questions only of quantity geometry is reduced to the single problem of the measurement of magnitudes that is the ascertainment of the equalities which exist between them Now when we consider that by one of the general axioms any equality when ascertained is proof of as many other equalities as there are other things equal to either of the two equals and that by another of those axioms any ascertained equality is proof of the equality of as many pairs of magnitudes as can be formed by the numerous operations which resolve themselves into the addition of the equals to themselves or to other equals we cease to wonder that in proportion as a science is conversant about equality it should afford a more copious supply of marks of marks and that the sciences of number and extension which are conversant with little else than equality should be the most deductive of all the sciences There are also two or three of the principal laws of space or extension which are unusually fitted for rendering one position or magnitude a mark of another and thereby contributing to render the science largely deductive First the magnitudes of enclosed spaces whether superficial or solid are completely determined by the magnitudes of the lines and angles which bound them Secondly the length of any line whether straight or curve is measured certain other things being given by the angle which it subtends and vic versa Lastly the angle which any two straight lines make with each other at an inaccessible point is measured by the angles they severally make with any third line we choose to select By means of these general laws the measurement of all lines angles and spaces whatsoever might be accomplished by measuring a single straight line and a sufficient number of angles which is the plan actually pursued in the trigonometrical survey of a country and fortunate it is that this is practicable the exact measurement of long straight lines being always difficult and often impossible but that of angles very easy Three such generalizations as the foregoing afford such facilities for the indirect measurement of magnitudes by supplying us with known lines or angles which are marks of the magnitude of unknown ones and thereby of the spaces which they enclose that it is easily intelligible how from a few data we can go on to ascertain the magnitude of an indefinite multitude of lines angles and spaces which we could not easily or could not at all measure by any more direct process Such are the remarks which it seems necessary to make in this place respecting the laws of nature which are the peculiar subject of the sciences of number and extension The immense part which those laws take in giving a deductive character to the other departments of physical science is well known and is not surprising when we consider that all causes operate according to mathematical laws The effect is always dependent on or is a function of the quantity of the agent and generally of its position also We can not therefore reason respecting causation without introducing considerations of quantity and extension at every step and if the nature of the phenomena admits of our obtaining numerical data of sufficient accuracy the laws of quantity become the grand instrument for calculating forward to an effect or backward to a cause That in all other sciences as well as in geometry questions of quality are scarcely ever independent of questions of quantity may be seen from the most familiar phenomena Even when several colours are mixed on a painter’s palette the comparative quantity of each entirely determines the colour of the mixture With this mere suggestion of the general causes which render mathematical principles and processes so predominant in those deductive sciences which afford precise numerical data I must on the present occasion content myself referring the reader who desires a more thorough acquaintance with the subject to the first two volumes of M Comte’s systematic work In the same work and more particularly in the third volume are also fully discussed the limits of the applicability of mathematical principles to the improvement of other sciences Such principles are manifestly inapplicable where the causes on which any class of phenomena depend are so imperfectly accessible to our observation that we can not ascertain by a proper induction their numerical laws or where the causes are so numerous and intermixed in so complex a manner with one another that even supposing their laws known the computation of the aggregate effect transcends the powers of the calculus as it is or is likely to be or lastly where the causes themselves are in a state of perpetual fluctuation as in physiology and still more if possible in the social science The mathematical solutions of physical questions become progressively more difficult and imperfect in proportion as the questions divest themselves of their abstract and hypothetical character and approach nearer to the degree of complication actually existing in nature insomuch that beyond the limits of astronomical phenomena and of those most nearly analogous to them mathematical accuracy is generally obtained at the expense of the reality of the inquiry while even in astronomical questions notwithstanding the admirable simplicity of their mathematical elements our feeble intelligence becomes incapable of following out effectually the logical combinations of the laws on which the phenomena are dependent as soon as we attempt to take into simultaneous consideration more than two or three essential influences Of this the problem of the Three Bodies has already been cited more than once as a remarkable instance the complete solution of so comparatively simple a question having vainly tried the skill of the most profound mathematicians We may conceive then how chimerical would be the hope that mathematical principles could be advantageously applied to phenomena dependent on the mutual action of the innumerable minute particles of bodies as those of chemistry and still more of physiology and for similar reasons those principles remain inapplicable to the still more complex inquiries the subjects of which are phenomena of society and government The value of mathematical instruction as a preparation for those more difficult investigations consists in the applicability not of its doctrines but of its method Mathematics will ever remain the most perfect type of the Deductive Method in general and the applications of mathematics to the deductive branches of physics furnish the only school in which philosophers can effectually learn the most difficult and important portion of their art the employment of the laws of simpler phenomena for explaining and predicting those of the more complex These grounds are quite sufficient for deeming mathematical training an indispensable basis of real scientific education and regarding according to the dictum which an old but unauthentic tradition ascribes to Plato one who is as wanting in one of the most essential qualifications for the successful cultivation of the higher branches of philosophy
The method of arriving at general truths or general propositions fit to be believed and the nature of the evidence on which they are grounded have been discussed as far as space and the writer’s faculties permitted in the twentyfour preceding chapters But the result of the examination of evidence is not always belief nor even suspension of judgment it is sometimes disbelief The philosophy therefore of induction and experimental inquiry is incomplete unless the grounds not only of belief but of disbelief are treated of and to this topic we shall devote one and the final chapter By disbelief is not here to be understood the mere absence of belief The ground for abstaining from belief is simply the absence or insufficiency of proof and in considering what is sufficient evidence to support any given conclusion we have already by implication considered what evidence is not sufficient for the same purpose By disbelief is here meant not the state of mind in which we form no opinion concerning a subject but that in which we are fully persuaded that some opinion is not true insomuch that if evidence even of great apparent strength whether grounded on the testimony of others or on our own supposed perceptions were produced in favour of the opinion we should believe that the witnesses spoke falsely or that they or we ourselves if we were the direct percipients were mistaken That there are such cases no one is likely to dispute Assertions for which there is abundant positive evidence are often disbelieved on account of what is called their improbability or impossibility And the question for consideration is what in the present case these words mean and how far and in what circumstances the properties which they express are sufficient grounds for disbelief It is to be remarked in the first place that the positive evidence produced in support of an assertion which is nevertheless rejected on the score of impossibility or improbability is never such as amounts to full proof It is always grounded on some approximate generalization The fact may have been asserted by a hundred witnesses but there are many exceptions to the universality of the generalization that what a hundred witnesses affirm is true We may seem to ourselves to have actually seen the fact but that we really see what we think we see is by no means a universal truth our organs may have been in a morbid state or we may have inferred something and imagined that we perceived it The evidence then in the affirmative being never more than an approximate generalization all will depend on what the evidence in the negative is If that also rests on an approximate generalization it is a case for comparison of probabilities If the approximate generalizations leading to the affirmative are when added together less strong or, in other words, farther from being universal than the approximate generalizations which support the negative side of the question the proposition is said to be improbable and is to be disbelieved provisionally If however an alleged fact be in contradiction not to any number of approximate generalizations but to a completed generalization grounded on a rigorous induction it is said to be impossible and is to be disbelieved totally This last principle simple and evident as it appears is the doctrine which on the occasion of an attempt to apply it to the question of the credibility of miracles excited so violent a controversy Hume’s celebrated doctrine that nothing is credible which is contradictory to experience or at variance with laws of nature is merely this very plain and harmless proposition that whatever is contradictory to a complete induction is incredible That such a maxim as this should either be accounted a dangerous heresy or mistaken for a great and recondite truth speaks ill for the state of philosophical speculation on such subjects But does not it may be asked the very statement of the proposition imply a contradiction An alleged fact according to this theory is not to be believed if it contradict a complete induction But it is essential to the completeness of an induction that it shall not contradict any known fact Is it not then a petitio principii to say that the fact ought to be disbelieved because the induction opposed to it is complete How can we have a right to declare the induction complete while facts supported by credible evidence present themselves in opposition to it I answer we have that right whenever the scientific canons of induction give it to us that is whenever the induction can be complete We have it for example in a case of causation in which there has been an experimentum crucis If an antecedent A superadded to a set of antecedents in all other respects unaltered is followed by an effect B which did not exist before A is in that instance at least the cause of B or an indispensable part of its cause and if A be tried again with many totally different sets of antecedents and B still follows then it is the whole cause If these observations or experiments have been repeated so often and by so many persons as to exclude all supposition of error in the observer a law of nature is established and so long as this law is received as such the assertion that on any particular occasion A took place and yet B did not follow without any counteracting cause must be disbelieved Such an assertion is not to be credited on any less evidence than what would suffice to overturn the law The general truths that whatever has a beginning has a cause and that when none but the same causes exist the same effects follow rest on the strongest inductive evidence possible the proposition that things affirmed by even a crowd of respectable witnesses are true is but an approximate generalization and even if we fancy we actually saw or felt the fact which is in contradiction to the law what a human being can see is no more than a set of appearances from which the real nature of the phenomenon is merely an inference and in this inference approximate generalizations usually have a large share If therefore we make our election to hold by the law no quantity of evidence whatever ought to persuade us that there has occurred any thing in contradiction to it If indeed the evidence produced is such that it is more likely that the set of observations and experiments on which the law rests should have been inaccurately performed or incorrectly interpreted than that the evidence in question should be false we may believe the evidence but then we must abandon the law And since the law was received on what seemed a complete induction it can only be rejected on evidence equivalent namely as being inconsistent not with any number of approximate generalizations but with some other and better established law of nature This extreme case of a conflict between two supposed laws of nature has probably never actually occurred where in the process of investigating both the laws the true canons of scientific induction had been kept in view but if it did occur it must terminate in the total rejection of one of the supposed laws It would prove that there must be a flaw in the logical process by which either one or the other was established and if there be so that supposed general truth is no truth at all We can not admit a proposition as a law of nature and yet believe a fact in real contradiction to it We must disbelieve the alleged fact or believe that we were mistaken in admitting the supposed law But in order that any alleged fact should be contradictory to a law of causation the allegation must be not simply that the cause existed without being followed by the effect for that would be no uncommon occurrence but that this happened in the absence of any adequate counteracting cause Now in the case of an alleged miracle the assertion is the exact opposite of this It is that the effect was defeated not in the absence but in consequence of a counteracting cause namely a direct interposition of an act of the will of some being who has power over nature and in particular of a Being whose will being assumed to have endowed all the causes with the powers by which they produce their effects may well be supposed able to counteract them A miracle as was justly remarked by Brown is no contradiction to the law of cause and effect; it is a new effect supposed to be produced by the introduction of a new cause Of the adequacy of that cause if present there can be no doubt and the only antecedent improbability which can be ascribed to the miracle is the improbability that any such cause existed All therefore which Hume has made out and this he must be considered to have made out is that at least in the imperfect state of our knowledge of natural agencies which leaves it always possible that some of the physical antecedents may have been hidden from us no evidence can prove a miracle to any one who did not previously believe the existence of a being or beings with supernatural power or who believes himself to have full proof that the character of the Being whom he recognizes is inconsistent with his having seen fit to interfere on the occasion in question If we do not already believe in supernatural agencies no miracle can prove to us their existence The miracle itself considered merely as an extraordinary fact may be satisfactorily certified by our senses or by testimony but nothing can ever prove that it is a miracle there is still another possible hypothesis that of its being the result of some unknown natural cause and this possibility can not be so completely shut out as to leave no alternative but that of admitting the existence and intervention of a being superior to nature Those however who already believe in such a being have two hypotheses to choose from a supernatural and an unknown natural agency and they have to judge which of the two is the most probable in the particular case In forming this judgment an important element of the question will be the conformity of the result to the laws of the supposed agent that is to the character of the Deity as they conceive it But with the knowledge which we now possess of the general uniformity of the course of nature religion following in the wake of science has been compelled to acknowledge the government of the universe as being on the whole carried on by general laws and not by special interpositions To whoever holds this belief there is a general presumption against any supposition of divine agency not operating through general laws or, in other words, there is an antecedent improbability in every miracle which in order to outweigh it requires an extraordinary strength of antecedent probability derived from the special circumstances of the case It appears from what has been said, that the assertion that a cause has been defeated of an effect which is connected with it by a completely ascertained law of causation is to be disbelieved or not according to the probability or improbability that there existed in the particular instance an adequate counteracting cause To form an estimate of this is not more difficult than of other probabilities With regard to all known causes capable of counteracting the given causes we have generally some previous knowledge of the frequency or rarity of their occurrence from which we may draw an inference as to the antecedent improbability of their having been present in any particular case And neither in respect to known nor unknown causes are we required to pronounce on the probability of their existing in nature but only of their having existed at the time and place at which the transaction is alleged to have happened We are seldom therefore without the means when the circumstances of the case are at all known to us of judging how far it is likely that such a cause should have existed at that time and place without manifesting its presence by some other marks and in the case of an unknown cause without having hitherto manifested its existence in any other instance According as this circumstance or the falsity of the testimony appears more improbable that is conflicts with an approximate generalization of a higher order we believe the testimony or disbelieve it with a stronger or a weaker degree of conviction according to the preponderance at least until we have sifted the matter further So much then for the case in which the alleged fact conflicts or appears to conflict with a real law of causation But a more common case perhaps is that of its conflicting with uniformities of mere coexistence not proved to be dependent on causation in other words with the properties of Kinds It is with these uniformities principally that the marvelous stories related by travelers are apt to be at variance as of men with tails or with wings and until confirmed by experience of flying fish or of ice in the celebrated anecdote of the Dutch travelers and the King of Siam Facts of this description facts previously unheard of but which could not from any known law of causation be pronounced impossible are what Hume characterizes as not contrary to experience but merely unconformable to it and Bentham in his treatise on Evidence denominates them facts disconformable in specie as distinguished from such as are disconformable in toto or in degree In a case of this description the fact asserted is the existence of a new Kind which in itself is not in the slightest degree incredible and only to be rejected if the improbability that any variety of object existing at the particular place and time should not have been discovered sooner be greater than that of error or mendacity in the witnesses Accordingly such assertions when made by credible persons and of unexplored places are not disbelieved but at most regarded as requiring confirmation from subsequent observers unless the alleged properties of the supposed new Kind are at variance with known properties of some larger kind which includes it or, in other words, unless in the new Kind which is asserted to exist some properties are said to have been found disjoined from others which have always been known to accompany them as in the case of Pliny’s men or any other kind of animal of a structure different from that which has always been found to coexist with animal life On the mode of dealing with any such case little needs be added to what has been said on the same topic in the twentysecond chapter When the uniformities of coexistence which the alleged fact would violate are such as to raise a strong presumption of their being the result of causation the fact which conflicts with them is to be disbelieved at least provisionally and subject to further investigation When the presumption amounts to a virtual certainty as in the case of the general structure of organized beings the only question requiring consideration is whether in phenomena so little understood there may not be liabilities to counteraction from causes hitherto unknown or whether the phenomena may not be capable of originating in some other way which would produce a different set of derivative uniformities Where as in the case of the flying fish or the ornithorhynchus the generalization to which the alleged fact would be an exception is very special and of limited range neither of the above suppositions can be deemed very improbable and it is generally in the case of such alleged anomalies wise to suspend our judgment pending the subsequent inquiries which will not fail to confirm the assertion if it be true But when the generalization is very comprehensive embracing a vast number and variety of observations and covering a considerable province of the domain of nature then for reasons which have been fully explained such an empirical law comes near to the certainty of an ascertained law of causation and any alleged exception to it can not be admitted unless on the evidence of some law of causation proved by a still more complete induction Such uniformities in the course of nature as do not bear marks of being the results of causation are as we have already seen admissible as universal truths with a degree of credence proportioned to their generality Those which are true of all things whatever or at least which are totally independent of the varieties of Kinds namely the laws of number and extension to which we may add the law of causation itself are probably the only ones an exception to which is absolutely and permanently incredible Accordingly it is to assertions supposed to be contradictory to these laws or to some others coming near to them in generality that the word impossibility at least total impossibility seems to be generally confined Violations of other laws of special laws of causation for instance are said by persons studious of accuracy in expression to be impossible in the circumstances of the case or impossible unless some cause had existed which did not exist in the particular case Of no assertion not in contradiction to some of these very general laws will more than improbability be asserted by any cautious person and improbability not of the highest degree unless the time and place in which the fact is said to have occurred render it almost certain that the anomaly if real could not have been overlooked by other observers Suspension of judgment is in all other cases the resource of the judicious inquirer provided the testimony in favour of the anomaly presents when well sifted no suspicious circumstances But the testimony is scarcely ever found to stand that test in cases in which the anomaly is not real In the instances on record in which a great number of witnesses of good reputation and scientific acquirements have testified to the truth of something which has turned out untrue there have almost always been circumstances which to a keen observer who had taken due pains to sift the matter would have rendered the testimony untrustworthy There have generally been means of accounting for the impression on the senses or minds of the alleged percipients by fallacious appearances or some epidemic delusion propagated by the contagious influence of popular feeling has been concerned in the case or some strong interest has been implicated religious zeal party feeling vanity or at least the passion for the marvelous in persons strongly susceptible of it When none of these or similar circumstances exist to account for the apparent strength of the testimony and where the assertion is not in contradiction either to those universal laws which know no counteraction or anomaly or to the generalizations next in comprehensiveness to them but would only amount if admitted to the existence of an unknown cause or an anomalous Kind in circumstances not so thoroughly explored but that it is credible that things hitherto unknown may still come to light a cautious person will neither admit nor reject the testimony but will wait for confirmation at other times and from other unconnected sources Such ought to have been the conduct of the King of Siam when the Dutch travelers affirmed to him the existence of ice But an ignorant person is as obstinate in his contemptuous incredulity as he is unreasonably credulous Any thing unlike his own narrow experience he disbelieves if it flatters no propensity any nursery tale is swallowed implicitly by him if it does I shall now advert to a very serious misapprehension of the principles of the subject which has been committed by some of the writers against Hume’s Essay on Miracles and by Bishop Butler before them in their anxiety to destroy what appeared to them a formidable weapon of assault against the Christian religion and the effect of which is entirely to confound the doctrine of the Grounds of Disbelief The mistake consists in overlooking the distinction between what may be called improbability before the fact and improbability after it or since as Mr Venn remarks the distinction of past and future is not the material circumstance between the improbability of a mere guess being right and the improbability of an alleged fact being true Many events are altogether improbable to us before they have happened or before we are informed of their happening which are not in the least incredible when we are informed of them because not contrary to any even approximate induction In the cast of a perfectly fair die the chances are five to one against throwing ace that is ace will be thrown on an average only once in six throws But this is no reason against believing that ace was thrown on a given occasion if any credible witness asserts it since though ace is only thrown once in six times some number which is only thrown once in six times must have been thrown if the die was thrown at all The improbability then or, in other words, the unusualness of any fact is no reason for disbelieving it if the nature of the case renders it certain that either that or something equally improbable that is equally unusual did happen Nor is this all for even if the other five sides of the die were all twos or all threes yet as ace would still on the average come up once in every six throws its coming up in a given throw would be not in any way contradictory to experience If we disbelieved all facts which had the chances against them beforehand we should believe hardly any thing We are told that A B died yesterday the moment before we were so told the chances against his having died on that day may have been ten thousand to one but since he was certain to die at some time or other and when he died must necessarily die on some particular day while the preponderance of chances is very great against every day in particular experience affords no ground for discrediting any testimony which may be produced to the event’s having taken place on a given day Yet it has been considered by Dr Campbell and others as a complete answer to Hume’s doctrine that things are incredible which are contrary to the uniform course of experience that we do not disbelieve merely because the chances were against them things in strict conformity to the uniform course of experience that we do not disbelieve an alleged fact merely because the combination of causes on which it depends occurs only once in a certain number of times It is evident that whatever is shown by observation or can be proved from laws of nature to occur in a certain proportion however small of the whole number of possible cases is not contrary to experience though we are right in disbelieving it if some other supposition respecting the matter in question involves on the whole a less departure from the ordinary course of events Yet on such grounds as this have able writers been led to the extraordinary conclusion that nothing supported by credible testimony ought ever to be disbelieved We have considered two species of events commonly said to be improbable one kind which are in no way extraordinary but which having an immense preponderance of chances against them are improbable until they are affirmed but no longer another kind which being contrary to some recognized law of nature are incredible on any amount of testimony except such as would be sufficient to shake our belief in the law itself But between these two classes of events there is an intermediate class consisting of what are commonly termed Coincidences in other words those combinations of chances which present some peculiar and unexpected regularity assimilating them in so far to the results of law As if for example in a lottery of a thousand tickets the numbers should be drawn in the exact order of what are called the natural numbers 1 2 3 etc We have still to consider the principles of evidence applicable to this case whether there is any difference between coincidences and ordinary events in the amount of testimony or other evidence necessary to render them credible It is certain that on every rational principle of expectation a combination of this peculiar sort may be expected quite as often as any other given series of a thousand numbers that with perfectly fair dice sixes will be thrown twice thrice or any number of times in succession quite as often in a thousand or a million throws as any other succession of numbers fixed upon beforehand and that no judicious player would give greater odds against the one series than against the other Notwithstanding this there is a general disposition to regard the one as much more improbable than the other and as requiring much stronger evidence to make it credible Such is the force of this impression that it has led some thinkers to the conclusion that nature has greater difficulty in producing regular combinations than irregular ones or in other words, that there is some general tendency of things some law which prevents regular combinations from occurring or at least from occurring so often as others Among these thinkers may be numbered D’Alembert who in an Essay on Probabilities to be found in the fifth volume of his Mlanges contends that regular combinations though equally probable according to the mathematical theory with any others are physically less probable He appeals to common sense or, in other words, to common impressions saying if dice thrown repeatedly in our presence gave sixes every time should we not before the number of throws had reached ten not to speak of thousands of millions be ready to affirm with the most positive conviction that the dice were false The common and natural impression is in favour of D’Alembert the regular series would be thought much more unlikely than an irregular But this common impression is I apprehend merely grounded on the fact that scarcely any body remembers to have ever seen one of these peculiar coincidences the reason of which is simply that no one’s experience extends to any thing like the number of trials within which that or any other given combination of events can be expected to happen The chance of sixes on a single throw of two dice being 136 the chance of sixes ten times in succession is 1 divided by the tenth power of 36 in other words such a concurrence is only likely to happen once in 3656158440062976 trials a number which no diceplayer’s experience comes up to a millionth part of But if instead of sixes ten times any other given succession of ten throws had been fixed upon it would have been exactly as unlikely that in any individual’s experience that particular succession had ever occurred although this does not seem equally improbable because no one would be likely to have remembered whether it had occurred or not and because the comparison is tacitly made not between sixes ten times and any one particular series of throws but between all regular and all irregular successions taken together That as D’Alembert says if the succession of sixes was actually thrown before our eyes we should ascribe it not to chance but to unfairness in the dice is unquestionably true But this arises from a totally different principle We should then be considering not the probability of the fact in itself but the comparative probability with which when it is known to have happened it may be referred to one or to another cause The regular series is not at all less likely than the irregular one to be brought about by chance but it is much more likely than the irregular one to be produced by design or by some general cause operating through the structure of the dice It is the nature of casual combinations to produce a repetition of the same event as often and no oftener than any other series of events But it is the nature of general causes to reproduce in the same circumstances always the same event Common sense and science alike dictate that all other things being the same we should rather attribute the effect to a cause which if real would be very likely to produce it than to a cause which would be very unlikely to produce it According to Laplace’s sixth theorem which we demonstrated in a former chapter the difference of probability arising from the superior efficacy of the constant cause unfairness in the dice would after a very few throws far outweigh any antecedent probability which there could be against its existence D’Alembert should have put the question in another manner He should have supposed that we had ourselves previously tried the dice and knew by ample experience that they were fair Another person then tries them in our absence and assures us that he threw sixes ten times in succession Is the assertion credible or not Here the effect to be accounted for is not the occurrence itself but the fact of the witness’s asserting it This may arise either from its having really happened or from some other cause What we have to estimate is the comparative probability of these two suppositions If the witness affirmed that he had thrown any other series of numbers supposing him to be a person of veracity and tolerable accuracy and to profess that he took particular notice we should believe him But the ten sixes are exactly as likely to have been really thrown as the other series If therefore this assertion is less credible than the other the reason must be not that it is less likely than the other to be made truly but that it is more likely than the other to be made falsely One reason obviously presents itself why what is called a coincidence should be oftener asserted falsely than an ordinary combination It excites wonder It gratifies the love of the marvelous The motives therefore to falsehood one of the most frequent of which is the desire to astonish operate more strongly in favour of this kind of assertion than of the other kind Thus far there is evidently more reason for discrediting an alleged coincidence than a statement in itself not more probable but which if made would not be thought remarkable There are cases however in which the presumption on this ground would be the other way There are some witnesses who the more extraordinary an occurrence might appear would be the more anxious to verify it by the utmost carefulness of observation before they would venture to believe it and still more before they would assert it to others Independently however of any peculiar chances of mendacity arising from the nature of the assertion Laplace contends that merely on the general ground of the fallibility of testimony a coincidence is not credible on the same amount of testimony on which we should be warranted in believing an ordinary combination of events In order to do justice to his argument it is necessary to illustrate it by the example chosen by himself If says Laplace there were one thousand tickets in a box and one only has been drawn out then if an eyewitness affirms that the number drawn was 79 this though the chances were 999 in 1000 against it is not on that account the less credible its credibility is equal to the antecedent probability of the witness’s veracity But if there were in the box 999 black balls and only one white and the witness affirms that the white ball was drawn the case according to Laplace is very different the credibility of his assertion is but a small fraction of what it was in the former case the reason of the difference being as follows The witnesses of whom we are speaking must from the nature of the case be of a kind whose credibility falls materially short of certainty let us suppose then the credibility of the witness in the case in question to be 910 that is let us suppose that in every ten statements which the witness makes nine on an average are correct and one incorrect Let us now suppose that there have taken place a sufficient number of drawings to exhaust all the possible combinations the witness deposing in every one In one case out of every ten in all these drawings he will actually have made a false announcement But in the case of the thousand tickets these false announcements will have been distributed impartially over all the numbers and of the 999 cases in which No 79 was not drawn there will have been only one case in which it was announced On the contrary in the case of the thousand balls the announcement being always either black or white if white was not drawn and there was a false announcement that false announcement must have been white and since by the supposition there was a false announcement once in every ten times white will have been announced falsely in onetenth part of all the cases in which it was not drawn that is in onetenth part of 999 cases out of every thousand White then is drawn on an average exactly as often as No 79 but it is announced without having been really drawn 999 times as often as No 79 the announcement therefore requires a much greater amount of testimony to render it credible To make this argument valid it must of course be supposed that the announcements made by the witness are average specimens of his general veracity and accuracy or at least that they are neither more nor less so in the case of the black and white balls than in the case of the thousand tickets This assumption however is not warranted A person is far less likely to mistake who has only one form of error to guard against than if he had 999 different errors to avoid For instance in the example chosen a messenger who might make a mistake once in ten times in reporting the number drawn in a lottery might not err once in a thousand times if sent simply to observe whether a ball was black or white Laplace’s argument therefore is faulty even as applied to his own case Still less can that case be received as completely representing all cases of coincidence Laplace has so contrived his example that though black answers to 999 distinct possibilities and white only to one the witness has nevertheless no bias which can make him prefer black to white The witness did not know that there were 999 black balls in the box and only one white or if he did Laplace has taken care to make all the 999 cases so undistinguishably alike that there is hardly a possibility of any cause of falsehood or error operating in favour of any of them which would not operate in the same manner if there were only one Alter this supposition and the whole argument falls to the ground Let the balls for instance be numbered and let the white ball be No 79 Considered in respect of their colour there are but two things which the witness can be interested in asserting or can have dreamed or hallucinated or has to choose from if he answers at random viz black and white but considered in respect of the numbers attached to them there are a thousand and if his interest or error happens to be connected with the numbers though the only assertion he makes is about the colour the case becomes precisely assimilated to that of the thousand tickets Or instead of the balls suppose a lottery with 1000 tickets and but one prize and that I hold No 79 and being interested only in that ask the witness not what was the number drawn but whether it was 79 or some other There are now only two cases as in Laplace’s example yet he surely would not say that if the witness answered 79 the assertion would be in an enormous proportion less credible than if he made the same answer to the same question asked in the other way If for instance to put a case supposed by Laplace himself he has staked a large sum on one of the chances and thinks that by announcing its occurrence he shall increase his credit he is equally likely to have betted on any one of the 999 numbers which are attached to black balls and so far as the chances of mendacity from this cause are concerned there will be 999 times as many chances of his announcing black falsely as white Or suppose a regiment of 1000 men 999 Englishmen and one Frenchman and that of these one man has been killed and it is not known which I ask the question and the witness answers the Frenchman This was not only as improbable a priori but is in itself as singular a circumstance as remarkable a coincidence as the drawing of the white ball yet we should believe the statement as readily as if the answer had been John Thompson Because though the 999 Englishmen were all alike in the point in which they differed from the Frenchman they were not like the 999 black balls undistinguishable in every other respect but being all different they admitted as many chances of interest or error as if each man had been of a different nation and if a lie was told or a mistake made the misstatement was as likely to fall on any Jones or Thompson of the set as on the Frenchman The example of a coincidence selected by D’Alembert that of sixes thrown on a pair of dice ten times in succession belongs to this sort of cases rather than to such as Laplace’s The coincidence is here far more remarkable because of far rarer occurrence than the drawing of the white ball But though the improbability of its really occurring is greater the superior probability of its being announced falsely can not be established with the same evidence The announcement black represented 999 cases but the witness may not have known this and if he did the 999 cases are so exactly alike that there is really only one set of possible causes of mendacity corresponding to the whole The announcement sixes not drawn ten times represents and is known by the witness to represent a great multitude of contingencies every one of which being unlike every other there may be a different and a fresh set of causes of mendacity corresponding to each It appears to me therefore that Laplace’s doctrine is not strictly true of any coincidences and is wholly inapplicable to most and that to know whether a coincidence does or does not require more evidence to render it credible than an ordinary event we must refer in every instance to first principles and estimate afresh what is the probability that the given testimony would have been delivered in that instance supposing the fact which it asserts not to be true With these remarks we close the discussion of the Grounds of Disbelief and along with it such exposition as space admits and as the writer has it in his power to furnish of the Logic of Induction Clear and distinct ideas are terms which though familiar and frequent in men’s mouths I have reason to think every one who uses does not perfectly understand And possibly it is but here and there one who gives himself the trouble to consider them so far as to know what he himself or others precisely mean by them I have therefore in most places chose to put determinate or determined instead of clear and distinct as more likely to direct men’s thoughts to my meaning in this matter LOCKE’S Essay on the Human Understanding Epistle to the Reader Il ne peut y avoir qu’une mthode parfaite qui est la mthode naturelle on nomme ainsi un arrangement dans lequel les tres du mme genre seraient plus voisins entre eux que ceux de tous les autres genres les genres du mme ordre plus que ceux de tous les autres ordres et ainsi de suite Cette mthode est l’idal auquel l’histoire naturelle doit tendre car il est vident que si l’on y parvenait l’on aurait l’expression exacte et complte de la nature entire CUVIER Rgne Animal Introduction Deux grandes notions philosophiques dominent la thorie fondamentale de la mthode naturelle proprement dite savoir la formation des groupes naturels et ensuite leur succession hirarchique COMTE Cours de Philosophie Positive 42me leon The inquiry which occupied us in the two preceding Books has conducted us to what appears a satisfactory solution of the principal problem of Logic according to the conception I have formed of the science We have found that the mental process with which Logic is conversant the operation of ascertaining truths by means of evidence is always even when appearances point to a different theory of it a process of induction And we have particularized the various modes of induction and obtained a clear view of the principles to which it must conform in order to lead to results which can be relied on The consideration of Induction however does not end with the direct rules for its performance Something must be said of those other operations of the mind which are either necessarily presupposed in all induction or are instrumental to the more difficult and complicated inductive processes The present Book will be devoted to the consideration of these subsidiary operations among which our attention must first be given to those which are indispensable preliminaries to all induction whatsoever Induction being merely the extension to a class of cases of something which has been observed to be true in certain individual instances of the class the first place among the operations subsidiary to induction is claimed by Observation This is not however the place to lay down rules for making good observers nor is it within the competence of Logic to do so but of the art of intellectual Education Our business with observation is only in its connection with the appropriate problem of logic the estimation of evidence We have to consider not how or what to observe but under what conditions observation is to be relied on what is needful in order that the fact supposed to be observed may safely be received as true The answer to this question is very simple at least in its first aspect The sole condition is that what is supposed to have been observed shall really have been observed that it be an observation not an inference For in almost every act of our perceiving faculties observation and inference are intimately blended What we are said to observe is usually a compound result of which onetenth may be observation and the remaining ninetenths inference I affirm for example that I hear a man’s voice This would pass in common language for a direct perception All however which is really perception is that I hear a sound That the sound is a voice and that voice the voice of a man are not perceptions but inferences I affirm again that I saw my brother at a certain hour this morning If any proposition concerning a matter of fact would commonly be said to be known by the direct testimony of the senses this surely would be so The truth however is far otherwise I only saw a certain coloured surface or rather I had the kind of visual sensations which are usually produced by a coloured surface and from these as marks known to be such by previous experience I concluded that I saw my brother I might have had sensations precisely similar when my brother was not there I might have seen some other person so nearly resembling him in appearance as at the distance and with the degree of attention which I bestowed to be mistaken for him I might have been asleep and have dreamed that I saw him or in a state of nervous disorder which brought his image before me in a waking hallucination In all these modes many have been led to believe that they saw persons well known to them who were dead or far distant If any of these suppositions had been true the affirmation that I saw my brother would have been erroneous but whatever was matter of direct perception namely the visual sensations would have been real The inference only would have been ill grounded I should have ascribed those sensations to a wrong cause Innumerable instances might be given and analysed in the same manner of what are vulgarly called errors of sense There are none of them properly errors of sense they are erroneous inferences from sense When I look at a candle through a multiplying glass I see what seems a dozen candles instead of one and if the real circumstances of the case were skillfully disguised I might suppose that there were really that number there would be what is called an optical deception In the kaleidoscope there really is that deception when I look through the instrument instead of what is actually there namely a casual arrangement of coloured fragments the appearance presented is that of the same combination several times repeated in symmetrical arrangement round a point The delusion is of course effected by giving me the same sensations which I should have had if such a symmetrical combination had really been presented to me If I cross two of my fingers and bring any small object a marble for instance into contact with both at points not usually touched simultaneously by one object I can hardly if my eyes are shut help believing that there are two marbles instead of one But it is not my touch in this case nor my sight in the other which is deceived the deception whether durable or only momentary is in my judgment From my senses I have only the sensations and those are genuine Being accustomed to have those or similar sensations when and only when a certain arrangement of outward objects is present to my organs I have the habit of instantly when I experience the sensations inferring the existence of that state of outward things This habit has become so powerful that the inference performed with the speed and certainty of an instinct is confounded with intuitive perceptions When it is correct I am unconscious that it ever needed proof even when I know it to be incorrect I can not without considerable effort abstain from making it In order to be aware that it is not made by instinct but by an acquired habit I am obliged to reflect on the slow process through which I learned to judge by the eye of many things which I now appear to perceive directly by sight and on the reverse operation performed by persons learning to draw who with difficulty and labour divest themselves of their acquired perceptions and learn afresh to see things as they appear to the eye It would be easy to prolong these illustrations were there any need to expatiate on a topic so copiously exemplified in various popular works From the examples already given it is seen sufficiently that the individual facts from which we collect our inductive generalizations are scarcely ever obtained by observation alone Observation extends only to the sensations by which we recognize objects but the propositions which we make use of either in science or in common life relate mostly to the objects themselves In every act of what is called observation there is at least one inference from the sensations to the presence of the object from the marks or diagnostics to the entire phenomenon And hence among other consequences follows the seeming paradox that a general proposition collected from particulars is often more certainly true than any one of the particular propositions from which by an act of induction it was inferred For each of those particular or rather singular propositions involved an inference from the impression on the senses to the fact which caused that impression and this inference may have been erroneous in any one of the instances but can not well have been erroneous in all of them provided their number was sufficient to eliminate chance The conclusion therefore that is the general proposition may deserve more complete reliance than it would be safe to repose in any one of the inductive premises The logic of observation then consists solely in a correct discrimination between that in a result of observation which has really been perceived and that which is an inference from the perception Whatever portion is inference is amenable to the rules of induction already treated of and requires no further notice here the question for us in this place is when all which is inference is taken away what remains There remains in the first place the mind’s own feelings or states of consciousness namely its outward feelings or sensations and its inward feelings its thoughts emotions and volitions Whether any thing else remains or all else is inference from this whether the mind is capable of directly perceiving or apprehending any thing except states of its own consciousness is a problem of metaphysics not to be discussed in this place But after excluding all questions on which metaphysicians differ it remains true that for most purposes the discrimination we are called upon practically to exercise is that between sensations or other feelings of our own or of other people and inferences drawn from them And on the theory of Observation this is all which seems necessary to be said for the purposes of the present work If in the simplest observation or in what passes for such there is a large part which is not observation but something else so in the simplest description of an observation there is and must always be much more asserted than is contained in the perception itself We can not describe a fact without implying more than the fact The perception is only of one individual thing but to describe it is to affirm a connection between it and every other thing which is either denoted or connoted by any of the terms used To begin with an example than which none can be conceived more elementary I have a sensation of sight and I endeavour to describe it by saying that I see something white In saying this I do not solely affirm my sensation I also class it I assert a resemblance between the thing I see and all things which I and others are accustomed to call white I assert that it resembles them in the circumstance in which they all resemble one another in that which is the ground of their being called by the name This is not merely one way of describing an observation but the only way If I would either register my observation for my own future use or make it known for the benefit of others I must assert a resemblance between the fact which I have observed and something else It is inherent in a description to be the statement of a resemblance or resemblances We thus see that it is impossible to express in words any result of observation without performing an act possessing what Dr Whewell considers to be characteristic of Induction There is always something introduced which was not included in the observation itself some conception common to the phenomenon with other phenomena to which it is compared An observation can not be spoken of in language at all without declaring more than that one observation without assimilating it to other phenomena already observed and classified But this identification of an object this recognition of it as possessing certain known characteristics has never been confounded with Induction It is an operation which precedes all induction and supplies it with its materials It is a perception of resemblances obtained by comparison These resemblances are not always apprehended directly by merely comparing the object observed with some other present object or with our recollection of an object which is absent They are often ascertained through intermediate marks that is deductively In describing some new kind of animal suppose me to say that it measures ten feet in length from the forehead to the extremity of the tail I did not ascertain this by the unassisted eye I had a twofoot rule which I applied to the object and as we commonly say measured it an operation which was not wholly manual but partly also mathematical involving the two propositions Five times two is ten and Things which are equal to the same thing are equal to one another Hence the fact that the animal is ten feet long is not an immediate perception but a conclusion from reasoning the minor premises alone being furnished by observation of the object Nevertheless this is called an observation or a description of the animal not an induction respecting it To pass at once from a very simple to a very complex example I affirm that the earth is globular The assertion is not grounded on direct perception for the figure of the earth can not by us be directly perceived though the assertion would not be true unless circumstances could be supposed under which its truth could be so perceived That the form of the earth is globular is inferred from certain marks as for instance from this that its shadow thrown upon the moon is circular or this that on the sea or any extensive plain our horizon is always a circle either of which marks is incompatible with any other than a globular form I assert further that the earth is that particular kind of a globe which is termed an oblate spheroid because it is found by measurement in the direction of the meridian that the length on the surface of the earth which subtends a given angle at its centre diminishes as we recede from the equator and approach the poles But these propositions that the earth is globular and that it is an oblate spheroid assert each of them an individual fact in its own nature capable of being perceived by the senses when the requisite organs and the necessary position are supposed and only not actually perceived because those organs and that position are wanting This identification of the earth first as a globe and next as an oblate spheroid which if the fact could have been seen would have been called a description of the figure of the earth may without impropriety be so called when instead of being seen it is inferred But we could not without impropriety call either of these assertions an induction from facts respecting the earth They are not general propositions collected from particular facts but particular facts deduced from general propositions They are conclusions obtained deductively from premises originating in induction but of these premises some were not obtained by observation of the earth nor had any peculiar reference to it If then the truth respecting the figure of the earth is not an induction why should the truth respecting the figure of the earth’s orbit be so The two cases only differ in this that the form of the orbit was not like the form of the earth itself deduced by ratiocination from facts which were marks of ellipticity but was got at by boldly guessing that the path was an ellipse and finding afterward on examination that the observations were in harmony with the hypothesis According to Dr Whewell however this process of guessing and verifying our guesses is not only induction but the whole of induction no other exposition can be given of that logical operation That he is wrong in the latter assertion the whole of the preceding book has I hope sufficiently proved and that the process by which the ellipticity of the planetary orbits was ascertained is not induction at all was attempted to be shown in the second chapter of the same Book We are now however prepared to go more into the heart of the matter than at that earlier period of our inquiry and to show not merely what the operation in question is not but what it is We observed in the second chapter that the proposition the earth moves in an ellipse so far as it only serves for the colligation or connecting together of actual observations that is as it only affirms that the observed positions of the earth may be correctly represented by as many points in the circumference of an imaginary ellipse is not an induction but a description it is an induction only when it affirms that the intermediate positions of which there has been no direct observation would be found to correspond to the remaining points of the same elliptic circumference Now though this real induction is one thing and the description another we are in a very different condition for making the induction before we have obtained the description and after it For inasmuch as the description like all other descriptions contains the assertion of a resemblance between the phenomenon described and something else in pointing out something which the series of observed places of a planet resembles it points out something in which the several places themselves agree If the series of places correspond to as many points of an ellipse the places themselves agree in being situated in that ellipse We have therefore by the same process which gave us the description obtained the requisites for an induction by the Method of Agreement The successive observed places of the earth being considered as effects and its motion as the cause which produces them we find that those effects that is those places agree in the circumstance of being in an ellipse We conclude that the remaining effects the places which have not been observed agree in the same circumstance and that the law of the motion of the earth is motion in an ellipse The Colligation of Facts therefore by means of hypotheses or as Dr Whewell prefers to say by means of Conceptions instead of being as he supposes Induction itself takes its proper place among operations subsidiary to Induction All Induction supposes that we have previously compared the requisite number of individual instances and ascertained in what circumstances they agree The Colligation of Facts is no other than this preliminary operation When Kepler after vainly endeavouring to connect the observed places of a planet by various hypotheses of circular motion at last tried the hypotheses of an ellipse and found it answer to the phenomena what he really attempted first unsuccessfully and at last successfully was to discover the circumstance in which all the observed positions of the planet agreed And when he in like manner connected another set of observed facts the periodic times of the different planets by the proposition that the squares of the times are proportional to the cubes of the distances what he did was simply to ascertain the property in which the periodic times of all the different planets agreed Since therefore all that is true and to the purpose in Dr Whewell’s doctrine of Conceptions might be fully expressed by the more familiar term Hypothesis and since his Colligation of Facts by means of appropriate Conceptions is but the ordinary process of finding by a comparison of phenomena in what consists their agreement or resemblance I would willingly have confined myself to those better understood expressions and persevered to the end in the same abstinence which I have hitherto observed from ideological discussions considering the mechanism of our thoughts to be a topic distinct from and irrelevant to the principles and rules by which the trustworthiness of the results of thinking is to be estimated Since however a work of such high pretensions and it must also be said of so much real merit has rested the whole theory of Induction upon such ideological considerations it seems necessary for others who follow to claim for themselves and their doctrines whatever position may properly belong to them on the same metaphysical ground And this is the object of the succeeding chapter
The metaphysical inquiry into the nature and composition of what have been called Abstract Ideas or, in other words, of the notions which answer in the mind to classes and to general names belongs not to Logic but to a different science and our purpose does not require that we should enter upon it here We are only concerned with the universally acknowledged fact that such notions or conceptions do exist The mind can conceive a multitude of individual things as one assemblage or class and general names do really suggest to us certain ideas or mental representations otherwise we could not use the names with consciousness of a meaning Whether the idea called up by a general name is composed of the various circumstances in which all the individuals denoted by the name agree and of no others which is the doctrine of Locke Brown and the Conceptualists or whether it be the idea of some one of those individuals clothed in its individualizing peculiarities but with the accompanying knowledge that those peculiarities are not properties of the class which is the doctrine of Berkeley Mr Bailey and the modern Nominalists or whether as held by Mr James Mill the idea of the class is that of a miscellaneous assemblage of individuals belonging to the class or whether finally it be any one or any other of all these according to the accidental circumstances of the case certain it is that some idea or mental conception is suggested by a general name whenever we either hear it or employ it with consciousness of a meaning And this which we may call if we please a general idea represents in our minds the whole class of things to which the name is applied Whenever we think or reason concerning the class we do so by means of this idea And the voluntary power which the mind has of attending to one part of what is present to it at any moment and neglecting another part enables us to keep our reasonings and conclusions respecting the class unaffected by any thing in the idea or mental image which is not really or at least which we do not really believe to be common to the whole class There are then such things as general conceptions or conceptions by means of which we can think generally and when we form a set of phenomena into a class that is when we compare them with one another to ascertain in what they agree some general conception is implied in this mental operation And inasmuch as such a comparison is a necessary preliminary to Induction it is most true that Induction could not go on without general conceptions But it does not therefore follow that these general conceptions must have existed in the mind previously to the comparison It is not a law of our intellect that in comparing things with each other and taking note of their agreement we merely recognize as realized in the outward world something that we already had in our minds The conception originally found its way to us as the result of such a comparison It was obtained in metaphysical phrase by abstraction from individual things These things may be things which we perceived or thought of on former occasions but they may also be the things which we are perceiving or thinking of on the very occasion When Kepler compared the observed places of the planet Mars and found that they agreed in being points of an elliptic circumference he applied a general conception which was already in his mind having been derived from his former experience But this is by no means universally the case When we compare several objects and find them to agree in being white or when we compare the various species of ruminating animals and find them to agree in being clovenfooted we have just as much a general conception in our minds as Kepler had in his we have the conception of a white thing or the conception of a clovenfooted animal But no one supposes that we necessarily bring these conceptions with us and superinduce them to adopt Dr Whewell’s expression upon the facts because in these simple cases every body sees that the very act of comparison which ends in our connecting the facts by means of the conception may be the source from which we derive the conception itself If we had never seen any white object or had never seen any clovenfooted animal before we should at the same time and by the same mental act acquire the idea and employ it for the colligation of the observed phenomena Kepler on the contrary really had to bring the idea with him and superinduce it upon the facts he could not evolve it out of them if he had not already had the idea he would not have been able to acquire it by a comparison of the planet’s positions But this inability was a mere accident the idea of an ellipse could have been acquired from the paths of the planets as effectually as from any thing else if the paths had not happened to be invisible If the planet had left a visible track and we had been so placed that we could see it at the proper angle we might have abstracted our original idea of an ellipse from the planetary orbit Indeed every conception which can be made the instrument for connecting a set of facts might have been originally evolved from those very facts The conception is a conception of something and that which it is a conception of is really in the facts and might under some supposable circumstances or by some supposable extension of the faculties which we actually possess have been detected in them And not only is this always in itself possible but it actually happens in almost all cases in which the obtaining of the right conception is a matter of any considerable difficulty For if there be no new conception required if one of those already familiar to mankind will serve the purpose the accident of being the first to whom the right one occurs may happen to almost any body at least in the case of a set of phenomena which the whole scientific world are engaged in attempting to connect The honour in Kepler’s case was that of the accurate patient and toilsome calculations by which he compared the results that followed from his different guesses with the observations of Tycho Brahe but the merit was very small of guessing an ellipse the only wonder is that men had not guessed it before nor could they have failed to do so if there had not existed an obstinate a priori prejudice that the heavenly bodies must move if not in a circle in some combination of circles The really difficult cases are those in which the conception destined to create light and order out of darkness and confusion has to be sought for among the very phenomena which it afterward serves to arrange Why according to Dr Whewell himself did the ancients fail in discovering the laws of mechanics that is of equilibrium and of the communication of motion Because they had not or at least had not clearly the ideas or conceptions of pressure and resistance momentum and uniform and accelerating force And whence could they have obtained these ideas except from the very facts of equilibrium and motion The tardy development of several of the physical sciences for example of optics electricity magnetism and the higher generalizations of chemistry he ascribes to the fact that mankind had not yet possessed themselves of the Idea of Polarity that is the idea of opposite properties in opposite directions But what was there to suggest such an idea until by a separate examination of several of these different branches of knowledge it was shown that the facts of each of them did present in some instances at least the curious phenomenon of opposite properties in opposite directions The thing was superficially manifest only in two cases those of the magnet and of electrified bodies and there the conception was encumbered with the circumstance of material poles or fixed points in the body itself in which points this opposition of properties seemed to be inherent The first comparison and abstraction had led only to this conception of poles and if any thing corresponding to that conception had existed in the phenomena of chemistry or optics the difficulty now justly considered so great would have been extremely small The obscurity arose from the fact that the polarities in chemistry and optics were distinct species though of the same genus with the polarities in electricity and magnetism and that in order to assimilate the phenomena to one another it was necessary to compare a polarity without poles such for instance as is exemplified in the polarization of light and the polarity with apparent poles which we see in the magnet and to recognize that these polarities while different in many other respects agree in the one character which is expressed by the phrase opposite properties in opposite directions From the result of such a comparison it was that the minds of scientific men formed this new general conception between which and the first confused feeling of an analogy between some of the phenomena of light and those of electricity and magnetism there is a long interval filled up by the labours and more or less sagacious suggestions of many superior minds The conceptions then which we employ for the colligation and methodization of facts do not develop themselves from within but are impressed upon the mind from without they are never obtained otherwise than by way of comparison and abstraction and in the most important and the most numerous cases are evolved by abstraction from the very phenomena which it is their office to colligate I am far however from wishing to imply that it is not often a very difficult thing to perform this process of abstraction well or that the success of an inductive operation does not in many cases principally depend on the skill with which we perform it Bacon was quite justified in designating as one of the principal obstacles to good induction general conceptions wrongly formed notiones temer ˆ rebus abstractae to which Dr Whewell adds that not only does bad abstraction make bad induction but that in order to perform induction well we must have abstracted well our general conceptions must be clear and appropriate to the matter in hand In attempting to show what the difficulty in this matter really is and how it is surmounted I must beg the reader once for all to bear this in mind that although in discussing the opinions of a different school of philosophy I am willing to adopt their language and to speak therefore of connecting facts through the instrumentality of a conception this technical phraseology means neither more nor less than what is commonly called comparing the facts with one another and determining in what they agree Nor has the technical expression even the advantage of being metaphysically correct The facts are not connected except in a merely metaphorical acceptation of the term The ideas of the facts may become connected that is we may be led to think of them together but this consequence is no more than what may be produced by any casual association What really takes place is I conceive more philosophically expressed by the common word Comparison than by the phrases to connect or to superinduce For as the general conception is itself obtained by a comparison of particular phenomena so when obtained the mode in which we apply it to other phenomena is again by comparison We compare phenomena with each other to get the conception and we then compare those and other phenomena with the conception We get the conception of an animal for instance by comparing different animals and when we afterward see a creature resembling an animal we compare it with our general conception of an animal and if it agrees with that general conception we include it in the class The conception becomes the type of comparison And we need only consider what comparison is to see that where the objects are more than two and still more when they are an indefinite number a type of some sort is an indispensable condition of the comparison When we have to arrange and classify a great number of objects according to their agreements and differences we do not make a confused attempt to compare all with all We know that two things are as much as the mind can easily attend to at a time and we therefore fix upon one of the objects either at hazard or because it offers in a peculiarly striking manner some important character and taking this as our standard compare it with one object after another If we find a second object which presents a remarkable agreement with the first inducing us to class them together the question instantly arises in what particular circumstances do they agree and to take notice of these circumstances is already a first stage of abstraction giving rise to a general conception Having advanced thus far when we now take in hand a third object we naturally ask ourselves the question not merely whether this third object agrees with the first but whether it agrees with it in the same circumstances in which the second did in other words whether it agrees with the general conception which has been obtained by abstraction from the first and second Thus we see the tendency of general conceptions as soon as formed to substitute themselves as types for whatever individual objects previously answered that purpose in our comparisons We may perhaps find that no considerable number of other objects agree with this first general conception and that we must drop the conception and beginning again with a different individual case proceed by fresh comparisons to a different general conception Sometimes again we find that the same conception will serve by merely leaving out some of its circumstances and by this higher effort of abstraction we obtain a still more general conception as in the case formerly referred to the scientific world rose from the conception of poles to the general conception of opposite properties in opposite directions or as those SouthSea islanders whose conception of a quadruped had been abstracted from hogs the only animals of that description which they had seen when they afterward compared that conception with other quadrupeds dropped some of the circumstances and arrived at the more general conception which Europeans associate with the term These brief remarks contain I believe all that is well grounded in the doctrine that the conception by which the mind arranges and gives unity to phenomena must be furnished by the mind itself and that we find the right conception by a tentative process trying first one and then another until we hit the mark The conception is not furnished by the mind until it has been furnished to the mind and the facts which supply it are sometimes extraneous facts but more often the very facts which we are attempting to arrange by it It is quite true however that in endeavouring to arrange the facts at whatever point we begin we never advance three steps without forming a general conception more or less distinct and precise and that this general conception becomes the clue which we instantly endeavour to trace through the rest of the facts or rather becomes the standard with which we thenceforth compare them If we are not satisfied with the agreements which we discover among the phenomena by comparing them with this type or with some still more general conception which by an additional stage of abstraction we can form from the type we change our path and look out for other agreements we recommence the comparison from a different startingpoint and so generate a different set of general conceptions This is the tentative process which Dr Whewell speaks of and which has not unnaturally suggested the theory that the conception is supplied by the mind itself since the different conceptions which the mind successively tries it either already possessed from its previous experience or they were supplied to it in the first stage of the corresponding act of comparison so that in the subsequent part of the process the conception manifested itself as something compared with the phenomena not evolved from them If this be a correct account of the instrumentality of general conceptions in the comparison which necessarily precedes Induction we are now able to translate into our own language what Dr Whewell means by saying that conceptions to be subservient to Induction must be clear and appropriate If the conception corresponds to a real agreement among the phenomena if the comparison which we have made of a set of objects has led us to class them according to real resemblances and differences the conception which does this can not fail to be appropriate for some purpose or other The question of appropriateness is relative to the particular object we have in view As soon as by our comparison we have ascertained some agreement something which can be predicated in common of a number of objects we have obtained a basis on which an inductive process is capable of being founded But the agreements or the ulterior consequences to which those agreements lead may be of very different degrees of importance If for instance we only compare animals according to their colour and class those together which are coloured alike we form the general conceptions of a white animal a black animal etc which are conceptions legitimately formed and if an induction were to be attempted concerning the causes of the colours of animals this comparison would be the proper and necessary preparation for such an induction but would not help us toward a knowledge of the laws of any other of the properties of animals while if with Cuvier we compare and class them according to the structure of the skeleton or with Blainville according to the nature of their outward integuments the agreements and differences which are observable in these respects are not only of much greater importance in themselves but are marks of agreements and differences in many other important particulars of the structure and mode of life of the animals If therefore the study of their structure and habits be our object the conceptions generated by these last comparisons are far more appropriate than those generated by the former Nothing other than this can be meant by the appropriateness of a conception When Dr Whewell says that the ancients or the schoolmen or any modern inquirers missed discovering the real law of a phenomenon because they applied to it an inappropriate instead of an appropriate conception he can only mean that in comparing various instances of the phenomenon to ascertain in what those instances agreed they missed the important points of agreement and fastened upon such as were either imaginary and not agreements at all or if real agreements were comparatively trifling and had no connection with the phenomenon the law of which was sought Aristotle philosophizing on the subject of motion remarked that certain motions apparently take place spontaneously bodies fall to the ground flame ascends bubbles of air rise in water etc and these he called natural motions while others not only never take place without external incitement but even when such incitement is applied tend spontaneously to cease which to distinguish them from the former he called violent motions Now in comparing the socalled natural motions with one another it appeared to Aristotle that they agreed in one circumstance namely that the body which moved or seemed to move spontaneously was moving toward its own place meaning thereby the place from whence it originally came or the place where a great quantity of matter similar to itself was assembled In the other class of motions as when bodies are thrown up in the air they are on the contrary moving from their own place Now this conception of a body moving toward its own place may justly be considered inappropriate because though it expresses a circumstance really found in some of the most familiar instances of motion apparently spontaneous yet first there are many other cases of such motion in which that circumstance is absent the motion for instance of the earth and planets Secondly even when it is present the motion on closer examination would often be seen not to be spontaneous as when air rises in water it does not rise by its own nature but is pushed up by the superior weight of the water which presses upon it Finally there are many cases in which the spontaneous motion takes place in the contrary direction to what the theory considers as the body’s own place for instance when a fog rises from a lake or when water dries up The agreement therefore which Aristotle selected as his principle of classification did not extend to all cases of the phenomenon he wanted to study spontaneous motion while it did include cases of the absence of the phenomenon cases of motion not spontaneous The conception was hence inappropriate We may add that in the case in question no conception would be appropriate there is no agreement which runs through all the cases of spontaneous or apparently spontaneous motion and no others they can not be brought under one law it is a case of Plurality of Causes So much for the first of Dr Whewell’s conditions that conceptions must be appropriate The second is that they shall be clear and let us consider what this implies Unless the conception corresponds to a real agreement it has a worse defect than that of not being clear it is not applicable to the case at all Among the phenomena therefore which we are attempting to connect by means of the conception we must suppose that there really is an agreement and that the conception is a conception of that agreement In order then that it may be clear the only requisite is that we shall know exactly in what the agreement consists that it shall have been carefully observed and accurately remembered We are said not to have a clear conception of the resemblance among a set of objects when we have only a general feeling that they resemble without having analysed their resemblance or perceived in what points it consists and fixed in our memory an exact recollection of those points This want of clearness or as it may be otherwise called this vagueness in the general conception may be owing either to our having no accurate knowledge of the objects themselves or merely to our not having carefully compared them Thus a person may have no clear idea of a ship because he has never seen one or because he remembers but little and that faintly of what he has seen Or he may have a perfect knowledge and remembrance of many ships of various kinds frigates among the rest but he may have no clear but only a confused idea of a frigate because he has never been told and has not compared them sufficiently to have remarked and remembered in what particular points a frigate differs from some other kind of ship It is not however necessary in order to have clear ideas that we should know all the common properties of the things which we class together That would be to have our conception of the class complete as well as clear It is sufficient if we never class things together without knowing exactly why we do so without having ascertained exactly what agreements we are about to include in our conception and if after having thus fixed our conception we never vary from it never include in the class any thing which has not those common properties nor exclude from it any thing which has A clear conception means a determinate conception one which does not fluctuate which is not one thing today and another tomorrow but remains fixed and invariable except when from the progress of our knowledge or the correction of some error we consciously add to it or alter it A person of clear ideas is a person who always knows in virtue of what properties his classes are constituted what attributes are connoted by his general names The principal requisites therefore of clear conceptions are habits of attentive observation an extensive experience and a memory which receives and retains an exact image of what is observed And in proportion as any one has the habit of observing minutely and comparing carefully a particular class of phenomena and an accurate memory for the results of the observation and comparison so will his conceptions of that class of phenomena be clear provided he has the indispensable habit naturally however resulting from those other endowments of never using general names without a precise connotation As the clearness of our conceptions chiefly depends on the carefulness and accuracy of our observing and comparing faculties so their appropriateness or rather the chance we have of hitting upon the appropriate conception in any case mainly depends on the activity of the same faculties He who by habit grounded on sufficient natural aptitude has acquired a readiness in accurately observing and comparing phenomena will perceive so many more agreements and will perceive them so much more rapidly than other people that the chances are much greater of his perceiving in any instance the agreement on which the important consequences depend It is of so much importance that the part of the process of investigating truth discussed in this chapter should be rightly understood that I think it is desirable to restate the results we have arrived at in a somewhat different mode of expression We can not ascertain general truths that is truths applicable to classes unless we have formed the classes in such a manner that general truths can be affirmed of them In the formation of any class there is involved a conception of it as a class that is a conception of certain circumstances as being those which characterize the class and distinguish the objects composing it from all other things When we know exactly what these circumstances are we have a clear idea or conception of the class and of the meaning of the general name which designates it The primary condition implied in having this clear idea is that the class be really a class that it correspond to a real distinction that the things it includes really do agree with one another in certain particulars and differ in those same particulars from all other things A person without clear ideas is one who habitually classes together under the same general names things which have no common properties or none which are not possessed also by other things or who if the usage of other people prevents him from actually misclassing things is unable to state to himself the common properties in virtue of which he classes them rightly But is it not the sole requisite of classification that the classes should be real classes framed by a legitimate mental process Some modes of classing things are more valuable than others for human uses whether of speculation or of practice and our classifications are not well made unless the things which they bring together not only agree with each other in something which distinguishes them from all other things but agree with each other and differ from other things in the very circumstances which are of primary importance for the purpose theoretical or practical which we have in view and which constitutes the problem before us In other words our conceptions though they may be clear are not appropriate for our purpose unless the properties we comprise in them are those which will help us toward what we wish to understand ie either those which go deepest into the nature of the things if our object be to understand that or those which are most closely connected with the particular property which we are endeavouring to investigate We can not therefore frame good general conceptions beforehand That the conception we have obtained is the one we want can only be known when we have done the work for the sake of which we wanted it when we completely understand the general character of the phenomena or the conditions of the particular property with which we concern ourselves General conceptions formed without this thorough knowledge are Bacon’s notiones temer ˆ rebus abstractae Yet such premature conceptions we must be continually making up in our progress to something better They are an impediment to the progress of knowledge only when they are permanently acquiesced in When it has become our habit to group things in wrong classes in groups which either are not really classes having no distinctive points of agreement absence of clear ideas or which are not classes of which any thing important to our purpose can be predicated absence of appropriate ideas and when in the belief that these badly made classes are those sanctioned by nature we refuse to exchange them for others and can not or will not make up our general conceptions from any other elements in that case all the evils which Bacon ascribes to his notiones temer abstractae really occur This was what the ancients did in physics and what the world in general does in morals and politics to the present day It would thus in my view of the matter be an inaccurate mode of expression to say that obtaining appropriate conceptions is a condition precedent to generalization Throughout the whole process of comparing phenomena with one another for the purpose of generalization the mind is trying to make up a conception but the conception which it is trying to make up is that of the really important point of agreement in the phenomena As we obtain more knowledge of the phenomena themselves and of the conditions on which their important properties depend our views on this subject naturally alter and thus we advance from a less to a more appropriate general conception in the progress of our investigations We ought not at the same time to forget that the really important agreement can not always be discovered by mere comparison of the very phenomena in question without the aid of a conception acquired elsewhere as in the case so often referred to of the planetary orbits The search for the agreement of a set of phenomena is in truth very similar to the search for a lost or hidden object At first we place ourselves in a sufficiently commanding position and cast our eyes round us and if we can see the object it is well if not we ask ourselves mentally what are the places in which it may be hid in order that we may there search for it and so on until we imagine the place where it really is And here too we require to have had a previous conception or knowledge of those different places As in this familiar process so in the philosophical operation which it illustrates we first endeavour to find the lost object or recognize the common attribute without conjecturally invoking the aid of any previously acquired conception or, in other words, of any hypothesis Having failed in this we call upon our imagination for some hypothesis of a possible place or a possible point of resemblance and then look to see whether the facts agree with the conjecture For such cases something more is required than a mind accustomed to accurate observation and comparison It must be a mind stored with general conceptions previously acquired of the sorts which bear affinity to the subject of the particular inquiry And much will also depend on the natural strength and acquired culture of what has been termed the scientific imagination on the faculty possessed of mentally arranging known elements into new combinations such as have not yet been observed in nature though not contradictory to any known laws But the variety of intellectual habits the purposes which they serve and the modes in which they may be fostered and cultivated are considerations belonging to the Art of Education a subject far wider than Logic and which this treatise does not profess to discuss Here therefore the present chapter may properly close It does not belong to the present undertaking to dwell on the importance of language as a medium of human intercourse whether for purposes of sympathy or of information Nor does our design admit of more than a passing allusion to that great property of names on which their functions as an intellectual instrument are in reality ultimately dependent their potency as a means of forming and of riveting associations among our other ideas a subject on which an able thinker has thus written Names are impressions of sense and as such take the strongest hold on the mind and of all other impressions can be most easily recalled and retained in view They therefore serve to give a point of attachment to all the more volatile objects of thought and feeling Impressions that when passed might be dissipated forever are by their connection with language always within reach Thoughts of themselves are perpetually slipping out of the field of immediate mental vision but the name abides with us and the utterance of it restores them in a moment Words are the custodiers of every product of mind less impressive than themselves All extensions of human knowledge all new generalizations are fixed and spread even unintentionally by the use of words The child growing up learns along with the vocables of his mothertongue that things which he would have believed to be different are in important points the same Without any formal instruction the language in which we grow up teaches us all the common philosophy of the age It directs us to observe and know things which we should have overlooked it supplies us with classifications ready made by which things are arranged as far as the light of bygone generations admits with the objects to which they bear the greatest total resemblance The number of general names in a language and the degree of generality of those names afford a test of the knowledge of the era and of the intellectual insight which is the birthright of any one born into it It is not however of the functions of Names considered generally that we have here to treat but only of the manner and degree in which they are directly instrumental to the investigation of truth in other words to the process of induction Observation and Abstraction the operations which formed the subject of the two foregoing chapters are conditions indispensable to induction there can be no induction where they are not It has been imagined that Naming is also a condition equally indispensable There are thinkers who have held that language is not solely according to a phrase generally current an instrument of thought but the instrument that names or something equivalent to them some species of artificial signs are necessary to reasoning that there could be no inference and consequently no induction without them But if the nature of reasoning was correctly explained in the earlier part of the present work this opinion must be held to be an exaggeration though of an important truth If reasoning be from particulars to particulars and if it consist in recognizing one fact as a mark of another or a mark of a mark of another nothing is required to render reasoning possible except senses and association senses to perceive that two facts are conjoined association as the law by which one of those two facts raises up the idea of the other For these mental phenomena as well as for the belief or expectation which follows and by which we recognize as having taken place or as about to take place that of which we have perceived a mark there is evidently no need of language And this inference of one particular fact from another is a case of induction It is of this sort of induction that brutes are capable it is in this shape that uncultivated minds make almost all their inductions and that we all do so in the cases in which familiar experience forces our conclusions upon us without any active process of inquiry on our part and in which the belief or expectation follows the suggestion of the evidence with the promptitude and certainty of an instinct But though inference of an inductive character is possible without the use of signs it could never without them be carried much beyond the very simple cases which we have just described and which form in all probability the limit of the reasonings of those animals to whom conventional language is unknown Without language or something equivalent to it there could only be as much reasoning from experience as can take place without the aid of general propositions Now though in strictness we may reason from past experience to a fresh individual case without the intermediate stage of a general proposition yet without general propositions we should seldom remember what past experience we have had and scarcely ever what conclusions that experience will warrant The division of the inductive process into two parts the first ascertaining what is a mark of the given fact the second whether in the new case that mark exists is natural and scientifically indispensable It is indeed in a majority of cases rendered necessary by mere distance of time The experience by which we are to guide our judgments may be other people’s experience little of which can be communicated to us otherwise than by language when it is our own it is generally experience long past unless therefore it were recorded by means of artificial signs little of it except in cases involving our intenser sensations or emotions or the subjects of our daily and hourly contemplation would be retained in the memory It is hardly necessary to add that when the inductive inference is of any but the most direct and obvious nature when it requires several observations or experiments in varying circumstances and the comparison of one of these with another it is impossible to proceed a step without the artificial memory which words bestow Without words we should if we had often seen A and B in immediate and obvious conjunction expect B whenever we saw A but to discover their conjunction when not obvious or to determine whether it is really constant or only casual and whether there is reason to expect it under any given change of circumstances is a process far too complex to be performed without some contrivance to make our remembrance of our own mental operations accurate Now language is such a contrivance When that instrument is called to our aid the difficulty is reduced to that of making our remembrance of the meaning of words accurate This being secured whatever passes through our minds may be remembered accurately by putting it carefully into words and committing the words either to writing or to memory The function of Naming and particularly of General Names in Induction may be recapitulated as follows Every inductive inference which is good at all is good for a whole class of cases and that the inference may have any better warrant of its correctness than the mere clinging together of two ideas a process of experimentation and comparison is necessary in which the whole class of cases must be brought to view and some uniformity in the course of nature evolved and ascertained since the existence of such a uniformity is required as a justification for drawing the inference in even a single case This uniformity therefore may be ascertained once for all and if being ascertained it can be remembered it will serve as a formula for making in particular cases all such inferences as the previous experience will warrant But we can only secure its being remembered or give ourselves even a chance of carrying in our memory any considerable number of such uniformities by registering them through the medium of permanent signs which being from the nature of the case signs not of an individual fact but of a uniformity that is of an indefinite number of facts similar to one another are general signs universals general names and general propositions And here I can not omit to notice an oversight committed by some eminent thinkers who have said that the cause of our using general names is the infinite multitude of individual objects which making it impossible to have a name for each compels us to make one name serve for many This is a very limited view of the function of general names Even if there were a name for every individual object we should require general names as much as we now do Without them we could not express the result of a single comparison nor record any one of the uniformities existing in nature and should be hardly better off in respect to Induction than if we had no names at all With none but names of individuals or, in other words, proper names we might by pronouncing the name suggest the idea of the object but we could not assert any proposition except the unmeaning ones formed by predicating two proper names one of another It is only by means of general names that we can convey any information predicate any attribute even of an individual much more of a class Rigorously speaking we could get on without any other general names than the abstract names of attributes all our propositions might be of the form such an individual object possesses such an attribute or such an attribute is always or never conjoined with such another attribute In fact however mankind have always given general names to objects as well as attributes and indeed before attributes but the general names given to objects imply attributes derive their whole meaning from attributes and are chiefly useful as the language by means of which we predicate the attributes which they connote It remains to be considered what principles are to be adhered to in giving general names so that these names and the general propositions in which they fill a place may conduce most to the purposes of Induction In order that we may possess a language perfectly suitable for the investigation and expression of general truths there are two principal and several minor requisites The first is that every general name should have a meaning steadily fixed and precisely determined When by the fulfilment of this condition such names as we possess are fitted for the due performance of their functions the next requisite and the second in order of importance is that we should possess a name wherever one is needed wherever there is any thing to be designated by it which it is of importance to express The former of these requisites is that to which our attention will be exclusively directed in the present chapter Every general name then must have a certain and knowable meaning Now the meaning as has so often been explained of a general connotative name resides in the connotation in the attribute on account of which and to express which the name is given Thus the name animal being given to all things which possess the attributes of sensation and voluntary motion the word connotes those attributes exclusively and they constitute the whole of its meaning If the name be abstract its denotation is the same with the connotation of the corresponding concrete it designates directly the attribute which the concrete term implies To give a precise meaning to general names is then to fix with steadiness the attribute or attributes connoted by each concrete general name and denoted by the corresponding abstract Since abstract names in the order of their creation do not precede but follow concrete ones as is proved by the etymological fact that they are almost always derived from them we may consider their meaning as determined by and dependent on the meaning of their concrete and thus the problem of giving a distinct meaning to general language is all included in that of giving a precise connotation to all concrete general names This is not difficult in the case of new names of the technical terms created by scientific inquirers for the purposes of science or art But when a name is in common use the difficulty is greater the problem in this case not being that of choosing a convenient connotation for the name but of ascertaining and fixing the connotation with which it is already used That this can ever be a matter of doubt is a sort of paradox But the vulgar including in that term all who have not accurate habits of thought seldom know exactly what assertion they intend to make what common property they mean to express when they apply the same name to a number of different things All which the name expresses with them when they predicate it of an object is a confused feeling of resemblance between that object and some of the other things which they have been accustomed to denote by the name They have applied the name Stone to various objects previously seen they see a new object which appears to them somewhat like the former and they call it a stone without asking themselves in what respect it is like or what mode or degree of resemblance the best authorities or even they themselves require as a warrant for using the name This rough general impression of resemblance is however made up of particular circumstances of resemblance and into these it is the business of the logician to analyse it to ascertain what points of resemblance among the different things commonly called by the name have produced in the common mind this vague feeling of likeness have given to the things the similarity of aspect which has made them a class and has caused the same name to be bestowed upon them But though general names are imposed by the vulgar without any more definite connotation than that of a vague resemblance general propositions come in time to be made in which predicates are applied to those names that is general assertions are made concerning the whole of the things which are denoted by the name And since by each of these propositions some attribute more or less precisely conceived is of course predicated the ideas of these various attributes thus become associated with the name and in a sort of uncertain way it comes to connote them there is a hesitation to apply the name in any new case in which any of the attributes familiarly predicated of the class do not exist And thus to common minds the propositions which they are in the habit of hearing or uttering concerning a class make up in a loose way a sort of connotation for the class name Let us take for instance the word Civilized How few could be found even among the most educated persons who would undertake to say exactly what the term Civilized connotes Yet there is a feeling in the minds of all who use it that they are using it with a meaning and this meaning is made up in a confused manner of every thing which they have heard or read that civilized men or civilized communities are or may be expected to be It is at this stage probably in the progress of a concrete name that the corresponding abstract name generally comes into use Under the notion that the concrete name must of course convey a meaning or, in other words, that there is some property common to all things which it denotes people give a name to this common property from the concrete Civilized they form the abstract Civilization But since most people have never compared the different things which are called by the concrete name in such a manner as to ascertain what properties these things have in common or whether they have any each is thrown back upon the marks by which he himself has been accustomed to be guided in his application of the term and these being merely vague hearsays and current phrases are not the same in any two persons nor in the same person at different times Hence the word as Civilization for example which professes to be the designation of the unknown common property conveys scarcely to any two minds the same idea No two persons agree in the things they predicate of it and when it is itself predicated of any thing no other person knows nor does the speaker himself know with precision what he means to assert Many other words which could be named as the word honour or the word gentleman exemplify this uncertainty still more strikingly It needs scarcely be observed that general propositions of which no one can tell exactly what they assert can not possibly have been brought to the test of a correct induction Whether a name is to be used as an instrument of thinking or as a means of communicating the result of thought it is imperative to determine exactly the attribute or attributes which it is to express to give it in short a fixed and ascertained connotation It would however be a complete misunderstanding of the proper office of a logician in dealing with terms already in use if we were to think that because a name has not at present an ascertained connotation it is competent to any one to give it such a connotation at his own choice The meaning of a term actually in use is not an arbitrary quantity to be fixed but an unknown quantity to be sought In the first place it is obviously desirable to avail ourselves as far as possible of the associations already connected with the name not enjoining the employment of it in a manner which conflicts with all previous habits and especially not so as to require the rupture of those strongest of all associations between names which are created by familiarity with propositions in which they are predicated of one another A philosopher would have little chance of having his example followed if he were to give such a meaning to his terms as should require us to call the North American Indians a civilized people or the higher classes in Europe savages or to say that civilized people live by hunting and savages by agriculture Were there no other reason the extreme difficulty of effecting so complete a revolution in speech would be more than a sufficient one The endeavour should be that all generally received propositions into which the term enters should be at least as true after its meaning is fixed as they were before and that the concrete name therefore should not receive such a connotation as shall prevent it from denoting things which in common language it is currently affirmed of The fixed and precise connotation which it receives should not be in deviation from but in agreement as far as it goes with the vague and fluctuating connotation which the term already had To fix the connotation of a concrete name or the denotation of the corresponding abstract is to define the name When this can be done without rendering any received assertions inadmissible the name can be defined in accordance with its received use which is vulgarly called defining not the name but the thing What is meant by the improper expression of defining a thing or rather a class of things for nobody talks of defining an individual is to define the name subject to the condition that it shall denote those things This of course supposes a comparison of the things feature by feature and property by property to ascertain what attributes they agree in and not unfrequently an operation strictly inductive for the purpose of ascertaining some unobvious agreement which is the cause of the obvious agreements For in order to give a connotation to a name consistently with its denoting certain objects we have to make our selection from among the various attributes in which those objects agree To ascertain in what they do agree is therefore the first logical operation requisite When this has been done as far as is necessary or practicable the question arises which of these common attributes shall be selected to be associated with the name For if the class which the name denotes be a Kind the common properties are innumerable and even if not they are often extremely numerous Our choice is first limited by the preference to be given to properties which are well known and familiarly predicated of the class but even these are often too numerous to be all included in the definition and besides the properties most generally known may not be those which serve best to mark out the class from all others We should therefore select from among the common properties if among them any such are to be found those on which it has been ascertained by experience or proved by deduction that many others depend or at least which are sure marks of them and from whence therefore many others will follow by inference We thus see that to frame a good definition of a name already in use is not a matter of choice but of discussion and discussion not merely respecting the usage of language but respecting the properties of things and even the origin of those properties And hence every enlargement of our knowledge of the objects to which the name is applied is liable to suggest an improvement in the definition It is impossible to frame a perfect set of definitions on any subject until the theory of the subject is perfect and as science makes progress its definitions are also progressive The discussion of Definitions in so far as it does not turn on the use of words but on the properties of things Dr Whewell calls the Explication of Conceptions The act of ascertaining better than before in what particulars any phenomena which are classed together agree he calls in his technical phraseology unfolding the general conception in virtue of which they are so classed Making allowance for what appears to me the darkening and misleading tendency of this mode of expression several of his remarks are so much to the purpose that I shall take the liberty of transcribing them He observes that many of the controversies which have had an important share in the formation of the existing body of science have assumed the form of a battle of Definitions For example the inquiry concerning the laws of falling bodies led to the question whether the proper definition of a uniform force is that it generates a velocity proportional to the space from rest or to the time The controversy of the vis viva was what was the proper definition of the measure of force A principal question in the classification of minerals is what is the definition of a mineral species Physiologists have endeavoured to throw light on their subject by defining organization or some similar term Questions of the same nature were long open and are not yet completely closed respecting the definitions of Specific Heat Latent Heat Chemical Combination and Solution It is very important for us to observe that these controversies have never been questions of insulated and arbitrary definitions as men seem often tempted to imagine them to have been In all cases there is a tacit assumption of some proposition which is to be expressed by means of the definition and which gives it its importance The dispute concerning the definition thus acquires a real value and becomes a question concerning true and false Thus in the discussion of the question What is a uniform force it was taken for granted that gravity is a uniform force In the debate of the vis viva it was assumed that in the mutual action of bodies the whole effect of the force is unchanged In the zoological definition of species that it consists of individuals which have or may have sprung from the same parents it is presumed that individuals so related resemble each other more than those which are excluded by such a definition or perhaps that species so defined have permanent and definite differences A definition of organization or of some other term which was not employed to express some principle would be of no value The establishment therefore of a right definition of a term may be a useful step in the explication of our conceptions but this will be the case then only when we have under our consideration some proposition in which the term is employed For then the question really is how the conception shall be understood and defined in order that the proposition may be true To unfold our conceptions by means of definitions has never been serviceable to science except when it has been associated with an immediate use of the definitions The endeavour to define a Uniform Force was combined with the assertion that gravity is a uniform force the attempt to define Accelerating Force was immediately followed by the doctrine that accelerating forces may be compounded the process of defining Momentum was connected with the principle that momenta gained and lost are equal naturalists would have given in vain the definition of Species which we have quoted if they had not also given the characters of species so separated Definition may be the best mode of explaining our conception but that which alone makes it worth while to explain it in any mode is the opportunity of using it in the expression of truth When a definition is propounded to us as a useful step in knowledge we are always entitled to ask what principle it serves to enunciate In giving then an exact connotation to the phrase a uniform force the condition was understood that the phrase should continue to denote gravity The discussion therefore respecting the definition resolved itself into this question What is there of a uniform nature in the motions produced by gravity By observations and comparisons it was found that what was uniform in those motions was the ratio of the velocity acquired to the time elapsed equal velocities being added in equal times A uniform force therefore was defined a force which adds equal velocities in equal times So again in defining momentum It was already a received doctrine that when two objects impinge upon one another the momentum lost by the one is equal to that gained by the other This proposition it was deemed necessary to preserve not from the motive which operates in many other cases that it was firmly fixed in popular belief for the proposition in question had never been heard of by any but the scientifically instructed But it was felt to contain a truth even a superficial observation of the phenomena left no doubt that in the propagation of motion from one body to another there was something of which the one body gained precisely what the other lost and the word momentum had been invented to express this unknown something The settlement therefore of the definition of momentum involved the determination of the question What is that of which a body when it sets another body in motion loses exactly as much as it communicates And when experiment had shown that this something was the product of the velocity of the body by its mass or quantity of matter this became the definition of momentum The following remarks therefore are perfectly just The business of definition is part of the business of discovery To define so that our definition shall have any scientific value requires no small portion of that sagacity by which truth is detected When it has been clearly seen what ought to be our definition it must be pretty well known what truth we have to state The definition as well as the discovery supposes a decided step in our knowledge to have been made The writers on Logic in the Middle Ages made Definition the last stage in the progress of knowledge and in this arrangement at least the history of science and the philosophy derived from the history confirm their speculative views For in order to judge finally how the name which denotes a class may best be defined we must know all the properties common to the class and all the relations of causation or dependence among those properties If the properties which are fittest to be selected as marks of other common properties are also obvious and familiar and especially if they bear a great part in producing that general air of resemblance which was the original inducement to the formation of the class the definition will then be most felicitous But it is often necessary to define the class by some property not familiarly known provided that property be the best mark of those which are known M De Blainville for instance founded his definition of life on the process of decomposition and recomposition which incessantly takes place in every living body so that the particles composing it are never for two instants the same This is by no means one of the most obvious properties of living bodies it might escape altogether the notice of an unscientific observer Yet great authorities independently of M De Blainville who is himself a firstrate authority have thought that no other property so well answers the conditions required for the definition Having laid down the principles which ought for the most part to be observed in attempting to give a precise connotation to a term in use I must now add that it is not always practicable to adhere to those principles and that even when practicable it is occasionally not desirable Cases in which it is impossible to comply with all the conditions of a precise definition of a name in agreement with usage occur very frequently There is often no one connotation capable of being given to a word so that it shall still denote every thing it is accustomed to denote or that all the propositions into which it is accustomed to enter and which have any foundation in truth shall remain true Independently of accidental ambiguities in which the different meanings have no connection with one another it continually happens that a word is used in two or more senses derived from each other but yet radically distinct So long as a term is vague that is so long as its connotation is not ascertained and permanently fixed it is constantly liable to be applied by extension from one thing to another until it reaches things which have little or even no resemblance to those which were first designated by it Suppose says Dugald Stewart in his Philosophical Essays that the letters A B C D E denote a series of objects that A possesses some one quality in common with B B a quality in common with C C a quality in common with D D a quality in common with E while at the same time no quality can be found which belongs in common to any three objects in the series Is it not conceivable that the affinity between A and B may produce a transference of the name of the first to the second and that in consequence of the other affinities which connect the remaining objects together the same name may pass in succession from B to C from C to D and from D to E In this manner a common appellation will arise between A and E although the two objects may in their nature and properties be so widely distant from each other that no stretch of imagination can conceive how the thoughts were led from the former to the latter The transitions nevertheless may have been all so easy and gradual that were they successfully detected by the fortunate ingenuity of a theorist we should instantly recognize not only the verisimilitude but the truth of the conjecture in the same way as we admit with the confidence of intuitive conviction the certainty of the wellknown etymological process which connects the Latin preposition e or ex with the English substantive stranger the moment that the intermediate links of the chain are submitted to our examination The applications which a word acquires by this gradual extension of it from one set of objects to another Stewart adopting an expression from Mr Payne Knight calls its transitive applications and after briefly illustrating such of them as are the result of local or casual associations he proceeds as follows But although by far the greater part of the transitive or derivative applications of words depend on casual and unaccountable caprices of the feelings or the fancy there are certain cases in which they open a very interesting field of philosophical speculation Such are those in which an analogous transference of the corresponding term may be remarked universally or very generally in other languages and in which of course the uniformity of the result must be ascribed to the essential principles of the human frame Even in such cases however it will by no means be always found on examination that the various applications of the same term have arisen from any common quality or qualities in the objects to which they relate In the greater number of instances they may be traced to some natural and universal associations of ideas founded in the common faculties common organs and common condition of the human race According to the different degrees of intimacy and strength in the associations on which the transitions of language are founded very different effects may be expected to arise Where the association is slight and casual the several meanings will remain distinct from each other and will often in process of time assume the appearance of capricious varieties in the use of the same arbitrary sign Where the association is so natural and habitual as to become virtually indissoluble the transitive meanings will coalesce in one complex conception and every new transition will become a more comprehensive generalization of the term in question I solicit particular attention to the law of mind expressed in the last sentence and which is the source of the perplexity so often experienced in detecting these transitions of meaning Ignorance of that law is the shoal on which some of the most powerful intellects which have adorned the human race have been stranded The inquiries of Plato into the definitions of some of the most general terms of moral speculation are characterized by Bacon as a far nearer approach to a true inductive method than is elsewhere to be found among the ancients and are indeed almost perfect examples of the preparatory process of comparison and abstraction but from being unaware of the law just mentioned he often wasted the powers of this great logical instrument on inquiries in which it could realize no result since the phenomena whose common properties he so elaborately endeavoured to detect had not really any common properties Bacon himself fell into the same error in his speculations on the nature of heat in which he evidently confounded under the name hot classes of phenomena which have no property in common Stewart certainly overstates the matter when he speaks of a prejudice which has descended to modern times from the scholastic ages that when a word admits of a variety of significations these different significations must all be species of the same genus and must consequently include some essential idea common to every individual to which the generic term can be applied for both Aristotle and his followers were well aware that there are such things as ambiguities of language and delighted in distinguishing them But they never suspected ambiguity in the cases where as Stewart remarks the association on which the transition of meaning was founded is so natural and habitual that the two meanings blend together in the mind and a real transition becomes an apparent generalization Accordingly they wasted infinite pains in endeavouring to find a definition which would serve for several distinct meanings at once as in an instance noticed by Stewart himself that of causation the ambiguity of the word which in the Greek language corresponds to the English word cause having suggested to them the vain attempt of tracing the common idea which in the case of any effect belongs to the efficient to the matter to the form and to the end The idle generalities he adds we meet with in other philosophers about the ideas of the good the fit and the becoming have taken their rise from the same undue influence of popular epithets on the speculations of the learned Among the words which have undergone so many successive transitions of meaning that every trace of a property common to all the things they are applied to or at least common and also peculiar to those things has been lost Stewart considers the word Beautiful to be one And without attempting to decide a question which in no respect belongs to logic I can not but feel with him considerable doubt whether the word beautiful connotes the same property when we speak of a beautiful colour a beautiful face a beautiful scene a beautiful character and a beautiful poem The word was doubtless extended from one of these objects to another on account of a resemblance between them or more probably between the emotions they excited and by this progressive extension it has at last reached things very remote from those objects of sight to which there is no doubt that it was first appropriated and it is at least questionable whether there is now any property common to all the things which consistently with usage may be called beautiful except the property of agreeableness which the term certainly does connote but which can not be all that people usually intend to express by it since there are many agreeable things which are never called beautiful If such be the case it is impossible to give to the word Beautiful any fixed connotation such that it shall denote all the objects which in common use it now denotes but no others A fixed connotation however it ought to have for so long as it has not it is unfit to be used as a scientific term and is a perpetual source of false analogies and erroneous generalizations This then constitutes a case in exemplification of our remark that even when there is a property common to all the things denoted by a name to erect that property into the definition and exclusive connotation of the name is not always desirable The various things called beautiful unquestionably resemble one another in being agreeable but to make this the definition of beauty and so extend the word Beautiful to all agreeable things would be to drop altogether a portion of meaning which the word really though indistinctly conveys and to do what depends on us toward causing those qualities of the objects which the word previously though vaguely pointed at to be overlooked and forgotten It is better in such a case to give a fixed connotation to the term by restricting than by extending its use rather excluding from the epithet Beautiful some things to which it is commonly considered applicable than leaving out of its connotation any of the qualities by which though occasionally lost sight of the general mind may have been habitually guided in the commonest and most interesting applications of the term For there is no question that when people call any thing beautiful they think they are asserting more than that it is merely agreeable They think they are ascribing a peculiar sort of agreeableness analogous to that which they find in some other of the things to which they are accustomed to apply the same name If therefore there be any peculiar sort of agreeableness which is common though not to all yet to the principal things which are called beautiful it is better to limit the denotation of the term to those things than to leave that kind of quality without a term to connote it and thereby divert attention from its peculiarities The last remark exemplifies a rule of terminology which is of great importance and which has hardly yet been recognized as a rule but by a few thinkers of the present century In attempting to rectify the use of a vague term by giving it a fixed connotation we must take care not to discard unless advisedly and on the ground of a deeper knowledge of the subject any portion of the connotation which the word in however indistinct a manner previously carried with it For otherwise language loses one of its inherent and most valuable properties that of being the conservator of ancient experience the keeperalive of those thoughts and observations of former ages which may be alien to the tendencies of the passing time This function of language is so often overlooked or undervalued that a few observations on it appear to be extremely required Even when the connotation of a term has been accurately fixed and still more if it has been left in the state of a vague unanalyzed feeling of resemblance there is a constant tendency in the word through familiar use to part with a portion of its connotation It is a wellknown law of the mind that a word originally associated with a very complex cluster of ideas is far from calling up all those ideas in the mind every time the word is used it calls up only one or two from which the mind runs on by fresh associations to another set of ideas without waiting for the suggestion of the remainder of the complex cluster If this were not the case processes of thought could not take place with any thing like the rapidity which we know they possess Very often indeed when we are employing a word in our mental operations we are so far from waiting until the complex idea which corresponds to the meaning of the word is consciously brought before us in all its parts that we run on to new trains of ideas by the other associations which the mere word excites without having realized in our imagination any part whatever of the meaning thus using the word and even using it well and accurately and carrying on important processes of reasoning by means of it in an almost mechanical manner so much so that some metaphysicians generalizing from an extreme case have fancied that all reasoning is but the mechanical use of a set of terms according to a certain form We may discuss and settle the most important interests of towns or nations by the application of general theorems or practical maxims previously laid down without having had consciously suggested to us once in the whole process the houses and green fields the thronged marketplaces and domestic hearths of which not only those towns and nations consist but which the words town and nation confessedly mean Since then general names come in this manner to be used and even to do a portion of their work well without suggesting to the mind the whole of their meaning and often with the suggestion of a very small or no part at all of that meaning we can not wonder that words so used come in time to be no longer capable of suggesting any other of the ideas appropriated to them than those with which the association is most immediate and strongest or most kept up by the incidents of life the remainder being lost altogether unless the mind by often consciously dwelling on them keeps up the association Words naturally retain much more of their meaning to persons of active imagination who habitually represent to themselves things in the concrete with the detail which belongs to them in the actual world To minds of a different description the only antidote to this corruption of language is predication The habit of predicating of the name all the various properties which it originally connoted keeps up the association between the name and those properties But in order that it may do so it is necessary that the predicates should themselves retain their association with the properties which they severally connote For the propositions can not keep the meaning of the words alive if the meaning of the propositions themselves should die And nothing is more common than for propositions to be mechanically repeated mechanically retained in the memory and their truth undoubtingly assented to and relied on while yet they carry no meaning distinctly home to the mind and while the matter of fact or law of nature which they originally expressed is as much lost sight of and practically disregarded as if it never had been heard of at all In those subjects which are at the same time familiar and complicated and especially in those which are so in as great a degree as moral and social subjects are it is a matter of common remark how many important propositions are believed and repeated from habit while no account could be given and no sense is practically manifested of the truths which they convey Hence it is that the traditional maxims of old experience though seldom questioned have often so little effect on the conduct of life because their meaning is never by most persons really felt until personal experience has brought it home And thus also it is that so many doctrines of religion ethics and even politics so full of meaning and reality to first converts have manifested after the association of that meaning with the verbal formulas has ceased to be kept up by the controversies which accompanied their first introduction a tendency to degenerate rapidly into lifeless dogmas which tendency all the efforts of an education expressly and skillfully directed to keeping the meaning alive are barely sufficient to counteract Considering then that the human mind in different generations occupies itself with different things and in one age is led by the circumstances which surround it to fix more of its attention upon one of the properties of a thing in another age upon another it is natural and inevitable that in every age a certain portion of our recorded and traditional knowledge not being continually suggested by the pursuits and inquiries with which mankind are at that time engrossed should fall asleep as it were and fade from the memory It would be in danger of being totally lost if the propositions or formulas the results of the previous experience did not remain as forms of words it may be but of words that once really conveyed and are still supposed to convey a meaning which meaning though suspended may be historically traced and when suggested may be recognized by minds of the necessary endowments as being still matter of fact or truth While the formulas remain the meaning may at any time revive and as on the one hand the formulas progressively lose the meaning they were intended to convey so on the other when this forgetfulness has reached its height and begun to produce obvious consequences minds arise which from the contemplation of the formulas rediscover the truth when truth it was which was contained in them and announce it again to mankind not as a discovery but as the meaning of that which they have been taught and still profess to believe Thus there is a perpetual oscillation in spiritual truths and in spiritual doctrines of any significance even when not truths Their meaning is almost always in a process either of being lost or of being recovered Whoever has attended to the history of the more serious convictions of mankind of the opinions by which the general conduct of their lives is or as they conceive ought to be more especially regulated is aware that even when recognizing verbally the same doctrines they attach to them at different periods a greater or a less quantity and even a different kind of meaning The words in their original acceptation connoted and the propositions expressed a complication of outward facts and inward feelings to different portions of which the general mind is more particularly alive in different generations of mankind To common minds only that portion of the meaning is in each generation suggested of which that generation possesses the counterpart in its own habitual experience But the words and propositions lie ready to suggest to any mind duly prepared the remainder of the meaning Such individual minds are almost always to be found and the lost meaning revived by them again by degrees works its way into the general mind The arrival of this salutary reaction may however be materially retarded by the shallow conceptions and incautious proceedings of mere logicians It sometimes happens that toward the close of the downward period when the words have lost part of their significance and have not yet begun to recover it persons arise whose leading and favourite idea is the importance of clear conceptions and precise thought and the necessity therefore of definite language These persons in examining the old formulas easily perceive that words are used in them without a meaning and if they are not the sort of persons who are capable of rediscovering the lost signification they naturally enough dismiss the formula and define the name without reference to it In so doing they fasten down the name to what it connotes in common use at the time when it conveys the smallest quantity of meaning and introduce the practice of employing it consistently and uniformly according to that connotation The word in this way acquires an extent of denotation far beyond what it had before it becomes extended to many things to which it was previously in appearance capriciously refused Of the propositions in which it was formerly used those which were true in virtue of the forgotten part of its meaning are now by the clearer light which the definition diffuses seen not to be true according to the definition which however is the recognized and sufficiently correct expression of all that is perceived to be in the mind of any one by whom the term is used at the present day The ancient formulas are consequently treated as prejudices and people are no longer taught as before though not to understand them yet to believe that there is truth in them They no longer remain in the general mind surrounded by respect and ready at any time to suggest their original meaning Whatever truths they contain are not only in these circumstances rediscovered far more slowly but when rediscovered the prejudice with which novelties are regarded is now in some degree at least against them instead of being on their side An example may make these remarks more intelligible In all ages except where moral speculation has been silenced by outward compulsion or where the feelings which prompt to it still continue to be satisfied by the traditional doctrines of an established faith one of the subjects which have most occupied the minds of thinking persons is the inquiry What is virtue or What is a virtuous character Among the different theories on the subject which have at different times grown up and obtained partial currency every one of which reflected as in the clearest mirror the express image of the age which gave it birth there was one according to which virtue consists in a correct calculation of our own personal interests either in this world only or also in another To make this theory plausible it was of course necessary that the only beneficial actions which people in general were accustomed to see or were therefore accustomed to praise should be such as were or at least might without contradicting obvious facts be supposed to be the result of a prudential regard to selfinterest so that the words really connoted no more in common acceptation than was set down in the definition Suppose now that the partisans of this theory had contrived to introduce a consistent and undeviating use of the term according to this definition Suppose that they had seriously endeavoured and had succeeded in the endeavour to banish the word disinterestedness from the language had obtained the disuse of all expressions attaching odium to selfishness or commendation to selfsacrifice or which implied generosity or kindness to be any thing but doing a benefit in order to receive a greater personal advantage in return Need we say that this abrogation of the old formulas for the sake of preserving clear ideas and consistency of thought would have been a great evil while the very inconsistency incurred by the coexistence of the formulas with philosophical opinions which seemed to condemn them as absurdities operated as a stimulus to the reexamination of the subject and thus the very doctrines originating in the oblivion into which a part of the truth had fallen were rendered indirectly but powerfully instrumental to its revival The doctrine of the Coleridge school that the language of any people among whom culture is of old date is a sacred deposit the property of all ages and which no one age should consider itself empowered to alter borders indeed as thus expressed on an extravagance but it is grounded on a truth frequently overlooked by that class of logicians who think more of having a clear than of having a comprehensive meaning and who perceive that every age is adding to the truths which it has received from its predecessors but fail to see that a counter process of losing truths already possessed is also constantly going on and requiring the most sedulous attention to counteract it Language is the depository of the accumulated body of experience to which all former ages have contributed their part and which is the inheritance of all yet to come We have no right to prevent ourselves from transmitting to posterity a larger portion of this inheritance than we may ourselves have profited by However much we may be able to improve on the conclusions of our forefathers we ought to be careful not inadvertently to let any of their premises slip through our fingers It may be good to alter the meaning of a word but it is bad to let any part of the meaning drop Whoever seeks to introduce a more correct use of a term with which important associations are connected should be required to possess an accurate acquaintance with the history of the particular word and of the opinions which in different stages of its progress it served to express To be qualified to define the name we must know all that has ever been known of the properties of the class of objects which are or originally were denoted by it For if we give it a meaning according to which any proposition will be false which has ever been generally held to be true it is incumbent on us to be sure that we know and have considered all which those who believed the proposition understood by it It is not only in the mode which has now been pointed out namely by gradual inattention to a portion of the ideas conveyed that words in common use are liable to shift their connotation The truth is that the connotation of such words is perpetually varying as might be expected from the manner in which words in common use acquire their connotation A technical term invented for purposes of art or science has from the first the connotation given to it by its inventor but a name which is in every one’s mouth before any one thinks of defining it derives its connotation only from the circumstances which are habitually brought to mind when it is pronounced Among these circumstances the properties common to the things denoted by the name have naturally a principal place and would have the sole place if language were regulated by convention rather than by custom and accident But besides these common properties which if they exist are certainly present whenever the name is employed any other circumstance may casually be found along with it so frequently as to become associated with it in the same manner and as strongly as the common properties themselves In proportion as this association forms itself people give up using the name in cases in which those casual circumstances do not exist They prefer using some other name or the same name with some adjunct rather than employ an expression which will call up an idea they do not want to excite The circumstance originally casual thus becomes regularly a part of the connotation of the word It is this continual incorporation of circumstances originally accidental into the permanent signification of words which is the cause that there are so few exact synonyms It is this also which renders the dictionary meaning of a word by universal remark so imperfect an exponent of its real meaning The dictionary meaning is marked out in a broad blunt way and probably includes all that was originally necessary for the correct employment of the term but in process of time so many collateral associations adhere to words that whoever should attempt to use them with no other guide than the dictionary would confound a thousand nice distinctions and subtle shades of meaning which dictionaries take no account of as we notice in the use of a language in conversation or writing by a foreigner not thoroughly master of it The history of a word by showing the causes which determine its use is in these cases a better guide to its employment than any definition for definitions can only show its meaning at the particular time or at most the series of its successive meanings but its history may show the law by which the succession was produced The word gentleman for instance to the correct employment of which a dictionary would be no guide originally meant simply a man born in a certain rank From this it came by degrees to connote all such qualities or adventitious circumstances as were usually found to belong to persons of that rank This consideration at once explains why in one of its vulgar acceptations it means any one who lives without labor in another without manual labor and in its more elevated signification it has in every age signified the conduct character habits and outward appearance in whomsoever found which according to the ideas of that age belonged or were expected to belong to persons born and educated in a high social position It continually happens that of two words whose dictionary meanings are either the same or very slightly different one will be the proper word to use in one set of circumstances another in another without its being possible to show how the custom of so employing them originally grew up The accident that one of the words was used and not the other on a particular occasion or in a particular social circle will be sufficient to produce so strong an association between the word and some specialty of circumstances that mankind abandon the use of it in any other case and the specialty becomes part of its signification The tide of custom first drifts the word on the shore of a particular meaning then retires and leaves it there An instance in point is the remarkable change which in the English language at least has taken place in the signification of the word loyalty That word originally meant in English as it still means in the language from whence it came fair open dealing and fidelity to engagements in that sense the quality it expressed was part of the ideal chivalrous or knightly character By what process in England the term became restricted to the single case of fidelity to the throne I am not sufficiently versed in the history of courtly language to be able to pronounce The interval between a loyal chevalier and a loyal subject is certainly great I can only suppose that the word was at some period the favourite term at court to express fidelity to the oath of allegiance until at length those who wished to speak of any other and as it was probably deemed inferior sort of fidelity either did not venture to use so dignified a term or found it convenient to employ some other in order to avoid being misunderstood Cases are not unfrequent in which a circumstance at first casually incorporated into the connotation of a word which originally had no reference to it in time wholly supersedes the original meaning and becomes not merely a part of the connotation but the whole of it This is exemplified in the word pagan paganus which originally as its etymology imports was equivalent to villager the inhabitant of a pagus or village At a particular era in the extension of Christianity over the Roman empire the adherents of the old religion and the villagers or country people were nearly the same body of individuals the inhabitants of the towns having been earliest converted as in our own day and at all times the greater activity of social intercourse renders them the earliest recipients of new opinions and modes while old habits and prejudices linger longest among the country people not to mention that the towns were more immediately under the direct influence of the Government which at that time had embraced Christianity From this casual coincidence the word paganus carried with it and began more and more steadily to suggest the idea of a worshiper of the ancient divinities until at length it suggested that idea so forcibly that people who did not desire to suggest the idea avoided using the word But when paganus had come to connote heathenism the very unimportant circumstance with reference to that fact of the place of residence was soon disregarded in the employment of the word As there was seldom any occasion for making separate assertions respecting heathens who lived in the country there was no need for a separate word to denote them and pagan came not only to mean heathen but to mean that exclusively A case still more familiar to most readers is that of the word villain or villein This term as every body knows had in the Middle Ages a connotation as strictly defined as a word could have being the proper legal designation for those persons who were the subjects of the less onerous forms of feudal bondage The scorn of the semibarbarous military aristocracy for these their abject dependants rendered the act of likening any person to this class of people a mark of the greatest contumely the same scorn led them to ascribe to the same people all manner of hateful qualities which doubtless also in the degrading situation in which they were held were often not unjustly imputed to them These circumstances combined to attach to the term villain ideas of crime and guilt in so forcible a manner that the application of the epithet even to those to whom it legally belonged became an affront and was abstained from whenever no affront was intended From that time guilt was part of the connotation and soon became the whole of it since mankind were not prompted by any urgent motive to continue making a distinction in their language between bad men of servile station and bad men of any other rank in life These and similar instances in which the original signification of a term is totally lost another and an entirely distinct meaning being first ingrafted upon the former and finally substituted for it afford examples of the double movement which is always taking place in language two countermovements one of Generalization by which words are perpetually losing portions of their connotation and becoming of less meaning and more general acceptation the other of Specialization by which other or even these same words are continually taking on fresh connotation acquiring additional meaning by being restricted in their employment to a part only of the occasions on which they might properly be used before This double movement is of sufficient importance in the natural history of language to which natural history the artificial modifications ought always to have some degree of reference to justify our dwelling a little longer on the nature of the twofold phenomenon and the causes to which it owes its existence To begin with the movement of generalization It might seem unnecessary to dwell on the changes in the meaning of names which take place merely from their being used ignorantly by persons who not having properly mastered the received connotation of a word apply it in a looser and wider sense than belongs to it This however is a real source of alterations in the language for when a word from being often employed in cases where one of the qualities which it connotes does not exist ceases to suggest that quality with certainty then even those who are under no mistake as to the proper meaning of the word prefer expressing that meaning in some other way and leave the original word to its fate The word ‘Squire as standing for an owner of a landed estate Parson as denoting not the rector of the parish but clergymen in general Artist to denote only a painter or sculptor are cases in point Such cases give a clear insight into the process of the degeneration of languages in periods of history when literary culture was suspended and we are now in danger of experiencing a similar evil through the superficial extension of the same culture So many persons without any thing deserving the name of education have become writers by profession that written language may almost be said to be principally wielded by persons ignorant of the proper use of the instrument and who are spoiling it more and more for those who understand it Vulgarisms which creep in nobody knows how are daily depriving the English language of valuable modes of expressing thought To take a present instance the verb transpire formerly conveyed very expressively its correct meaning viz to become known through unnoticed channels to exhale as it were into publicity through invisible pores like a vapor or gas disengaging itself But of late a practice has commenced of employing this word for the sake of finery as a mere synonym of to happen the events which have transpired in the Crimea meaning the incidents of the war This vile specimen of bad English is already seen in the dispatches of noblemen and viceroys and the time is apparently not far distant when nobody will understand the word if used in its proper sense In other cases it is not the love of finery but simple want of education which makes writers employ words in senses unknown to genuine English The use of aggravating for provoking in my boyhood a vulgarism of the nursery has crept into almost all newspapers and into many books and when the word is used in its proper sense as when writers on criminal law speak of aggravating and extenuating circumstances their meaning it is probable is already misunderstood It is a great error to think that these corruptions of language do no harm Those who are struggling with the difficulty and who know by experience how great it already is of expressing one’s self clearly with precision find their resources continually narrowed by illiterate writers who seize and twist from its purpose some form of speech which once served to convey briefly and compactly an unambiguous meaning It would hardly be believed how often a writer is compelled to a circumlocution by the single vulgarism introduced during the last few years of using the word alone as an adverb only not being fine enough for the rhetoric of ambitious ignorance A man will say to which I am not alone bound by honour but also by law unaware that what he has unintentionally said is that he is not alone bound some other person being bound with him Formerly if any one said I am not alone responsible for this he was understood to mean what alone his words mean in correct English that he is not the sole person responsible but if he now used such an expression the reader would be confused between that and two other meanings that he is not only responsible but something more or that he is responsible not only for this but for something besides The time is coming when Tennyson’s Înone could not say I will not die alone lest she should be supposed to mean that she would not only die but do something else The blunder of writing predicate for predict has become so widely diffused that it bids fair to render one of the most useful terms in the scientific vocabulary of Logic unintelligible The mathematical and logical term to eliminate is undergoing a similar destruction All who are acquainted either with the proper use of the word or with its etymology know that to eliminate a thing is to thrust it out but those who know nothing about it except that it is a finelooking phrase use it in a sense precisely the reverse to denote not turning any thing out but bringing it in They talk of eliminating some truth or other useful result from a mass of details A similar permanent deterioration in the language is in danger of being produced by the blunders of translators The writers of telegrams and the foreign correspondents of newspapers have gone on so long translating demander by to demand without a suspicion that it means only to ask that the context generally showing that nothing else is meant English readers are gradually associating the English word demand with simple asking thus leaving the language without a term to express a demand in its proper sense In like manner transaction the French word for a compromise is translated into the English word transaction while curiously enough the inverse change is taking place in France where the word compromis has lately begun to be used for expressing the same idea If this continues the two countries will have exchanged phrases Independently however of the generalization of names through their ignorant misuse there is a tendency in the same direction consistently with a perfect knowledge of their meaning arising from the fact that the number of things known to us and of which we feel a desire to speak multiply faster than the names for them Except on subjects for which there has been constructed a scientific terminology with which unscientific persons do not meddle great difficulty is generally found in bringing a new name into use and independently of that difficulty it is natural to prefer giving to a new object a name which at least expresses its resemblance to something already known since by predicating of it a name entirely new we at first convey no information In this manner the name of a species often becomes the name of a genus as salt for example or oil the former of which words originally denoted only the muriate of soda the latter as its etymology indicates only oliveoil but which now denote large and diversified classes of substances resembling these in some of their qualities and connote only those common qualities instead of the whole of the distinctive properties of oliveoil and seasalt The words glass and soap are used by modern chemists in a similar manner to denote genera of which the substances vulgarly so called are single species And it often happens as in those instances that the term keeps its special signification in addition to its more general one and becomes ambiguous that is two names instead of one These changes by which words in ordinary use become more and more generalized and less and less expressive take place in a still greater degree with the words which express the complicated phenomena of mind and society Historians travelers and in general those who speak or write concerning moral and social phenomena with which they are not familiarly acquainted are the great agents in this modification of language The vocabulary of all except unusually instructed as well as thinking persons is on such subjects eminently scanty They have a certain small set of words to which they are accustomed and which they employ to express phenomena the most heterogeneous because they have never sufficiently analysed the facts to which those words correspond in their own country to have attached perfectly definite ideas to the words The first English conquerors of Bengal for example carried with them the phrase landed proprietor into a country where the rights of individuals over the soil were extremely different in degree and even in nature from those recognized in England Applying the term with all its English associations in such a state of things to one who had only a limited right they gave an absolute right from another because he had not an absolute right they took away all right drove whole classes of people to ruin and despair filled the country with banditti created a feeling that nothing was secure and produced with the best intentions a disorganization of society which had not been produced in that country by the most ruthless of its barbarian invaders Yet the usage of persons capable of so gross a misapprehension determines the meaning of language and the words they thus misuse grow in generality until the instructed are obliged to acquiesce and to employ those words first freeing them from vagueness by giving them a definite connotation as generic terms subdividing the genera into species While the more rapid growth of ideas than of names thus creates a perpetual necessity for making the same names serve even if imperfectly on a greater number of occasions a counteroperation is going on by which names become on the contrary restricted to fewer occasions by taking on as it were additional connotation from circumstances not originally included in the meaning but which have become connected with it in the mind by some accidental cause We have seen above in the words pagan and villain remarkable examples of the specialization of the meaning of words from casual associations as well as of the generalization of it in a new direction which often follows Similar specializations are of frequent occurrence in the history even of scientific nomenclature It is by no means uncommon says Dr Paris in his Pharmacologia to find a word which is used to express general characters subsequently become the name of a specific substance in which such characters are predominant and we shall find that some important anomalies in nomenclature may be thus explained The term from which the word Arsenic is derived was an ancient epithet applied to those natural substances which possessed strong and acrimonious properties and as the poisonous quality of arsenic was found to be remarkably powerful the term was especially applied to Orpiment the form in which this metal most usually occurred So the term Verbena quasi Herbena originally denoted all those herbs that were held sacred on account of their being employed in the rites of sacrifice as we learn from the poets but as one herb was usually adopted upon these occasions the word Verbena came to denote that particular herb only and it is transmitted to us to this day under the same title viz Verbena or Vervain and indeed until lately it enjoyed the medical reputation which its sacred origin conferred upon it for it was worn suspended around the neck as an amulet Vitriol in the original application of the word denoted any crystalline body with a certain degree of transparency vitrum it is hardly necessary to observe that the term is now appropriated to a particular species in the same manner Bark which is a general term is applied to express one genus and by way of eminence it has the article The prefixed as The bark the same observation will apply to the word Opium which in its primitive sense signifies any juice ¹ Succus while it now only denotes one species viz that of the poppy So again Elaterium was used by Hippocrates to signify various internal applications especially purgatives of a violent and drastic nature from the word agito moveo stimulo but by succeeding authors it was exclusively applied to denote the active matter which subsides from the juice of the wild cucumber The word Fecula again originally meant to imply any substance which was derived by spontaneous subsidence from a liquid from faex the grounds or settlement of any liquor afterward it was applied to Starch which is deposited in this manner by agitating the flour of wheat in water and lastly it has been applied to a peculiar vegetable principle which like starch is insoluble in cold but completely soluble in boiling water with which it forms a gelatinous solution This indefinite meaning of the word fecula has created numerous mistakes in pharmaceutic chemistry Elaterium for instance is said to be fecula and in the original sense of the word it is properly so called inasmuch as it is procured from a vegetable juice by spontaneous subsidence but in the limited and modern acceptation of the term it conveys an erroneous idea for instead of the active principle of the juice residing in fecula it is a peculiar proximate principle sui generis to which I have ventured to bestow the name of Elatin For the same reason much doubt and obscurity involve the meaning of the word Extract because it is applied generally to any substance obtained by the evaporation of a vegetable solution and specifically to a peculiar proximate principle possessed of certain characters by which it is distinguished from every other elementary body A generic term is always liable to become thus limited to a single species or even individual if people have occasion to think and speak of that individual or species much oftener than of any thing else which is contained in the genus Thus by cattle a stagecoachman will understand horses beasts in the language of agriculturists stands for oxen and birds with some sportsmen for partridges only The law of language which operates in these trivial instances is the very same in conformity to which the terms Deus and God were adopted from Polytheism by Christianity to express the single object of its own adoration Almost all the terminology of the Christian Church is made up of words originally used in a much more general acceptation Ecclesia Assembly Bishop Episcopus Overseer Priest Presbyter Elder Deacon Diaconus Administrator Sacrament a vow of allegiance Evangelium good tidings and some words as Minister are still used both in the general and in the limited sense It would be interesting to trace the progress by which author came in its most familiar sense to signify a writer and ¹ or maker a poet Of the incorporation into the meaning of a term of circumstances accidentally connected with it at some particular period as in the case of Pagan instances might easily be multiplied Physician or naturalist became in England synonymous with a healer of diseases because until a comparatively late period medical practitioners were the only naturalists Clerc or clericus a scholar came to signify an ecclesiastic because the clergy were for many centuries the only scholars Of all ideas however the most liable to cling by association to any thing with which they have ever been connected by proximity are those of our pleasures and pains or of the things which we habitually contemplate as sources of our pleasures or pains The additional connotation therefore which a word soonest and most readily takes on is that of agreeableness or painfulness in their various kinds and degrees of being a good or bad thing desirable or to be avoided an object of hatred of dread contempt admiration hope or love Accordingly there is hardly a single name expressive of any moral or social fact calculated to call forth strong affections either of a favourable or of a hostile nature which does not carry with it decidedly and irresistibly a connotation of those strong affections or at the least of approbation or censure insomuch that to employ those names in conjunction with others by which the contrary sentiments were expressed would produce the effect of a paradox or even a contradiction in terms The baneful influence of a connotation thus acquired on the prevailing habits of thought especially in morals and politics has been well pointed out on many occasions by Bentham It gives rise to the fallacy of questionbegging names The very property which we are inquiring whether a thing possesses or not has become so associated with the name of the thing as to be part of its meaning insomuch that by merely uttering the name we assume the point which was to be made out one of the most frequent sources of apparently selfevident propositions Without any further multiplication of examples to illustrate the changes which usage is continually making in the signification of terms I shall add as a practical rule that the logician not being able to prevent such transformations should submit to them with a good grace when they are irrevocably effected and if a definition is necessary define the word according to its new meaning retaining the former as a second signification if it is needed and if there is any chance of being able to preserve it either in the language of philosophy or in common use Logicians can not make the meaning of any but scientific terms that of all other words is made by the collective human race But logicians can ascertain clearly what it is which working obscurely has guided the general mind to a particular employment of a name and when they have found this they can clothe it in such distinct and permanent terms that mankind shall see the meaning which before they only felt and shall not suffer it to be afterward forgotten or misapprehended We have thus far considered only one of the requisites of a language adapted for the investigation of truth that its terms shall each of them convey a determinate and unmistakable meaning There are however as we have already remarked other requisites some of them important only in the second degree but one which is fundamental and barely yields in point of importance if it yields at all to the quality which we have already discussed at so much length That the language may be fitted for its purposes not only should every word perfectly express its meaning but there should be no important meaning without its word Whatever we have occasion to think of often and for scientific purposes ought to have a name appropriated to it This requisite of philosophical language may be considered under three different heads that number of separate conditions being involved in it First there ought to be all such names as are needful for making such a record of individual observations that the words of the record shall exactly show what fact it is which has been observed In other words there should be an accurate Descriptive Terminology The only things which we can observe directly being our own sensations or other feelings a complete descriptive language would be one in which there should be a name for every variety of elementary sensation or feeling Combinations of sensations or feelings may always be described if we have a name for each of the elementary feelings which compose them but brevity of description and clearness which often depends very much on brevity are greatly promoted by giving distinctive names not to the elements alone but also to all combinations which are of frequent recurrence On this occasion I can not do better than quote from Dr Whewell some of the excellent remarks which he has made on this important branch of our subject The meaning of descriptive technical terms can be fixed in the first instance only by convention and can be made intelligible only by presenting to the senses that which the terms are to signify The knowledge of a colour by its name can only be taught through the eye No description can convey to a hearer what we mean by applegreen or French gray It might perhaps be supposed that in the first example the term apple referring to so familiar an object sufficiently suggests the colour intended But it may easily be seen that this is not true for apples are of many different hues of green and it is only by a conventional selection that we can appropriate the term to one special shade When this appropriation is once made the term refers to the sensation and not to the parts of the term for these enter into the compound merely as a help to the memory whether the suggestion be a natural connection as in applegreen’ or a casual one as in French gray’ In order to derive due advantage from technical terms of the kind they must be associated immediately with the perception to which they belong and not connected with it through the vague usages of common language The memory must retain the sensation and the technical word must be understood as directly as the most familiar word and more distinctly When we find such terms as tinwhite or pinchbeckbrown the metallic colour so denoted ought to start up in our memory without delay or search This which it is most important to recollect with respect to the simpler properties of bodies as colour and form is no less true with respect to more compound notions In all cases the term is fixed to a peculiar meaning by convention and the student in order to use the word must be completely familiar with the convention so that he has no need to frame conjectures from the word itself Such conjectures would always be insecure and often erroneous Thus the term papilionaceous applied to a flower is employed to indicate not only a resemblance to a butterfly but a resemblance arising from five petals of a certainpeculiar shape and arrangement and even if the resemblance were much stronger than it is in such cases yet if it were produced in a different way as for example by one petal or two only instead of a standard’ two wings’ and a keel’ consisting of two parts more or less united into one we should be no longer justified in speaking of it as a papilionaceous’ flower When however the thing named is as in this last case a combination of simple sensations it is not necessary in order to learn the meaning of the word that the student should refer back to the sensations themselves it may be communicated to him through the medium of other words the terms in short may be defined But the names of elementary sensations or elementary feelings of any sort can not be defined nor is there any mode of making their signification known but by making the learner experience the sensation or referring him through some known mark to his remembrance of having experienced it before Hence it is only the impressions on the outward senses or those inward feelings which are connected in a very obvious and uniform manner with outward objects that are really susceptible of an exact descriptive language The countless variety of sensations which arise for instance from disease or from peculiar physiological states it would be in vain to attempt to name for as no one can judge whether the sensation I have is the same with his the name can not have to us two real community of meaning The same may be said to a considerable extent of purely mental feelings But in some of the sciences which are conversant with external objects it is scarcely possible to surpass the perfection to which this quality of a philosophical language has been carried The formation of an exact and extensive descriptive language for botany has been executed with a degree of skill and felicity which before it was attained could hardly have been dreamed of as attainable Every part of a plant has been named and the form of every part even the most minute has had a large assemblage of descriptive terms appropriated to it by means of which the botanist can convey and receive knowledge of form and structure as exactly as if each minute part were presented to him vastly magnified This acquisition was part of the Linnaean reform Tournefort’ says Decandolle appears to have been the first who really perceived the utility of fixing the sense of terms in such a way as always to employ the same word in the same sense and always to express the same idea by the same words but it was Linnaeus who really created and fixed this botanical language and this is his fairest claim to glory for by this fixation of language he has shed clearness and precision over all parts of the science’ It is not necessary here to give any detailed account of the terms of botany The fundamental ones have been gradually introduced as the parts of plants were more carefully and minutely examined Thus the flower was necessarily distinguished into the calyx the corolla the stamens and the pistils the sections of the corolla were termed petals by Columna those of the calyx were called sepals by Necker Sometimes terms of greater generality were devised as perianth to include the calyx and corolla whether one or both of these were present pericarp for the part inclosing the grain of whatever kind it be fruit nut pod etc And it may easily be imagined that descriptive terms may by definition and combination become very numerous and distinct Thus leaves may be called pinnatifid pinnatipartite pinnatisect pinnatilobate palmatifid palmatipartite etc and each of these words designates different combinations of the modes and extent of the divisions of the leaf with the divisions of its outline In some cases arbitrary numerical relations are introduced into the definition thus a leaf is called bilobate when it is divided into two parts by a notch but if the notch go to the middle of its length it is bifid if it go near the base of the leaf it is bipartite if to the base it is bisect Thus too a pod of a cruciferous plant is a siliqua if it is four times as long as it is broad but if it be shorter than this it is a silicula Such terms being established the form of the very complex leaf or frond of a fern Hymenophyllum Wilsoni is exactly conveyed by the following phrase fronds rigid pinnate pinnae recurved subunilateral pinnatifid the segments linear undivided or bifid spinulososerrate’ Other characters as well as form are conveyed with the like precision Color by means of a classified scale of colours This was done with most precision by Werner and his scale of colours is still the most usual standard of naturalists Werner also introduced a more exact terminology with regard to other characters which are important in mineralogy as lustre hardness But Mohs improved upon this step by giving a numerical scale of hardness in which talc is 1 gypsum 2 calc spar 3 and so on Some properties as specific gravity by their definition give at once a numerical measure and others as crystalline form require a very considerable array of mathematical calculation and reasoning to point out their relations and gradations Thus far of Descriptive Terminology or of the language requisite for placing on record our observation of individual instances But when we proceed from this to Induction or rather to that comparison of observed instances which is the preparatory step toward it we stand in need of an additional and a different sort of general names Whenever for purposes of Induction we find it necessary to introduce in Dr Whewell’s phraseology some new general conception that is whenever the comparison of a set of phenomena leads to the recognition in them of some common circumstance which our attention not having been directed to it on any former occasion is to us a new phenomenon it is of importance that this new conception or this new result of abstraction should have a name appropriated to it especially if the circumstance it involves be one which leads to many consequences or which is likely to be found also in other classes of phenomena No doubt in most cases of the kind the meaning might be conveyed by joining together several words already in use But when a thing has to be often spoken of there are more reasons than the saving of time and space for speaking of it in the most concise manner possible What darkness would be spread over geometrical demonstrations if wherever the word circle is used the definition of a circle were inserted instead of it In mathematics and its applications where the nature of the processes demands that the attention should be strongly concentrated but does not require that it should be widely diffused the importance of concentration also in the expressions has always been duly felt and a mathematician no sooner finds that he shall often have occasion to speak of the same two things together than he at once creates a term to express them whenever combined just as in his algebraical operations he substitutes for am bn pq or for ab bc cd etc the single letter P Q or S not solely to shorten his symbolical expressions but to simplify the purely intellectual part of his operations by enabling the mind to give its exclusive attention to the relation between the quantity S and the other quantities which enter into the equation without being distracted by thinking unnecessarily of the parts of which S is itself composed But there is another reason in addition to that of promoting perspicuity for giving a brief and compact name to each of the more considerable results of abstraction which are obtained in the course of our intellectual phenomena By naming them we fix our attention upon them we keep them more constantly before the mind The names are remembered and being remembered suggest their definition while if instead of specific and characteristic names the meaning had been expressed by putting together a number of other names that particular combination of words already in common use for other purposes would have had nothing to make itself remembered by If we want to render a particular combination of ideas permanent in the mind there is nothing which clinches it like a name specially devoted to express it If mathematicians had been obliged to speak of that to which a quantity in increasing or diminishing is always approaching nearer so that the difference becomes less than any assignable quantity but to which it never becomes exactly equal instead of expressing all this by the simple phrase the limit of a quantity we should probably have long remained without most of the important truths which have been discovered by means of the relation between quantities of various kinds and their limits If instead of speaking of momentum it had been necessary to say the product of the number of units of velocity in the velocity by the number of units of mass in the mass many of the dynamical truths now apprehended by means of this complex idea would probably have escaped notice for want of recalling the idea itself with sufficient readiness and familiarity And on subjects less remote from the topics of popular discussion whoever wishes to draw attention to some new or unfamiliar distinction among things will find no way so sure as to invent or select suitable names for the express purpose of marking it A volume devoted to explaining what the writer means by civilization does not raise so vivid a conception of it as the single expression that Civilization is a different thing from Cultivation the compactness of that brief designation for the contrasted quality being an equivalent for a long discussion So if we would impress forcibly upon the understanding and memory the distinction between the two different conceptions of a representative government we can not more effectually do so than by saying that Delegation is not Representation Hardly any original thoughts on mental or social subjects ever make their way among mankind or assume their proper importance in the minds even of their inventors until aptlyselected words or phrases have as it were nailed them down and held them fast Of the three essential parts of a philosophical language we have now mentioned two a terminology suited for describing with precision the individual facts observed and a name for every common property of any importance or interest which we detect by comparing those facts including as the concretes corresponding to those abstract terms names for the classes which we artificially construct in virtue of those properties or as many of them at least as we have frequent occasion to predicate any thing of But there is a sort of classes for the recognition of which no such elaborate process is necessary because each of them is marked out from all others not by some one property the detection of which may depend on a difficult act of abstraction but by its properties generally I mean the Kinds of things in the sense which in this treatise has been specially attached to that term By a Kind it will be remembered we mean one of those classes which are distinguished from all others not by one or a few definite properties but by an unknown multitude of them the combination of properties on which the class is grounded being a mere index to an indefinite number of other distinctive attributes The class horse is a Kind because the things which agree in possessing the characters by which we recognize a horse agree in a great number of other properties as we know and it can not be doubted in many more than we know Animal again is a Kind because no definition that could be given of the name animal could either exhaust the properties common to all animals or supply premises from which the remainder of those properties could be inferred But a combination of properties which does not give evidence of the existence of any other independent peculiarities does not constitute a Kind White horse therefore is not a Kind because horses which agree in whiteness do not agree in any thing else except the qualities common to all horses and whatever may be the causes or effects of that particular colour On the principle that there should be a name for every thing which we have frequent occasion to make assertions about there ought evidently to be a name for every Kind for as it is the very meaning of a Kind that the individuals composing it have an indefinite multitude of properties in common it follows that if not with our present knowledge yet with that which we may hereafter acquire the Kind is a subject to which there will have to be applied many predicates The third component element of a philosophical language therefore is that there shall be a name for every Kind In other words there must not only be a terminology but also a nomenclature The words Nomenclature and Terminology are employed by most authors almost indiscriminately Dr Whewell being as far as I am aware the first writer who has regularly assigned to the two words different meanings The distinction however which he has drawn between them being real and important his example is likely to be followed and as is apt to be the case when such innovations in language are felicitously made a vague sense of the distinction is found to have influenced the employment of the terms in common practice before the expediency had been pointed out of discriminating them philosophically Every one would say that the reform effected by Lavoisier and GuytonMorveau in the language of chemistry consisted in the introduction of a new nomenclature not of a new terminology Linear lanceolate oval or oblong serrated dentate or crenate leaves are expressions forming part of the terminology of botany while the names Viola odorata and Ulex Europaeus belong to its nomenclature A nomenclature may be defined the collection of the names of all the Kinds with which any branch of knowledge is conversant or more properly of all the lowest Kinds or infirmae species those which may be subdivided indeed but not into Kinds and which generally accord with what in natural history are termed simply species Science possesses two splendid examples of a systematic nomenclature that of plants and animals constructed by Linnaeus and his successors and that of chemistry which we owe to the illustrious group of chemists who flourished in France toward the close of the eighteenth century In these two departments not only has every known species or lowest Kind a name assigned to it but when new lowest Kinds are discovered names are at once given to them on a uniform principle In other sciences the nomenclature is not at present constructed on any system either because the species to be named are not numerous enough to require one as in geometry for example or because no one has yet suggested a suitable principle for such a system as in mineralogy in which the want of a scientifically constructed nomenclature is now the principal cause which retards the progress of the science A word which carries on its face that it belongs to a nomenclature seems at first sight to differ from other concrete general names in this that its meaning does not reside in its connotation in the attributes implied in it but in its denotation that is in the particular group of things which it is appointed to designate and can not therefore be unfolded by means of a definition but must be made known in another way This opinion however appears to me erroneous Words belonging to a nomenclature differ I conceive from other words mainly in this that besides the ordinary connotation they have a peculiar one of their own besides connoting certain attributes they also connote that those attributes are distinctive of a Kind The term peroxide of iron for example belonging by its form to the systematic nomenclature of chemistry bears on its face that it is the name of a peculiar Kind of substance It moreover connotes like the name of any other class some portion of the properties common to the class in this instance the property of being a compound of iron and the largest dose of oxygen with which iron will combine These two things the fact of being such a compound and the fact of being a Kind constitute the connotation of the name peroxide of iron When we say of the substance before us that it is the peroxide of iron we thereby assert first that it is a compound of iron and a maximum of oxygen and next that the substance so composed is a peculiar Kind of substance Now this second part of the connotation of any word belonging to a nomenclature is as essential a portion of its meaning as the first part while the definition only declares the first and hence the appearance that the signification of such terms can not be conveyed by a definition which appearance however is fallacious The name Viola odorata denotes a Kind of which a certain number of characters sufficient to distinguish it are enunciated in botanical works This enumeration of characters is surely as in other cases a definition of the name No say some it is not a definition for the name Viola odorata does not mean those characters it means that particular group of plants and the characters are selected from among a much greater number merely as marks by which to recognize the group But to this I reply that the name does not mean that group for it would be applied to that group no longer than while the group is believed to be an infima species if it were to be discovered that several distinct Kinds have been confounded under this one name no one would any longer apply the name Viola odorata to the whole of the group but would apply it if retained at all to one only of the Kinds retained therein What is imperative therefore is not that the name shall denote one particular collection of objects but that it shall denote a Kind and a lowest Kind The form of the name declares that happen what will it is to denote an infima species and that therefore the properties which it connotes and which are expressed in the definition are to be connoted by it no longer than while we continue to believe that those properties when found together indicate a Kind and that the whole of them are found in no more than one Kind With the addition of this peculiar connotation implied in the form of every word which belongs to a systematic nomenclature the set of characters which is employed to discriminate each Kind from all other Kinds and which is a real definition constitutes as completely as in any other case the whole meaning of the term It is no objection to say that as is often the case in natural history the set of characters may be changed and another substituted as being better suited for the purpose of distinction while the word still continuing to denote the same group or things is not considered to have changed its meaning For this is no more than may happen in the case of any other general name we may in reforming its connotation leave its denotation untouched and it is generally desirable to do so The connotation however is not the less for this the real meaning for we at once apply the name wherever the characters set down in the definition are found and that which exclusively guides us in applying the term must constitute its signification If we find contrary to our previous belief that the characters are not peculiar to one species we cease to use the term coextensively with the characters but then it is because the other portion of the connotation fails the condition that the class must be a Kind The connotation therefore is still the meaning the set of descriptive characters is a true definition and the meaning is unfolded not indeed as in other cases by the definition alone but by the definition and the form of the word taken together We have now analysed what is implied in the two principal requisites of a philosophical language first precision or definiteness and secondly completeness Any further remarks on the mode of constructing a nomenclature must be deferred until we treat of Classification the mode of naming the Kinds of things being necessarily subordinate to the mode of arranging those Kinds into larger classes With respect to the minor requisites of terminology some of them are well stated and illustrated in the Aphorisms concerning the Language of Science included in Dr Whewell’s Philosophy of the Inductive Sciences These as being of secondary importance in the peculiar point of view of Logic I shall not further refer to but shall confine my observations to one more quality which next to the two already treated of appears to be the most valuable which the language of science can possess Of this quality a general notion may be conveyed by the following aphorism Whenever the nature of the subject permits our reasoning processes to be without danger carried on mechanically the language should be constructed on as mechanical principles as possible while in the contrary case it should be so constructed that there shall be the greatest possible obstacles to a merely mechanical use of it I am aware that this maxim requires much explanation which I shall at once proceed to give At first as to what is meant by using a language mechanically The complete or extreme case of the mechanical use of language is when it is used without any consciousness of a meaning and with only the consciousness of using certain visible or audible marks in conformity to technical rules previously laid down This extreme case is nowhere realized except in the figures of arithmetic and still more the symbols of algebra a language unique in its kind and approaching as nearly to perfection for the purposes to which it is destined as can perhaps be said of any creation of the human mind Its perfection consists in the completeness of its adaptation to a purely mechanical use The symbols are mere counters without even the semblance of a meaning apart from the convention which is renewed each time they are employed and which is altered at each renewal the same symbol a or x being used on different occasions to represent things which except that like all things they are susceptible of being numbered have no property in common There is nothing therefore to distract the mind from the set of mechanical operations which are to be performed upon the symbols such as squaring both sides of the equation multiplying or dividing them by the same or by equivalent symbols and so forth Each of these operations it is true corresponds to a syllogism represents one step of a ratiocination relating not to the symbols but to the things signified by them But as it has been found practicable to frame a technical form by conforming to which we can make sure of finding the conclusion of the ratiocination our end can be completely attained without our ever thinking of any thing but the symbols Being thus intended to work merely as mechanism they have the qualities which mechanism ought to have They are of the least possible bulk so that they take up scarcely any room and waste no time in their manipulation they are compact and fit so closely together that the eye can take in the whole at once of almost every operation which they are employed to perform These admirable properties of the symbolical language of mathematics have made so strong an impression on the minds of many thinkers as to have led them to consider the symbolical language in question as the ideal type of philosophical language generally to think that names in general or as they are fond of calling them signs are fitted for the purposes of thought in proportion as they can be made to approximate to the compactness the entire unmeaningness and the capability of being used as counters without a thought of what they represent which are characteristic of the a and b the x and y of algebra This notion has led to sanguine views of the acceleration of the progress of science by means which I conceive can not possibly conduce to that end and forms part of that exaggerated estimate of the influence of signs which has contributed in no small degree to prevent the real laws of our intellectual operations from being rightly understood In the first place a set of signs by which we reason without consciousness of their meaning can be serviceable at most only in our deductive operations In our direct inductions we can not for a moment dispense with a distinct mental image of the phenomena since the whole operation turns on a perception of the particulars in which those phenomena agree and differ But further this reasoning by counters is only suitable to a very limited portion even of our deductive processes In our reasonings respecting numbers the only general principles which we ever have occasion to introduce are these Things which are equal to the same thing are equal to one another and The sums or differences of equal things are equal with their various corollaries Not only can no hesitation ever arise respecting the applicability of these principles since they are true of all magnitudes whatever but every possible application of which they are susceptible may be reduced to a technical rule and such in fact the rules of the calculus are But if the symbols represent any other things than mere numbers let us say even straight or curve lines we have then to apply theorems of geometry not true of all lines without exception and to select those which are true of the lines we are reasoning about And how can we do this unless we keep completely in mind what particular lines these are Since additional geometrical truths may be introduced into the ratiocination in any stage of its progress we can not suffer ourselves during even the smallest part of it to use the names mechanically as we use algebraical symbols without an image annexed to them It is only after ascertaining that the solution of a question concerning lines can be made to depend on a previous question concerning numbers or, in other words, after the question has been to speak technically reduced to an equation that the unmeaning signs become available and that the nature of the facts themselves to which the investigation relates can be dismissed from the mind Up to the establishment of the equation the language in which mathematicians carry on their reasoning does not differ in character from that employed by close reasoners on any other kind of subject I do not deny that every correct ratiocination when thrown into the syllogistic shape is conclusive from the mere form of the expression provided none of the terms used be ambiguous and this is one of the circumstances which have led some writers to think that if all names were so judiciously constructed and so carefully defined as not to admit of any ambiguity the improvement thus made in language would not only give to the conclusions of every deductive science the same certainty with those of mathematics but would reduce all reasonings to the application of a technical form and enable their conclusiveness to be rationally assented to after a merely mechanical process as is undoubtedly the case in algebra But if we except geometry the conclusions of which are already as certain and exact as they can be made there is no science but that of number in which the practical validity of a reasoning can be apparent to any person who has looked only at the reasoning itself Whoever has assented to what was said in the last Book concerning the case of the Composition of Causes and the still stronger case of the entire supersession of one set of laws by another is aware that geometry and algebra are the only sciences of which the propositions are categorically true the general propositions of all other sciences are true only hypothetically supposing that no counteracting cause happens to interfere A conclusion therefore however correctly deduced in point of form from admitted laws of nature will have no other than an hypothetical certainty At every step we must assure ourselves that no other law of nature has superseded or intermingled its operation with those which are the premises of the reasoning and how can this be done by merely looking at the words We must not only be constantly thinking of the phenomena themselves but we must be constantly studying them making ourselves acquainted with the peculiarities of every case to which we attempt to apply our general principles The algebraic notation considered as a philosophical language is perfect in its adaptation to the subjects for which it is commonly employed namely those of which the investigations have already been reduced to the ascertainment of a relation between numbers But admirable as it is for its own purpose the properties by which it is rendered such are so far from constituting it the ideal model of philosophical language in general that the more nearly the language of any other branch of science approaches to it the less fit that language is for its own proper functions On all other subjects instead of contrivances to prevent our attention from being distracted by thinking of the meaning of our signs we ought to wish for contrivances to make it impossible that we should ever lose sight of that meaning even for an instant With this view as much meaning as possible should be thrown into the formation of the word itself the aids of derivation and analogy being made available to keep alive a consciousness of all that is signified by it In this respect those languages have an immense advantage which form their compounds and derivatives from native roots like the German and not from those of a foreign or dead language as is so much the case with English French and Italian and the best are those which form them according to fixed analogies corresponding to the relations between the ideas to be expressed All languages do this more or less but especially among modern European languages the German while even that is inferior to the Greek in which the relation between the meaning of a derivative word and that of its primitive is in general clearly marked by its mode of formation except in the case of words compounded with prepositions which are often in both those languages extremely anomalous But all that can be done by the mode of constructing words to prevent them from degenerating into sounds passing through the mind without any distinct apprehension of what they signify is far too little for the necessity of the case Words however well constructed originally are always tending like coins to have their inscription worn off by passing from hand to hand and the only possible mode of reviving it is to be ever stamping it afresh by living in the habitual contemplation of the phenomena themselves and not resting in our familiarity with the words that express them If any one having possessed himself of the laws of phenomena as recorded in words whether delivered to him originally by others or even found out by himself is content from thenceforth to live among these formulae to think exclusively of them and of applying them to cases as they arise without keeping up his acquaintance with the realities from which these laws were collected not only will he continually fail in his practical efforts because he will apply his formulae without duly considering whether in this case and in that other laws of nature do not modify or supersede them but the formulae themselves will progressively lose their meaning to him and he will cease at last even to be capable of recognizing with certainty whether a case falls within the contemplation of his formula or not It is in short as necessary on all subjects not mathematical that the things on which we reason should be conceived by us in the concrete and clothed in circumstances as it is in algebra that we should keep all individualizing peculiarities sedulously out of view With this remark we close our observations on the Philosophy of Language There is as has been frequently remarked in this work a classification of things which is inseparable from the fact of giving them general names Every name which connotes an attribute divides by that very fact all things whatever into two classes those which have the attribute and those which have it not those of which the name can be predicated and those of which it can not And the division thus made is not merely a division of such things as actually exist or are known to exist but of all such as may hereafter be discovered and even of all which can be imagined On this kind of Classification we have nothing to add to what has previously been said The Classification which requires to be discussed as a separate act of the mind is altogether different In the one the arrangement of objects in groups and distribution of them into compartments is a mere incidental effect consequent on the use of names given for another purpose namely that of simply expressing some of their qualities In the other the arrangement and distribution are the main object and the naming is secondary to and purposely conforms itself to instead of governing that more important operation Classification thus regarded is a contrivance for the best possible ordering of the ideas of objects in our minds for causing the ideas to accompany or succeed one another in such a way as shall give us the greatest command over our knowledge already acquired and lead most directly to the acquisition of more The general problem of Classification in reference to these purposes may be stated as follows To provide that things shall be thought of in such groups and those groups in such an order as will best conduce to the remembrance and to the ascertainment of their laws Classification thus considered differs from classification in the wider sense in having reference to real objects exclusively and not to all that are imaginable its object being the due coordination in our minds of those things only with the properties of which we have actually occasion to make ourselves acquainted But on the other hand it embraces all really existing objects We can not constitute any one class properly except in reference to a general division of the whole of nature we can not determine the group in which any one object can most conveniently be placed without taking into consideration all the varieties of existing objects all at least which have any degree of affinity with it No one family of plants or animals could have been rationally constituted except as part of a systematic arrangement of all plants or animals nor could such a general arrangement have been properly made without first determining the exact place of plants and animals in a general division of nature There is no property of objects which may not be taken if we please as the foundation for a classification or mental grouping of those objects and in our first attempts we are likely to select for that purpose properties which are simple easily conceived and perceptible on a first view without any previous process of thought Thus Tournefort’s arrangement of plants was founded on the shape and divisions of the corolla and that which is commonly called the Linnaean though Linnaeus also suggested another and more scientific arrangement was grounded chiefly on the number of the stamens and pistils But these classifications which are at first recommended by the facility they afford of ascertaining to what class any individual belongs are seldom much adapted to the ends of that Classification which is the subject of our present remarks The Linnaean arrangement answers the purpose of making us think together of all those kinds of plants which possess the same number of stamens and pistils but to think of them in that manner is of little use since we seldom have any thing to affirm in common of the plants which have a given number of stamens and pistils If plants of the class Pentandria order Monogynia agreed in any other properties the habit of thinking and speaking of the plants under a common designation would conduce to our remembering those common properties so far as they were ascertained and would dispose us to be on the lookout for such of them as were not yet known But since this is not the case the only purpose of thought which the Linnaean classification serves is that of causing us to remember better than we should otherwise have done the exact number of stamens and pistils of every species of plants Now as this property is of little importance or interest the remembering it with any particular accuracy is of no moment And inasmuch as by habitually thinking of plants in those groups we are prevented from habitually thinking of them in groups which have a greater number of properties in common the effect of such a classification when systematically adhered to upon our habits of thought must be regarded as mischievous The ends of scientific classification are best answered when the objects are formed into groups respecting which a greater number of general propositions can be made and those propositions more important than could be made respecting any other groups into which the same things could be distributed The properties therefore according to which objects are classified should if possible be those which are causes of many other properties or at any rate which are sure marks of them Causes are preferable both as being the surest and most direct of marks and as being themselves the properties on which it is of most use that our attention should be strongly fixed But the property which is the cause of the chief peculiarities of a class is unfortunately seldom fitted to serve also as the diagnostic of the class Instead of the cause we must generally select some of its more prominent effects which may serve as marks of the other effects and of the cause A classification thus formed is properly scientific or philosophical and is commonly called a Natural in contradistinction to a Technical or Artificial classification or arrangement The phrase Natural Classification seems most peculiarly appropriate to such arrangements as correspond in the groups which they form to the spontaneous tendencies of the mind by placing together the objects most similar in their general aspect in opposition to those technical systems which arranging things according to their agreement in some circumstance arbitrarily selected often throw into the same group objects which in the general aggregate of their properties present no resemblance and into different and remote groups others which have the closest similarity It is one of the most valid recommendations of any classification to the character of a scientific one that it shall be a natural classification in this sense also for the test of its scientific character is the number and importance of the properties which can be asserted in common of all objects included in a group and properties on which the general aspect of the things depends are if only on that ground important as well as in most cases numerous But though a strong recommendation this circumstance is not a sine qua non since the most obvious properties of things may be of trifling importance compared with others that are not obvious I have seen it mentioned as a great absurdity in the Linnaean classification that it places which bytheway it does not the violet by the side of the oak it certainly dissevers natural affinities and brings together things quite as unlike as the oak and the violet are But the difference apparently so wide which renders the juxtaposition of those two vegetables so suitable an illustration of a bad arrangement depends to the common eye mainly on mere size and texture now if we made it our study to adopt the classification which would involve the least peril of similar rapprochements we should return to the obsolete division into trees shrubs and herbs which though of primary importance with regard to mere general aspect yet compared even with so petty and unobvious a distinction as that into dicotyledons and monocotyledons answers to so few differences in the other properties of plants that a classification founded on it independently of the indistinctness of the lines of demarcation would be as completely artificial and technical as the Linnaean Our natural groups therefore must often be founded not on the obvious but on the unobvious properties of things when these are of greater importance But in such cases it is essential that there should be some other property or set of properties more readily recognizable by the observer which coexist with and may be received as marks of the properties which are the real groundwork of the classification A natural arrangement for example of animals must be founded in the main on their internal structure but as M Comte remarks it would be absurd that we should not be able to determine the genus and species of an animal without first killing it On this ground the preference among zoological classifications is probably due to that of M De Blainville founded on the differences in the external integuments differences which correspond much more accurately than might be supposed to the really important varieties both in the other parts of the structure and in the habits and history of the animals This shows more strongly than ever how extensive a knowledge of the properties of objects is necessary for making a good classification of them And as it is one of the uses of such a classification that by drawing attention to the properties on which it is founded and which if the classification be good are marks of many others it facilitates the discovery of those others we see in what manner our knowledge of things and our classification of them tend mutually and indefinitely to the improvement of each other We said just now that the classification of objects should follow those of their properties which indicate not only the most numerous but also the most important peculiarities What is here meant by importance It has reference to the particular end in view and the same objects therefore may admit with propriety of several different classifications Each science or art forms its classification of things according to the properties which fall within its special cognizance or of which it must take account in order to accomplish its peculiar practical end A farmer does not divide plants like a botanist into dicotyledonous and monocotyledonous but into useful plants and weeds A geologist divides fossils not like a zoologist into families corresponding to those of living species but into fossils of the paleozoic mesozoic and tertiary periods above the coal and below the coal etc Whales are or are not fish according to the purpose for which we are considering them If we are speaking of the internal structure and physiology of the animal we must not call them fish for in these respects they deviate widely from fishes they have warm blood and produce and suckle their young as land quadrupeds do But this would not prevent our speaking of the whalefishery and calling such animals fish on all occasions connected with this employment for the relations thus arising depend upon the animal’s living in the water and being caught in a manner similar to other fishes A plea that human laws which mention fish do not apply to whales would be rejected at once by an intelligent judge These different classifications are all good for the purposes of their own particular departments of knowledge or practice But when we are studying objects not for any special practical end but for the sake of extending our knowledge of the whole of their properties and relations we must consider as the most important attributes those which contribute most either by themselves or by their effects to render the things like one another and unlike other things which give to the class composed of them the most marked individuality which fill as it were the largest space in their existence and would most impress the attention of a spectator who knew all their properties but was not specially interested in any Classes formed on this principle may be called in a more emphatic manner than any others natural groups On the subject of these groups Dr Whewell lays down a theory grounded on an important truth which he has in some respects expressed and illustrated very felicitously but also as it appears to me with some admixture of error It will be advantageous for both these reasons to extract the statement of his doctrine in the very words he has used Natural groups according to this theory are given by Type not by Definition And this consideration accounts for that indefiniteness and indecision which we frequently find in the descriptions of such groups and which must appear so strange and inconsistent to any one who does not suppose these descriptions to assume any deeper ground of connection than an arbitrary choice of the botanist Thus in the family of the rosetree we are told that the ovules are very rarely erect the stigmata usually simple Of what use it might be asked can such loose accounts be To which the answer is that they are not inserted in order to distinguish the species but in order to describe the family and the total relations of the ovules and the stigmata of the family are better known by this general statement A similar observation may be made with regard to the Anomalies of each group which occur so commonly that Dr Lindley in his Introduction to the Natural System of Botany makes the Anomalies’ an article in each family Thus part of the character of the Rosaceae is that they have alternate stipulate leaves and that the albumen is obliterated but yet in Lowea one of the genera of this family the stipulae are absent and the albumen is present in another Neillia This implies as we have already seen that the artificial character or diagnosis as Mr Lindley calls it is imperfect It is though very nearly yet not exactly commensurate with the natural group and hence in certain cases this character is made to yield to the general weight of natural affinities These views of classes determined by characters which can not be expressed in words of propositions which state not what happens in all cases but only usually of particulars which are included in a class though they transgress the definition of it may probably surprise the reader They are so contrary to many of the received opinions respecting the use of definitions and the nature of scientific propositions that they will probably appear to many persons highly illogical and unphilosophical But a disposition to such a judgment arises in a great measure from this that the mathematical and mathematicophysical sciences have in a great degree determined men’s views of the general nature and form of scientific truth while Natural History has not yet had time or opportunity to exert its due influence upon the current habits of philosophizing The apparent indefiniteness and inconsistency of the classifications and definitions of Natural History belongs in a far higher degree to all other except mathematical speculations and the modes in which approximations to exact distinctions and general truths have been made in Natural History may be worthy our attention even for the light they throw upon the best modes of pursuing truth of all kinds Though in a Natural group of objects a definition can no longer be of any use as a regulative principle classes are not therefore left quite loose without any certain standard or guide The class is steadily fixed though not precisely limited it is given though not circumscribed it is determined not by a boundaryline without but by a central point within not by what it strictly excludes but by what it eminently includes by an example not by a precept in short instead of a Definition we have a Type for our director A Type is an example of any class for instance a species of a genus which is considered as eminently possessing the character of the class All the species which have a greater affinity with this typespecies than with any others form the genus and are arranged about it deviating from it in various directions and different degrees Thus a genus may consist of several species which approach very near the type and of which the claim to a place with it is obvious while there may be other species which straggle farther from this central knot and which yet are clearly more connected with it than with any other And even if there should be some species of which the place is dubious and which appear to be equally bound to two generic types it is easily seen that this would not destroy the reality of the generic groups any more than the scattered trees of the intervening plain prevent our speaking intelligibly of the distinct forests of two separate hills The typespecies of every genus the typegenus of every family is then one which possesses all the characters and properties of the genus in a marked and prominent manner The type of the Rose family has alternate stipulate leaves wants the albumen has the ovules not erect has the stigmata simple and besides these features which distinguish it from the exceptions or varieties of its class it has the features which make it prominent in its class It is one of those which possess clearly several leading attributes and thus though we can not say of any one genus that it must be the type of the family or of any one species that it must be the type of the genus we are still not wholly to seek the type must be connected by many affinities with most of the others of its group it must be near the centre of the crowd and not one of the stragglers In this passage the latter part of which especially I can not help noticing as an admirable example of philosophic style Dr Whewell has stated very clearly and forcibly but I think without making all necessary distinctions one of the principles of a Natural Classification What this principle is what are its limits and in what manner he seems to me to have overstepped them will appear when we have laid down another rule of Natural Arrangement which appears to me still more fundamental The reader is by this time familiar with the general truth which I restate so often on account of the great confusion in which it is commonly involved that there are in nature distinctions of Kind distinctions not consisting in a given number of definite properties plus the effects which follow from those properties but running through the whole nature through the attributes generally of the things so distinguished Our knowledge of the properties of a Kind is never complete We are always discovering and expecting to discover new ones Where the distinction between two classes of things is not one of Kind we expect to find their properties alike except where there is some reason for their being different On the contrary when the distinction is in Kind we expect to find the properties different unless there be some cause for their being the same All knowledge of a Kind must be obtained by observation and experiment upon the Kind itself no inference respecting its properties from the properties of things not connected with it by Kind goes for more than the sort of presumption usually characterized as an analogy and generally in one of its fainter degrees Since the common properties of a true Kind and consequently the general assertions which can be made respecting it or which are certain to be made hereafter as our knowledge extends are indefinite and inexhaustible and since the very first principle of natural classification is that of forming the classes so that the objects composing each may have the greatest number of properties in common this principle prescribes that every such classification shall recognize and adopt into itself all distinctions of Kind which exist among the objects it professes to classify To pass over any distinctions of Kind and substitute definite distinctions which however considerable they may be do not point to ulterior unknown differences would be to replace classes with more by classes with fewer attributes in common and would be subversive of the Natural Method of Classification Accordingly all natural arrangements whether the reality of the distinction of Kinds was felt or not by their framers have been led by the mere pursuit of their own proper end to conform themselves to the distinctions of Kind so far as these have been ascertained at the time The species of Plants are not only real Kinds but are probably all of them real lowest Kinds Infimae Species which if we were to subdivide as of course it is open to us to do into subclasses the subdivision would necessarily be founded on definite distinctions not pointing apart from what may be known of their causes or effects to any difference beyond themselves In so far as a natural classification is grounded on real Kinds its groups are certainly not conventional it is perfectly true that they do not depend upon an arbitrary choice of the naturalist But it does not follow nor I conceive is it true that these classes are determined by a type and not by characters To determine them by a type would be as sure a way of missing the Kind as if we were to select a set of characters arbitrarily They are determined by characters but these are not arbitrary The problem is to find a few definite characters which point to the multitude of indefinite ones Kinds are Classes between which there is an impassable barrier and what we have to seek is marks whereby we may determine on which side of the barrier an object takes its place The characters which will best do this should be chosen if they are also important in themselves so much the better When we have selected the characters we parcel out the objects according to those characters and not I conceive according to resemblance to a type We do not compose the species Ranunculus acris of all plants which bear a satisfactory degree of resemblance to a model buttercup but of those which possess certain characters selected as marks by which we might recognize the possibility of a common parentage and the enumeration of those characters is the definition of the species The question next arises whether as all Kinds must have a place among the classes so all the classes in a natural arrangement must be Kinds And to this I answer certainly not The distinctions of Kinds are not numerous enough to make up the whole of a classification Very few of the genera of plants or even of the families can be pronounced with certainty to be Kinds The great distinctions of Vascular and Cellular Dicotyledonous or Exogenous and Monocotyledonous or Endogenous plants are perhaps differences of kind the lines of demarcation which divide those classes seem though even on this I would not pronounce positively to go through the whole nature of the plants But the different species of a genus or genera of a family usually have in common only a limited number of characters A Rose does not seem to differ from a Rubus or the Umbelliferae from the Ranunculaceae in much else than the characters botanically assigned to those genera or those families Unenumerated differences certainly do exist in some cases there are families of plants which have peculiarities of chemical composition or yield products having peculiar effects on the animal economy The Cruciferae and Fungi contain an unusual proportion of nitrogen the Labiatae are the chief sources of essential oils the Solaneae are very commonly narcotic etc In these and similar cases there are possibly distinctions of Kind but it is by no means indispensable that there should be Genera and Families may be eminently natural though marked out from one another by properties limited in number provided those properties are important and the objects contained in each genus or family resemble each other more than they resemble any thing which is excluded from the genus or family After the recognition and definition then of the infimae species the next step is to arrange those infimae species into larger groups making these groups correspond to Kinds wherever it is possible but in most cases without any such guidance And in doing this it is true that we are naturally and properly guided in most cases at least by resemblance to a type We form our groups round certain selected Kinds each of which serves as a sort of exemplar of its group But though the groups are suggested by types I can not think that a group when formed is determined by the type that in deciding whether a species belongs to the group a reference is made to the type and not to the characters that the characters can not be expressed in words This assertion is inconsistent with Dr Whewell’s own statement of the fundamental principle of classification namely that general assertions shall be possible If the class did not possess any characters in common what general assertions would be possible respecting it Except that they all resemble each other more than they resemble any thing else nothing whatever could be predicated of the class The truth is on the contrary that every genus or family is framed with distinct reference to certain characters and is composed first and principally of species which agree in possessing all those characters To these are added as a sort of appendix such other species generally in small number as possess nearly all the properties selected wanting some of them one property some another and which while they agree with the rest almost as much as these agree with one another do not resemble in an equal degree any other group Our conception of the class continues to be grounded on the characters and the class might be defined those things which either possess that set of characters or resemble the things that do so more than they resemble any thing else And this resemblance itself is not like resemblance between simple sensations an ultimate fact unsusceptible of analysis Even the inferior degree of resemblance is created by the possession of common characters Whatever resembles the genus Rose more than it resembles any other genus does so because it possesses a greater number of the characters of that genus than of the characters of any other genus Nor can there be any real difficulty in representing by an enumeration of characters the nature and degree of the resemblance which is strictly sufficient to include any object in the class There are always some properties common to all things which are included Others there often are to which some things which are nevertheless included are exceptions But the objects which are exceptions to one character are not exceptions to another the resemblance which fails in some particulars must be made up for in others The class therefore is constituted by the possession of all the characters which are universal and most of those which admit of exceptions If a plant had the ovules erect the stigmata divided possessed the albumen and was without stipules it possibly would not be classed among the Rosaceae But it may want any one or more than one of these characters and not be excluded The ends of a scientific classification are better answered by including it Since it agrees so nearly in its known properties with the sum of the characters of the class it is likely to resemble that class more than any other in those of its properties which are still undiscovered Not only therefore are natural groups no less than any artificial classes determined by characters they are constituted in contemplation of and by reason of characters But it is in contemplation not of those characters only which are rigorously common to all the objects included in the group but of the entire body of characters all of which are found in most of those objects and most of them in all And hence our conception of the class the image in our minds which is representative of it is that of a specimen complete in all the characters most naturally a specimen which by possessing them all in the greatest degree in which they are ever found is the best fitted to exhibit clearly and in a marked manner what they are It is by a mental reference to this standard not instead of but in illustration of the definition of the class that we usually and advantageously determine whether any individual or species belongs to the class or not And this as it seems to me is the amount of truth contained in the doctrine of Types We shall see presently that where the classification is made for the express purpose of a special inductive inquiry it is not optional but necessary for fulfilling the conditions of a correct Inductive Method that we should establish a typespecies or genus namely the one which exhibits in the most eminent degree the particular phenomenon under investigation But of this hereafter It remains for completing the theory of natural groups that a few words should be said on the principles of the nomenclature adapted to them A Nomenclature in science is as we have said a system of the names of Kinds These names like other classnames are defined by the enumeration of the characters distinctive of the class The only merit which a set of names can have beyond this is to convey by the mode of their construction as much information as possible so that a person who knows the thing may receive all the assistance which the name can give in remembering what he knows while he who knows it not may receive as much knowledge respecting it as the case admits of by merely being told its name There are two modes of giving to the name of a Kind this sort of significance The best but which unfortunately is seldom practicable is when the word can be made to indicate by its formation the very properties which it is designed to connote The name of a Kind does not of course connote all the properties of the Kind since these are inexhaustible but such of them as are sufficient to distinguish it such as are sure marks of all the rest Now it is very rarely that one property or even any two or three properties can answer this purpose To distinguish the common daisy from all other species of plants would require the specification of many characters And a name can not without being too cumbrous for use give indication by its etymology or mode of construction of more than a very small number of these The possibility therefore of an ideally perfect Nomenclature is probably confined to the one case in which we are happily in possession of something approaching to it the Nomenclature of elementary Chemistry The substances whether simple or compound with which chemistry is conversant are Kinds and as such the properties which distinguish each of them from the rest are innumerable but in the case of compound substances the simple ones are not numerous enough to require a systematic nomenclature there is one property the chemical composition which is of itself sufficient to distinguish the Kind and is with certain reservations not yet thoroughly understood a sure mark of all the other properties of the compound All that was needful therefore was to make the name of every compound express on the first hearing its chemical composition that is to form the name of the compound in some uniform manner from the names of the simple substances which enter into it as elements This was done most skillfully and successfully by the French chemists though their nomenclature has become inadequate to the convenient expression of the very complicated compounds now known to chemists The only thing left unexpressed by them was the exact proportion in which the elements were combined and even this since the establishment of the atomic theory it has been found possible to express by a simple adaptation of their phraseology But where the characters which must be taken into consideration in order sufficiently to designate the Kind are too numerous to be all signified in the derivation of the name and where no one of them is of such preponderant importance as to justify its being singled out to be so indicated we may avail ourselves of a subsidiary resource Though we can not indicate the distinctive properties of the Kind we may indicate its nearest natural affinities by incorporating into its name the name of the proximate natural group of which it is one of the species On this principle is founded the admirable binary nomenclature of botany and zoology In this nomenclature the name of every species consists of the name of the genus or natural group next above it with a word added to distinguish the particular species The last portion of the compound name is sometimes taken from some one of the peculiarities in which that species differs from others of the genus as Clematis integrifolia Potentilla alba Viola palustris Artemisia vulgaris sometimes from a circumstance of an historical nature as Narcissus poeticus Potentilla tormentilla indicating that the plant is that which was formerly known by the latter name Exacum Candollii from the fact that De Candolle was its first discoverer and sometimes the word is purely conventional as Thlaspi bursapastoris Ranunculus thora it is of little consequence which since the second or as it is usually called the specific name could at most express independently of convention no more than a very small portion of the connotation of the term But by adding to this the name of the superior genus we may make the best amends we can for the impossibility of so contriving the name as to express all the distinctive characters of the Kind We make it at all events express as many of those characters as are common to the proximate natural group in which the Kind is included If even those common characters are so numerous or so little familiar as to require a further extension of the same resource we might instead of a binary adopt a ternary nomenclature employing not only the name of the genus but that of the next natural group in order of generality above the genus commonly called the Family This was done in the mineralogical nomenclature proposed by Professor Mohs The names framed by him were not composed of two but of three elements designating respectively the Species the Genus and the Order thus he has such species as Rhombohedral Lime Haloide Octohedral Fluor Haloide Prismatic Hal Baryte The binary construction however has been found sufficient in botany and zoology the only sciences in which this general principle has hitherto been successfully adopted in the construction of a nomenclature Besides the advantage which this principle of nomenclature possesses in giving to the names of species the greatest quantity of independent significance which the circumstances of the case admit of it answers the further end of immensely economizing the use of names and preventing an otherwise intolerable burden on the memory When the names of species become extremely numerous some artifice as Dr Whewell observes becomes absolutely necessary to make it possible to recollect or apply them The known species of plants for example were ten thousand in the time of Linnaeus and are now probably sixty thousand It would be useless to endeavour to frame and employ separate names for each of these species The division of the objects into a subordinated system of classification enables us to introduce a Nomenclature which does not require this enormous number of names Each of the genera has its name and the species are marked by the addition of some epithet to the name of the genus In this manner about seventeen hundred generic names with a moderate number of specific names were found by Linnaeus sufficient to designate with precision all the species of vegetables known at his time And though the number of generic names has since greatly increased it has not increased in any thing like the proportion of the multiplication of known species Thus far we have considered the principles of scientific classification so far only as relates to the formation of natural groups and at this point most of those who have attempted a theory of natural arrangement including among the rest Dr Whewell have stopped There remains however another and a not less important portion of the theory which has not yet as far as I am aware been systematically treated of by any writer except M Comte This is the arrangement of the natural groups into a natural series The end of Classification as an instrument for the investigation of nature is as before stated to make us think of those objects together which have the greatest number of important common properties and which therefore we have oftenest occasion in the course of our inductions for taking into joint consideration Our ideas of objects are thus brought into the order most conducive to the successful prosecution of inductive inquiries generally But when the purpose is to facilitate some particular inductive inquiry more is required To be instrumental to that purpose the classification must bring those objects together the simultaneous contemplation of which is likely to throw most light upon the particular subject That subject being the laws of some phenomenon or some set of connected phenomena the very phenomenon or set of phenomena in question must be chosen as the groundwork of the classification The requisites of a classification intended to facilitate the study of a particular phenomenon are first to bring into one class all Kinds of things which exhibit that phenomenon in whatever variety of forms or degrees and secondly to arrange those Kinds in a series according to the degree in which they exhibit it beginning with those which exhibit most of it and terminating with those which exhibit least The principal example as yet of such a classification is afforded by comparative anatomy and physiology from which therefore our illustrations shall be taken The object being supposed to be the investigation of the laws of animal life the first step after forming the most distinct conception of the phenomenon itself possible in the existing state of our knowledge is to erect into one great class that of animals all the known Kinds of beings where that phenomenon presents itself in however various combinations with other properties and in however different degrees As some of these Kinds manifest the general phenomenon of animal life in a very high degree and others in an insignificant degree barely sufficient for recognition we must in the next place arrange the various Kinds in a series following one another according to the degrees in which they severally exhibit the phenomenon beginning therefore with man and ending with the most imperfect kinds of zoophytes This is merely saying that we should put the instances from which the law is to be inductively collected into the order which is implied in one of the four Methods of Experimental Inquiry discussed in the preceding Book the fourth Method that of Concomitant Variations As formerly remarked this is often the only method to which recourse can be had with assurance of a true conclusion in cases in which we have but limited means of effecting by artificial experiments a separation of circumstances usually conjoined The principle of the method is that facts which increase or diminish together and disappear together are either cause and effect or effects of a common cause When it has been ascertained that this relation really subsists between the variations a connection between the facts themselves may be confidently laid down either as a law of nature or only as an empirical law according to circumstances That the application of this Method must be preceded by the formation of such a series as we have described is too obvious to need being pointed out and the mere arrangement of a set of objects in a series according to the degrees in which they exhibit some fact of which we are seeking the law is too naturally suggested by the necessities of our inductive operations to require any lengthened illustration here But there are cases in which the arrangement required for the special purpose becomes the determining principle of the classification of the same objects for general purposes This will naturally and properly happen when those laws of the objects which are sought in the special inquiry enact so principal a part in the general character and history of those objects exercise so much influence in determining all the phenomena of which they are either the agents or the theatre that all other differences existing among the objects are fittingly regarded as mere modifications of the one phenomenon sought effects determined by the cooperation of some incidental circumstance with the laws of that phenomenon Thus in the case of animated beings the differences between one class of animals and another may reasonably be considered as mere modifications of the general phenomenon animal life modifications arising either from the different degrees in which that phenomenon is manifested in different animals or from the intermixture of the effects of incidental causes peculiar to the nature of each with the effects produced by the general laws of life those laws still exercising a predominant influence over the result Such being the case no other inductive inquiry respecting animals can be successfully carried on except in subordination to the great inquiry into the universal laws of animal life and the classification of animals best suited to that one purpose is the most suitable to all the other purposes of zoological science To establish a classification of this sort or even to apprehend it when established requires the power of recognizing the essential similarity of a phenomenon in its minuter degrees and obscurer forms with what is called the same phenomenon in the greatest perfection of its development that is of identifying with each other all phenomena which differ only in degree and in properties which we suppose to be caused by difference of degree In order to recognize this identity or, in other words, this exact similarity of quality the assumption of a typespecies is indispensable We must consider as the type of the class that among the Kinds included in it which exhibits the properties constitutive of the class in the highest degree conceiving the other varieties as instances of degeneracy as it were from that type deviations from it by inferior intensity of the characteristic property or properties For every phenomenon is best studied caeteris paribus where it exists in the greatest intensity It is there that the effects which either depend on it or depend on the same causes with it will also exist in the greatest degree It is there consequently and only there that those effects of it or joint effects with it can become fully known to us so that we may learn to recognize their smaller degrees or even their mere rudiments in cases in which the direct study would have been difficult or even impossible Not to mention that the phenomenon in its higher degrees may be attended by effects or collateral circumstances which in its smaller degrees do not occur at all requiring for their production in any sensible amount a greater degree of intensity of the cause than is there met with In man for example the species in which both the phenomenon of animal and that of organic life exist in the highest degree many subordinate phenomena develop themselves in the course of his animated existence which the inferior varieties of animals do not show The knowledge of these properties may nevertheless be of great avail toward the discovery of the conditions and laws of the general phenomenon of life which is common to man with those inferior animals And they are even rightly considered as properties of animated nature itself because they may evidently be affiliated to the general laws of animated nature because we may fairly presume that some rudiments or feeble degrees of those properties would be recognized in all animals by more perfect organs or even by more perfect instruments than ours and because those may be correctly termed properties of a class which a thing exhibits exactly in proportion as it belongs to the class that is in proportion as it possesses the main attributes constitutive of the class It remains to consider how the internal distribution of the series may most properly take place in what manner it should be divided into Orders Families and Genera The main principle of division must of course be natural affinity the classes formed must be natural groups and the formation of these has already been sufficiently treated of But the principles of natural grouping must be applied in subordination to the principle of a natural series The groups must not be so constituted as to place in the same group things which ought to occupy different points of the general scale The precaution necessary to be observed for this purpose is that the primary divisions must be grounded not on all distinctions indiscriminately but on those which correspond to variations in the degree of the main phenomenon The series of Animated Nature should be broken into parts at the points where the variation in the degree of intensity of the main phenomenon as marked by its principal characters Sensation Thought Voluntary Motion etc begins to be attended by conspicuous changes in the miscellaneous properties of the animal Such wellmarked changes take place for example where the class Mammalia ends at the points where Fishes are separated from Insects Insects from Mollusca etc When so formed the primary natural groups will compose the series by mere juxtaposition without redistribution each of them corresponding to a definite portion of the scale In like manner each family should if possible be so subdivided that one portion of it shall stand higher and the other lower though of course contiguous in the general scale and only when this is impossible is it allowable to ground the remaining subdivisions on characters having no determinable connection with the main phenomenon Where the principal phenomenon so far transcends in importance all other properties on which a classification could be grounded as it does in the case of animated existence any considerable deviation from the rule last laid down is in general sufficiently guarded against by the first principle of a natural arrangement that of forming the groups according to the most important characters All attempts at a scientific classification of animals since first their anatomy and physiology were successfully studied have been framed with a certain degree of instinctive reference to a natural series and have accorded in many more points than they have differed with the classification which would most naturally have been grounded on such a series But the accordance has not always been complete and it still is often a matter of discussion which of several classifications best accords with the true scale of intensity of the main phenomenon Cuvier for example has been justly criticised for having formed his natural groups with an undue degree of reference to the mode of alimentation a circumstance directly connected only with organic life and not leading to the arrangement most appropriate for the purposes of an investigation of the laws of animal life since both carnivorous and herbivorous or frugivorous animals are found at almost every degree in the scale of animal perfection Blainville’s classification has been considered by high authorities to be free from this defect as representing correctly by the mere order of the principal groups the successive degeneracy of animal nature from its highest to its most imperfect exemplification A classification of any large portion of the field of nature in conformity to the foregoing principles has hitherto been found practicable only in one great instance that of animals In the case even of vegetables the natural arrangement has not been carried beyond the formation of natural groups Naturalists have found and probably will continue to find it impossible to form those groups into any series the terms of which correspond to real gradations in the phenomenon of vegetative or organic life Such a difference of degree may be traced between the class of Vascular Plants and that of Cellular which includes lichens algae and other substances whose organization is simpler and more rudimentary than that of the higher order of vegetables and which therefore approach nearer to mere inorganic nature But when we rise much above this point we do not find any sufficient difference in the degree in which different plants possess the properties of organization and life The dicotyledons are of more complex structure and somewhat more perfect organization than the monocotyledons and some dicotyledonous families such as the Compositae are rather more complex in their organization than the rest But the differences are not of a marked character and do not promise to throw any particular light upon the conditions and laws of vegetable life and development If they did the classification of vegetables would have to be made like that of animals with reference to the scale or series indicated Although the scientific arrangements of organic nature afford as yet the only complete example of the true principles of rational classification whether as to the formation of groups or of series those principles are applicable to all cases in which mankind are called upon to bring the various parts of any extensive subject into mental coordination They are as much to the point when objects are to be classed for purposes of art or business as for those of science The proper arrangement for example of a code of laws depends on the same scientific conditions as the classifications in natural history nor could there be a better preparatory discipline for that important function than the study of the principles of a natural arrangement not only in the abstract but in their actual application to the class of phenomena for which they were first elaborated and which are still the best school for learning their use Of this the great authority on codification Bentham was perfectly aware and his early Fragment on Government the admirable introduction to a series of writings unequaled in their department contains clear and just views as far as they go on the meaning of a natural arrangement such as could scarcely have occurred to any one who lived anterior to the age of Linnaeus and Bernard de Jussieu Errare non modo affirmando et negando sed etiam sentiendo et in tacita hominum cogitatione contingit HOBBES Computatio sive Logica chap v Il leur semble qu’il n’y a qu’ˆ douter par fantaisie et qu’il n’y a qu’ˆ dire en gnral que notre nature est infirme que notre esprit est plein d’aveuglement qu’il faut avoir un grand soin de se dfaire de ses prjugs et autres choses semblables Ils pensent que cela suffit pour ne plus se laisser sduire ˆ ses sens et pour ne plus se tromper du tout Il ne suffit pas de dire que l’esprit est foible il faut lui faire sentir ses foiblesses Ce n’est pas assez de dire qu’il est sujet ˆ l’erreur il faut lui dcouvrir en quoi consistent ses erreurs MALEBRANCHE Recherche de la Vrit It is a maxim of the schoolmen that contrariorum eadem est scientia we never really know what a thing is unless we are also able to give a sufficient account of its opposite Conformably to this maxim one considerable section in most treatises on Logic is devoted to the subject of Fallacies and the practice is too well worthy of observance to allow of our departing from it The philosophy of reasoning to be complete ought to comprise the theory of bad as well as of good reasoning We have endeavoured to ascertain the principles by which the sufficiency of any proof can be tested and by which the nature and amount of evidence needful to prove any given conclusion can be determined beforehand If these principles were adhered to then although the number and value of the truths ascertained would be limited by the opportunities or by the industry ingenuity and patience of the individual inquirer at least error would not be embraced instead of truth But the general consent of mankind founded on their experience vouches for their being far indeed from even this negative kind of perfection in the employment of their reasoning powers In the conduct of life in the practical business of mankind wrong inferences incorrect interpretations of experience unless after much culture of the thinking faculty are absolutely inevitable and with most people after the highest degree of culture they ever attain such erroneous inferences producing corresponding errors in conduct are lamentably frequent Even in the speculations to which eminent intellects have systematically devoted themselves and in reference to which the collective mind of the scientific world is always at hand to aid the efforts and correct the aberrations of individuals it is only from the more perfect sciences from those of which the subjectmatter is the least complicated that opinions not resting on a correct induction have at length generally speaking been expelled In the departments of inquiry relating to the more complex phenomena of nature and especially those of which the subject is man whether as a moral and intellectual a social or even as a physical being the diversity of opinions still prevalent among instructed persons and the equal confidence with which those of the most contrary ways of thinking cling to their respective tenets are proof not only that right modes of philosophizing are not yet generally adopted on those subjects but that wrong ones are that inquirers have not only in general missed the truth but have often embraced error that even the most cultivated portion of our species have not yet learned to abstain from drawing conclusions which the evidence does not warrant The only complete safeguard against reasoning ill is the habit of reasoning well familiarity with the principles of correct reasoning and practice in applying those principles It is however not unimportant to consider what are the most common modes of bad reasoning by what appearances the mind is most likely to be seduced from the observance of true principles of induction what in short are the most common and most dangerous varieties of Apparent Evidence whereby persons are misled into opinions for which there does not exist evidence really conclusive A catalogue of the varieties of apparent evidence which are not real evidence is an enumeration of Fallacies Without such an enumeration therefore the present work would be wanting in an essential point And while writers who included in their theory of reasoning nothing more than ratiocination have in consistency with this limitation confined their remarks to the fallacies which have their seat in that portion of the process of investigation we who profess to treat of the whole process must add to our directions for performing it rightly warnings against performing it wrongly in any of its parts whether the ratiocinative or the experimental portion of it be in fault or the fault lie in dispensing with ratiocination and induction altogether In considering the sources of unfounded inference it is unnecessary to reckon the errors which arise not from a wrong method nor even from ignorance of the right one but from a casual lapse through hurry or inattention in the application of the true principles of induction Such errors like the accidental mistakes in casting up a sum do not call for philosophical analysis or classification theoretical considerations can throw no light upon the means of avoiding them In the present treatise our attention is required not to mere inexpertness in performing the operation in the right way the only remedies for which are increased attention and more sedulous practice but to the modes of performing it in a way fundamentally wrong the conditions under which the human mind persuades itself that it has sufficient grounds for a conclusion which it has not arrived at by any of the legitimate methods of induction which it has not even carelessly or overhastily endeavoured to test by those legitimate methods There is another branch of what may be called the Philosophy of Error which must be mentioned here though only to be excluded from our subject The sources of erroneous opinions are twofold moral and intellectual Of these the moral do not fall within the compass of this work They may be classed under two general heads Indifference to the attainment of truth and Bias of which last the most common case is that in which we are biased by our wishes but the liability is almost as great to the undue adoption of a conclusion which is disagreeable to us as of one which is agreeable if it be of a nature to bring into action any of the stronger passions Persons of timid character are the more predisposed to believe any statement the more it is calculated to alarm them Indeed it is a psychological law deducible from the most general laws of the mental constitution of man that any strong passion renders us credulous as to the existence of objects suitable to excite it But the moral causes of opinions though with most persons the most powerful of all are but remote causes they do not act directly but by means of the intellectual causes to which they bear the same relation that the circumstances called in the theory of medicine predisposing causes bear to exciting causes Indifference to truth can not in and by itself produce erroneous belief it operates by preventing the mind from collecting the proper evidences or from applying to them the test of a legitimate and rigid induction by which omission it is exposed unprotected to the influence of any species of apparent evidence which offers itself spontaneously or which is elicited by that smaller quantity of trouble which the mind may be willing to take As little is Bias a direct source of wrong conclusions We can not believe a proposition only by wishing or only by dreading to believe it The most violent inclination to find a set of propositions true will not enable the weakest of mankind to believe them without a vestige of intellectual grounds without any even apparent evidence It acts indirectly by placing the intellectual grounds of belief in an incomplete or distorted shape before his eyes It makes him shrink from the irksome labor of a rigorous induction when he has a misgiving that its result may be disagreeable and in such examination as he does institute it makes him exert that which is in a certain measure voluntary his attention unfairly giving a larger share of it to the evidence which seems favourable to the desired conclusion a smaller to that which seems unfavourable It operates too by making him look out eagerly for reasons or apparent reasons to support opinions which are conformable or resist those which are repugnant to his interests or feelings and when the interests or feelings are common to great numbers of persons reasons are accepted and pass current which would not for a moment be listened to in that character if the conclusion had nothing more powerful than its reasons to speak in its behalf The natural or acquired partialities of mankind are continually throwing up philosophical theories the sole recommendation of which consists in the premises they afford for proving cherished doctrines or justifying favourite feelings and when any one of these theories has been so thoroughly discredited as no longer to serve the purpose another is always ready to take its place This propensity when exercised in favour of any widelyspread persuasion or sentiment is often decorated with complimentary epithets and the contrary habit of keeping the judgment in complete subordination to evidence is stigmatized by various hard names as skepticism immorality coldness hardheartedness and similar expressions according to the nature of the case But though the opinions of the generality of mankind when not dependent on mere habit and inculcation have their root much more in the inclinations than in the intellect it is a necessary condition to the triumph of the moral bias that it should first pervert the understanding Every erroneous inference though originating in moral causes involves the intellectual operation of admitting insufficient evidence as sufficient and whoever was on his guard against all kinds of inconclusive evidence which can be mistaken for conclusive would be in no danger of being led into error even by the strongest bias There are minds so strongly fortified on the intellectual side that they could not blind themselves to the light of truth however really desirous of doing so they could not with all the inclination in the world pass off upon themselves bad arguments for good ones If the sophistry of the intellect could be rendered impossible that of the feelings having no instrument to work with would be powerless A comprehensive classification of all those things which not being evidence are liable to appear such to the understanding will therefore of itself include all errors of judgment arising from moral causes to the exclusion only of errors of practice committed against better knowledge To examine then the various kinds of apparent evidence which are not evidence at all and of apparently conclusive evidence which do not really amount to conclusiveness is the object of that part of our inquiry into which we are about to enter The subject is not beyond the compass of classification and comprehensive survey The things indeed which are not evidence of any given conclusion are manifestly endless and this negative property having no dependence on any positive ones can not be made the groundwork of a real classification But the things which not being evidence are susceptible of being mistaken for it are capable of a classification having reference to the positive property which they possess of appearing to be evidence We may arrange them at our choice on either of two principles according to the cause which makes them appear to be evidence not being so or according to the particular kind of evidence which they simulate The Classification of Fallacies which will be attempted in the ensuing chapter is founded on these considerations jointly In attempting to establish certain general distinctions which shall mark out from one another the various kinds of Fallacious Evidence we propose to ourselves an altogether different aim from that of several eminent thinkers who have given under the name of Political or other Fallacies a mere enumeration of a certain number of erroneous opinions false general propositions which happen to be often met with loci communes of bad arguments on some particular subject Logic is not concerned with the false opinions which people happen to entertain but with the manner in which they come to entertain them The question is not what facts have at any time been erroneously supposed to be proof of certain other facts but what property in the facts it was which led any one to this mistaken supposition When a fact is supposed though incorrectly to be evidentiary of or a mark of some other fact there must be a cause of the error the supposed evidentiary fact must be connected in some particular manner with the fact of which it is deemed evidentiary must stand in some particular relation to it without which relation it would not be regarded in that light The relation may either be one resulting from the simple contemplation of the two facts side by side with one another or it may depend on some process of mind by which a previous association has been established between them Some peculiarity of relation however there must be the fact which can even by the wildest aberration be supposed to prove another fact must stand in some special position with regard to it and if we could ascertain and define that special position we should perceive the origin of the error We can not regard one fact as evidentiary of another unless we believe that the two are always or in the majority of cases conjoined If we believe A to be evidentiary of B if when we see A we are inclined to infer B from it the reason is because we believe that wherever A is B also either always or for the most part exists either as an antecedent a consequent or a concomitant If when we see A we are inclined not to expect B if we believe A to be evidentiary of the absence of B it is because we believe that where A is B either is never or at least seldom found Erroneous conclusions in short no less than correct conclusions have an invariable relation to a general formula either expressed or tacitly implied When we infer some fact from some other fact which does not really prove it we either have admitted or if we maintained consistency ought to admit some groundless general proposition respecting the conjunction of the two phenomena For every property therefore in facts or in our mode of considering facts which leads us to believe that they are habitually conjoined when they are not or that they are not when in reality they are there is a corresponding kind of Fallacy and an enumeration of fallacies would consist in a specification of those properties in facts and those peculiarities in our mode of considering them which give rise to this erroneous opinion To begin then the supposed connection or repugnance between the two facts may either be a conclusion from evidence that is from some other proposition or propositions or may be admitted without any such ground admitted as the phrase is on its own evidence embraced as selfevident as an axiomatic truth This gives rise to the first great distinction that between Fallacies of Inference and Fallacies of Simple Inspection In the latter division must be included not only all cases in which a proposition is believed and held for true literally without any extrinsic evidence either of specific experience or general reasoning but those more frequent cases in which simple inspection creates a presumption in favour of a proposition not sufficient for belief but sufficient to cause the strict principles of a regular induction to be dispensed with and creating a predisposition to believe it on evidence which would be seen to be insufficient if no such presumption existed This class comprehending the whole of what may be termed Natural Prejudices and which I shall call indiscriminately Fallacies of Simple Inspection or Fallacies a priori shall be placed at the head of our list Fallacies of Inference or erroneous conclusions from supposed evidence must be subdivided according to the nature of the apparent evidence from which the conclusions are drawn or what is the same thing according to the particular kind of sound argument which the fallacy in question simulates But there is a distinction to be first drawn which does not answer to any of the divisions of sound arguments but arises out of the nature of bad ones We may know exactly what our evidence is and yet draw a false conclusion from it we may conceive precisely what our premises are what alleged matters of fact or general principles are the foundation of our inference and yet because the premises are false or because we have inferred from them what they will not support our conclusion may be erroneous But a case perhaps even more frequent is that in which the error arises from not conceiving our premises with due clearness that is as shown in the preceding Book with due fixity forming one conception of our evidence when we collect or receive it and another when we make use of it or unadvisedly and in general unconsciously substituting as we proceed different premises in the place of those with which we set out or a different conclusion for that which we undertook to prove This gives existence to a class of fallacies which may be justly termed in a phrase borrowed from Bentham Fallacies of Confusion comprehending among others all those which have their source in language whether arising from the vagueness or ambiguity of our terms or from casual associations with them When the fallacy is not one of Confusion that is when the proposition believed and the evidence on which it is believed are steadily apprehended and unambiguously expressed there remain to be made two cross divisions The Apparent Evidence may be either particular facts or foregone generalizations that is the process may simulate either simple Induction or Deduction and again the evidence whether consisting of supposed facts or of general propositions may be false in itself or being true may fail to bear out the conclusion attempted to be founded on it This gives us first Fallacies of Induction and Fallacies of Deduction and then a subdivision of each of these according as the supposed evidence is false or true but inconclusive Fallacies of Induction where the facts on which the induction proceeds are erroneous may be termed Fallacies of Observation The term is not strictly accurate or rather not accurately coextensive with the class of fallacies which I propose to designate by it Induction is not always grounded on facts immediately observed but sometimes on facts inferred and when these last are erroneous the error may not be in the literal sense of the term an instance of bad observation but of bad inference It will be convenient however to make only one class of all the inductions of which the error lies in not sufficiently ascertaining the facts on which the theory is grounded whether the cause of failure be malobservation or simple nonobservation and whether the malobservation be direct or by means of intermediate marks which do not prove what they are supposed to prove And in the absence of any comprehensive term to denote the ascertainment by whatever means of the facts on which an induction is grounded I will venture to retain for this class of fallacies under the explanation now given the title of Fallacies of Observation The other class of inductive fallacies in which the facts are correct but the conclusion not warranted by them are properly denominated Fallacies of Generalization and these again fall into various subordinate classes or natural groups some of which will be enumerated in their proper place When we now turn to Fallacies of Deduction namely those modes of incorrect argumentation in which the premises or some of them are general propositions and the argument a ratiocination we may of course subdivide these also into two species similar to the two preceding namely those which proceed on false premises and those of which the premises though true do not support the conclusion But of these species the first must necessarily fall under some one of the heads already enumerated For the error must be either in those premises which are general propositions or in those which assert individual facts In the former case it is an Inductive Fallacy of one or the other class in the latter it is a Fallacy of Observation unless in either case the erroneous premise has been assumed on simple inspection in which case the fallacy is a priori Or finally the premises of whichever kind they are may never have been conceived in so distinct a manner as to produce any clear consciousness by what means they were arrived at as in the case of what is called reasoning in a circle and then the fallacy is one of Confusion There remain therefore as the only class of fallacies having properly their seat in deduction those in which the premises of the ratiocination do not bear out its conclusion the various cases in short of vicious argumentation provided against by the rules of the syllogism We shall call these Fallacies of Ratiocination We must not however expect to find that men’s actual errors always or even commonly fall so unmistakably under some one of these classes as to be incapable of being referred to any other Erroneous arguments do not admit of such a sharply cut division as valid arguments do An argument fully stated with all its steps distinctly set out in language not susceptible of misunderstanding must if it be erroneous be so in some one of these five modes unequivocally or indeed of the first four since the fifth on such a supposition would vanish But it is not in the nature of bad reasoning to express itself thus unambiguously When a sophist whether he is imposing on himself or attempting to impose on others can be constrained to throw his sophistry into so distinct a form it needs in a large proportion of cases no further exposure In all arguments everywhere but in the schools some of the links are suppressed a fortiori when the arguer either intends to deceive or is a lame and inexpert thinker little accustomed to bring his reasoning processes to any test and it is in those steps of the reasoning which are made in this tacit and halfconscious or even wholly unconscious manner that the error oftenest lurks In order to detect the fallacy the proposition thus silently assumed must be supplied but the reasoner most likely has never really asked himself what he was assuming his confuter unless permitted to extort it from him by the Socratic mode of interrogation must himself judge what the suppressed premise ought to be in order to support the conclusion And hence in the words of Archbishop Whately it must be often a matter of doubt or rather of arbitrary choice not only to which genus each kind of fallacy should be referred but even to which kind to refer any one individual fallacy for since in any course of argument one premise is usually suppressed it frequently happens in the case of a fallacy that the hearers are left to the alternative of supplying either a premise which is not true or else one which does not prove the conclusion eg if a man expatiates on the distress of the country and thence argues that the government is tyrannical we must suppose him to assume either that every distressed country is under a tyranny’ which is a manifest falsehood or merely that every country under a tyranny is distressed’ which however true proves nothing the middle term being undistributed The former would be ranked in our distribution among fallacies of generalization the latter among those of ratiocination Which are we to suppose the speaker meant us to understand Surely if he understood himself just whichever each of his hearers might happen to prefer some might assent to the false premise others allow the unsound syllogism Almost all fallacies therefore might in strictness be brought under our fifth class Fallacies of Confusion A fallacy can seldom be absolutely referred to any of the other classes we can only say that if all the links were filled up which should be capable of being supplied in a valid argument it would either stand thus forming a fallacy of one class or thus a fallacy of another or at furthest we may say that the conclusion is most likely to have originated in a fallacy of such and such a class Thus in the illustration just quoted the error committed may be traced with most probability to a fallacy of generalization that of mistaking an uncertain mark or piece of evidence for a certain one concluding from an effect to some one of its possible causes when there are others which would have been equally capable of producing it Yet though the five classes run into each other and a particular error often seems to be arbitrarily assigned to one of them rather than to any of the rest there is considerable use in so distinguishing them We shall find it convenient to set apart as Fallacies of Confusion those of which confusion is the most obvious characteristic in which no other cause can be assigned for the mistake committed than neglect or inability to state the question properly and to apprehend the evidence with definiteness and precision In the remaining four classes I shall place not only the cases in which the evidence is clearly seen to be what it is and yet a wrong conclusion drawn from it but also those in which although there be confusion the confusion is not the sole cause of the error but there is some shadow of a ground for it in the nature of the evidence itself And in distributing these cases of partial confusion among the four classes I shall when there can be any hesitation as to the precise seat of the fallacy suppose it to be in that part of the process in which from the nature of the case and the tendencies of the human mind an error would in the particular circumstances be the most probable After these observations we shall proceed without further preamble to consider the five classes in their order
The tribe of errors of which we are to treat in the first instance, are those in which no actual inference takes place at all the proposition it can not in such cases be called a conclusion being embraced not as proved but as requiring no proof as a selfevident truth or else as having such intrinsic verisimilitude that external evidence not in itself amounting to proof is sufficient in aid of the antecedent presumption An attempt to treat this subject comprehensively would be a transgression of the bounds prescribed to this work since it would necessitate the inquiry which more than any other is the grand question of what is called metaphysics viz What are the propositions which may reasonably be received without proof That there must be some such propositions all are agreed since there can not be an infinite series of proof a chain suspended from nothing But to determine what these propositions are is the opus magnum of the more recondite mental philosophy Two principal divisions of opinion on the subject have divided the schools of philosophy from its first dawn The one recognizes no ultimate premises but the facts of our subjective consciousness our sensations emotions intellectual states of mind and volitions These and whatever by strict rules of induction can be derived from these it is possible according to this theory for us to know of all else we must remain in ignorance The opposite school hold that there are other existences suggested indeed to our minds by these subjective phenomena but not inferable from them by any process either of deduction or of induction which however we must by the constitution of our mental nature recognize as realities and realities too of a higher order than the phenomena of our consciousness being the efficient causes and necessary substrata of all Phenomena Among these entities they reckon Substances whether matter or spirit from the dust under our feet to the soul and from that to Deity All these according to them are preternatural or supernatural beings having no likeness in experience though experience is entirely a manifestation of their agency Their existence together with more or less of the laws to which they conform in their operations are on this theory apprehended and recognized as real by the mind itself intuitively experience whether in the form of sensation or of mental feeling having no other part in the matter than as affording facts which are consistent with these necessary postulates of reason and which are explained and accounted for by them As it is foreign to the purpose of the present treatise to decide between these conflicting theories we are precluded from inquiring into the existence or defining the extent and limits of knowledge a priori and from characterizing the kind of correct assumption which the fallacy of incorrect assumption now under consideration simulates Yet since it is allowed on both sides that such assumptions are often made improperly we may find it practicable without entering into the ultimate metaphysical grounds of the discussion to state some speculative propositions and suggest some practical cautions respecting the forms in which such unwarranted assumptions are most likely to be made In the cases in which according to the thinkers of the ontological school the mind apprehends by intuition things and the laws of things not cognizable by our sensitive faculty those intuitive or supposed intuitive perceptions are undistinguishable from what the opposite school are accustomed to call ideas of the mind When they themselves say that they perceive the things by an immediate act of a faculty given for that purpose by their Creator it would be said of them by their opponents that they find an idea or conception in their own minds and from the idea or conception infer the existence of a corresponding objective reality Nor would this be an unfair statement but a mere version into other words of the account given by many of themselves and one to which the more clearsighted of them might and generally do without hesitation subscribe Since therefore in the cases which lay the strongest claims to be examples of knowledge a priori the mind proceeds from the idea of a thing to the reality of the thing itself we can not be surprised by finding that illicit assumptions a priori consist in doing the same thing erroneously in mistaking subjective facts for objective laws of the percipient mind for laws of the perceived object properties of the ideas or conceptions for properties of the things conceived Accordingly a large proportion of the erroneous thinking which exists in the world proceeds on a tacit assumption that the same order must obtain among the objects in nature which obtains among our ideas of them That if we always think of two things together the two things must always exist together That if one thing makes us think of another as preceding or following it that other must precede it or follow it in actual fact And conversely that when we can not conceive two things together they can not exist together and that their combination may without further evidence be rejected from the list of possible occurrences Few persons I am inclined to think have reflected on the great extent to which this fallacy has prevailed and prevails in the actual beliefs and actions of mankind For a first illustration of it we may refer to a large class of popular superstitions If any one will examine in what circumstances most of those things agree which in different ages and by different portions of the human race have been considered as omens or prognostics of some interesting event whether calamitous or fortunate they will be found very generally characterized by this peculiarity that they cause the mind to think of that of which they are therefore supposed to forbode the actual occurrence Talk of the devil and he will appear has passed into a proverb Talk of the devil that is raise the idea and the reality will follow In times when the appearance of that personage in a visible form was thought to be no unfrequent occurrence it has doubtless often happened to persons of vivid imagination and susceptible nerves that talking of the devil has caused them to fancy they saw him as even in our more incredulous days listening to ghost stories predisposes us to see ghosts and thus as a prop to the a priori fallacy there might come to be added an auxiliary fallacy of malobservation with one of false generalization grounded on it Fallacies of different orders often herd or cluster together in this fashion one smoothing the way for another But the origin of the superstition is evidently that which we have assigned In like manner it has been universally considered unlucky to speak of misfortune The day on which any calamity happened has been considered an unfortunate day and there has been a feeling everywhere and in some nations a religious obligation against transacting any important business on that day For on such a day our thoughts are likely to be of misfortune For a similar reason any untoward occurrence in commencing an undertaking has been considered ominous of failure and often doubtless has really contributed to it by putting the persons engaged in the enterprise more or less out of spirits but the belief has equally prevailed where the disagreeable circumstance was independently of superstition too insignificant to depress the spirits by any influence of its own All know the story of Caesar’s accidentally stumbling in the act of landing on the African coast and the presence of mind with which he converted the direful presage into a favourable one by exclaiming Africa I embrace thee Such omens it is true were often conceived as warnings of the future given by a friendly or a hostile deity but this very superstition grew out of a preexisting tendency the god was supposed to send as an indication of what was to come something which people were already disposed to consider in that light So in the case of lucky or unlucky names Herodotus tells us how the Greeks on the way to Mycale were encouraged in their enterprise by the arrival of a deputation from Samos one of the members of which was named Hegesistratus the leader of armies Cases may be pointed out in which something which could have no real effect but to make persons think of misfortune was regarded not merely as a prognostic but as something approaching to an actual cause of it The of the Greeks and favete linguis or bona verba quaeso of the Romans evince the care with which they endeavoured to repress the utterance of any word expressive or suggestive of ill fortune not from notions of delicate politeness to which their general mode of conduct and feeling had very little reference but from bona fide alarm lest the event so suggested to the imagination should in fact occur Some vestige of a similar superstition has been known to exist among uneducated persons even in our own day it is thought an unchristian thing to talk of or suppose the death of any person while he is alive It is known how careful the Romans were to avoid by an indirect mode of speech the utterance of any word directly expressive of death or other calamity how instead of mortuus est they said vixit and be the event fortunate or otherwise instead of adverse The name Maleventum of which Salmasius so sagaciously detected the Thessalian origin they changed into the highly propitious denomination Beneventum Egesta into Segesta and Epidamnus a name so interesting in its associations to the reader of Thucydides they exchanged for Dyrrhachium to escape the perils of a word suggestive of damnum or detriment If a hare cross the highway says Sir Thomas Browne there are few above threescore that are not perplexed thereat which notwithstanding is but an augurial terror according to that received expression Inauspicatum dat iter oblatus lepus And the ground of the conceit was probably no greater than this that a fearful animal passing by us portended unto us something to be feared as upon the like consideration the meeting of a fox presaged some future imposture Such superstitions as these last must be the result of study they are too recondite for natural or spontaneous growth But when the attempt was once made to construct a science of predictions any association though ever so faint or remote by which an object could be connected in however farfetched a manner with ideas either of prosperity or of danger and misfortune was enough to determine its being classed among good or evil omens An example of rather a different kind from any of these but falling under the same principle is the famous attempt on which so much labour and ingenuity were expended by the alchemists to make gold potable The motive to this was a conceit that potable gold could be no other than the universal medicine and why gold Because it was so precious It must have all marvellous properties as a physical substance because the mind was already accustomed to marvel at it From a similar feeling every substance says Dr Paris whose origin is involved in mystery has at different times been eagerly applied to the purposes of medicine Not long since one of those showers which are now known to consist of the excrements of insects fell in the north of Italy the inhabitants regarded it as manna or some supernatural panacea and they swallowed it with such avidity that it was only by extreme address that a small quantity was obtained for a chemical examination The superstition in this instance though doubtless partly of a religious character probably in part also arose from the prejudice that a wonderful thing must of course have wonderful properties The instances of a priori fallacy which we have hitherto cited belong to the class of vulgar errors and do not now nor in any but a rude age ever could impose upon minds of any considerable attainments But those to which we are about to proceed have been and still are all but universally prevalent among thinkers The same disposition to give objectivity to a law of the mind to suppose that what is true of our ideas of things must be true of the things themselves exhibits itself in many of the most accredited modes of philosophical investigation both on physical and on metaphysical subjects In one of its most undisguised manifestations it embodies itself in two maxims which lay claim to axiomatic truth Things which we can not think of together can not coexist and Things which we can not help thinking of together must coexist I am not sure that the maxims were ever expressed in these precise words but the history both of philosophy and of popular opinions abounds with exemplifications of both forms of the doctrine To begin with the latter of them Things which we can not think of except together must exist together This is assumed in the generally received and accredited mode of reasoning which concludes that A must accompany B in point of fact, because it is involved in the idea Such thinkers do not reflect that the idea being a result of abstraction ought to conform to the facts and can not make the facts conform to it The argument is at most admissible as an appeal to authority a surmise that what is now part of the idea must before it became so have been found by previous inquirers in the facts Nevertheless the philosopher who more than all others made professions of rejecting authority Descartes constructed his system on this very basis His favourite device for arriving at truth even in regard to outward things was by looking into his own mind for it Credidi me says his celebrated maxim pro regula generali sumere posse omne id quod vald dilucid et distinct concipiebam verum esse whatever can be very clearly conceived must certainly exist that is as he afterward explains it if the idea includes existence And on this ground he infers that geometrical figures really exist because they can be distinctly conceived Whenever existence is involved in an idea a thing conformable to the idea must really exist which is as much as to say whatever the idea contains must have its equivalent in the thing and what we are not able to leave out of the idea can not be absent from the reality This assumption pervades the philosophy not only of Descartes but of all the thinkers who received their impulse mainly from him in particular the two most remarkable among them Spinoza and Leibnitz from whom the modern German metaphysical philosophy is essentially an emanation I am indeed disposed to think that the fallacy now under consideration has been the cause of twothirds of the bad philosophy and especially of the bad metaphysics which the human mind has never ceased to produce Our general ideas contain nothing but what has been put into them either by our passive experience or by our active habits of thought and the metaphysicians in all ages who have attempted to construct the laws of the universe by reasoning from our supposed necessities of thought have always proceeded and only could proceed by laboriously finding in their own minds what they themselves had formerly put there and evolving from their ideas of things what they had first involved in those ideas In this way all deeplyrooted opinions and feelings are enabled to create apparent demonstrations of their truth and reasonableness as it were out of their own substance The other form of the fallacy Things which we can not think of together can not exist together including as one of its branches that what we can not think of as existing can not exist at all may thus be briefly expressed Whatever is inconceivable must be false Against this prevalent doctrine I have sufficiently argued in a former Book and nothing is required in this place but examples It was long held that Antipodes were impossible because of the difficulty which was found in conceiving persons with their heads in the same direction as our feet And it was one of the received arguments against the Copernican system that we can not conceive so great a void space as that system supposes to exist in the celestial regions When men’s imaginations had always been used to conceive the stars as firmly set in solid spheres they naturally found much difficulty in imagining them in so different and as it doubtless appeared to them so precarious a situation But they had no right to mistake the limitation whether natural or as it in fact proved only artificial of their own faculties for an inherent limitation of the possible modes of existence in the universe It may be said in objection that the error in these cases was in the minor premise not the major an error of fact not of principle that it did not consist in supposing that what is inconceivable can not be true but in supposing antipodes to be inconceivable when present experience proves that they can be conceived Even if this objection were allowed and the proposition that what is inconceivable can not be true were suffered to remain unquestioned as a speculative truth it would be a truth on which no practical consequence could ever be founded since on this showing it is impossible to affirm of any proposition not being a contradiction in terms that it is inconceivable Antipodes were really not fictitiously inconceivable to our ancestors they are indeed conceivable to us and as the limits of our power of conception have been so largely extended by the extension of our experience and the more varied exercise of our imagination so may posterity find many combinations perfectly conceivable to them which are inconceivable to us But as beings of limited experience we must always and necessarily have limited conceptive powers while it does not by any means follow that the same limitation obtains in the possibilities of Nature nor even in her actual manifestations Rather more than a century and a half ago it was a scientific maxim disputed by no one and which no one deemed to require any proof that a thing can not act where it is not With this weapon the Cartesians waged a formidable war against the theory of gravitation which according to them involving so obvious an absurdity must be rejected in limine the sun could not possibly act upon the earth not being there It was not surprising that the adherents of the old systems of astronomy should urge this objection against the new but the false assumption imposed equally on Newton himself who in order to turn the edge of the objection imagined a subtle ether which filled up the space between the sun and the earth and by its intermediate agency was the proximate cause of the phenomena of gravitation It is inconceivable said Newton in one of his letters to Dr Bentley that inanimate brute matter should without the mediation of something else which is not material operate upon and affect other matter without mutual contact That gravity should be innate inherent and essential to matter so that one body may act on another at a distance through a vacuum without the mediation of any thing else by and through which their action and force may be conveyed from one to another is to me so great an absurdity that I believe no man who in philosophical matters has a competent faculty of thinking can ever fall into it This passage should be hung up in the cabinet of every cultivator of science who is ever tempted to pronounce a fact impossible because it appears to him inconceivable In our own day one would be more tempted though with equal injustice to reverse the concluding observation and consider the seeing any absurdity at all in a thing so simple and natural to be what really marks the absence of a competent faculty of thinking No one now feels any difficulty in conceiving gravity to be as much as any other property is inherent and essential to matter nor finds the comprehension of it facilitated in the smallest degree by the supposition of an ether though some recent inquirers do give this as an explanation of it nor thinks it at all incredible that the celestial bodies can and do act where they in actual bodily presence are not To us it is not more wonderful that bodies should act upon one another without mutual contact than that they should do so when in contact we are familiar with both these facts and we find them equally inexplicable but equally easy to believe To Newton the one because his imagination was familiar with it appeared natural and a matter of course while the other for the contrary reason seemed too absurd to be credited It is strange that any one after such a warning should rely implicitly on the evidence a priori of such propositions as these that matter can not think that space or extension is infinite that nothing can be made out of nothing ex nihilo nihil fit Whether these propositions are true or not this is not the place to determine nor even whether the questions are soluble by the human faculties But such doctrines are no more selfevident truths than the ancient maxim that a thing can not act where it is not which probably is not now believed by any educated person in Europe Matter can not think why because we can not conceive thought to be annexed to any arrangement of material particles Space is infinite because having never known any part of it which had not other parts beyond it we can not conceive an absolute termination Ex nihilo nihil fit because having never known any physical product without a preexisting physical material we can not or think we can not imagine a creation out of nothing But these things may in themselves be as conceivable as gravitation without an intervening medium which Newton thought too great an absurdity for any person of a competent faculty of philosophical thinking to admit and even supposing them not conceivable this for aught we know may be merely one of the limitations of our very limited minds and not in nature at all No writer has more directly identified himself with the fallacy now under consideration or has embodied it in more distinct terms than Leibnitz In his view unless a thing was not merely conceivable but even explainable it could not exist in nature All natural phenomena according to him must be susceptible of being accounted for a priori The only facts of which no explanation could be given but the will of God were miracles properly so called Je reconnais says he qu’il n’est pas permis de nier ce qu’on n’entend pas mais j’ajoute qu’on a droit de nier au moins dans l’ordre naturel ce que absolument n’est point intelligible ni explicable Je soutiens aussi qu’enfin la conception des cratures n’est pas la mesure du pouvoir de Dieu mais que leur conceptivit ou force de concevoir est la mesure du pouvoir de la nature tout ce qui est conforme ˆ l’ordre naturel pouvant tre conu ou entendu par quelque crature Not content with assuming that nothing can be true which we are unable to conceive scientific inquirers have frequently given a still further extension to the doctrine and held that even of things not altogether inconceivable that which we can conceive with the greatest ease is likeliest to be true It was long an admitted axiom and is not yet entirely discredited that nature always acts by the simplest means ie by those which are most easily conceivable A large proportion of all the errors ever committed in the investigation of the laws of nature have arisen from the assumption that the most familiar explanation or hypothesis must be the truest One of the most instructive facts in scientific history is the pertinacity with which the human mind clung to the belief that the heavenly bodies must move in circles or be carried round by the revolution of spheres merely because those were in themselves the simplest suppositions though to make them accord with the facts which were ever contradicting them more and more it became necessary to add sphere to sphere and circle to circle until the original simplicity was converted into almost inextricable complication We pass to another a priori fallacy or natural prejudice allied to the former and originating as that does in the tendency to presume an exact correspondence between the laws of the mind and those of things external to it The fallacy may be enunciated in this general form Whatever can be thought of apart exists apart and its most remarkable manifestation consists in the personification of abstractions Mankind in all ages have had a strong propensity to conclude that wherever there is a name there must be a distinguishable separate entity corresponding to the name and every complex idea which the mind has formed for itself by operating upon its conceptions of individual things was considered to have an outward objective reality answering to it Fate Chance Nature Time Space were real beings nay even gods If the analysis of qualities in the earlier part of this work be correct names of qualities and names of substances stand for the very same sets of facts or phenomena whiteness and a white thing are only different phrases required by convenience for speaking of the same external fact under different relations Not such however was the notion which this verbal distinction suggested of old either to the vulgar or to the scientific Whiteness was an entity inhering or sticking in the white substance and so of all other qualities So far was this carried that even concrete general terms were supposed to be not names of indefinite numbers of individual substances but names of a peculiar kind of entities termed Universal Substances Because we can think and speak of man in general that is of all persons in so far as possessing the common attributes of the species without fastening our thoughts permanently on some one individual person therefore man in general was supposed to be not an aggregate of individual persons but an abstract or universal man distinct from these It may be imagined what havoc metaphysicians trained in these habits made with philosophy when they came to the largest generalizations of all Substantiae Secundae of any kind were bad enough but such Substantiae Secundae as for example and standing for peculiar entities supposed to be inherent in all things which exist or in all which are said to be one were enough to put an end to all intelligible discussion especially since with a just perception that the truths which philosophy pursues are general truths it was soon laid down that these general substances were the only subjects of science being immutable while individual substances cognizable by the senses being in a perpetual flux could not be the subject of real knowledge This misapprehension of the import of general language constitutes Mysticism a word so much oftener written and spoken than understood Whether in the Vedas in the Platonists or in the Hegelians mysticism is neither more nor less than ascribing objective existence to the subjective creations of our own faculties to ideas or feelings of the mind and believing that by watching and contemplating these ideas of its own making it can read in them what takes place in the world without Proceeding with the enumeration of a priori fallacies and endeavouring to arrange them with as much reference as possible to their natural affinities we come to another which is also nearly allied to the fallacy preceding the last standing in the same relation to one variety of it as the fallacy last mentioned does to the other This too represents nature as under incapacities corresponding to those of our intellect but instead of only asserting that nature can not do a thing because we can not conceive it done goes the still greater length of averring that nature does a particular thing on the sole ground that we can see no reason why she should not Absurd as this seems when so plainly stated it is a received principle among scientific authorities for demonstrating a priori the laws of physical phenomena A phenomenon must follow a certain law because we see no reason why it should deviate from that law in one way rather than in another This is called the Principle of the Sufficient Reason and by means of it philosophers often flatter themselves that they are able to establish without any appeal to experience the most general truths of experimental physics Take for example two of the most elementary of all laws the law of inertia and the first law of motion A body at rest can not it is affirmed begin to move unless acted upon by some external force because if it did it must either move up or down forward or backward and so forth but if no outward force acts upon it there can be no reason for its moving up rather than down or down rather than up etc ergo it will not move at all This reasoning I conceive to be entirely fallacious as indeed Dr Brown in his treatise on Cause and Effect has shown with great acuteness and justness of thought We have before remarked that almost every fallacy may be referred to different genera by different modes of filling up the suppressed steps and this particular one may at our option be brought under petitio principii It supposes that nothing can be a sufficient reason for a body’s moving in one particular direction except some external force But this is the very thing to be proved Why not some internal force Why not the law of the thing’s own nature Since these philosophers think it necessary to prove the law of inertia they of course do not suppose it to be selfevident they must therefore be of opinion that previously to all proof the supposition of a body’s moving by internal impulse is an admissible hypothesis but if so why is not the hypothesis also admissible that the internal impulse acts naturally in some one particular direction not in another If spontaneous motion might have been the law of matter why not spontaneous motion toward the sun toward the earth or toward the zenith Why not as the ancients supposed toward a particular place in the universe appropriated to each particular kind of substance Surely it is not allowable to say that spontaneity of motion is credible in itself but not credible if supposed to take place in any determinate direction Indeed if any one chose to assert that all bodies when uncontrolled set out in a direct line toward the North Pole he might equally prove his point by the principle of the Sufficient Reason By what right is it assumed that a state of rest is the particular state which can not be deviated from without special cause Why not a state of motion and of some particular sort of motion Why may we not say that the natural state of a horse left to himself is to amble because otherwise he must either trot gallop or stand still and because we know no reason why he should do one of these rather than another If this is to be called an unfair use of the sufficient reason and the other a fair one there must be a tacit assumption that a state of rest is more natural to a horse than a state of ambling If this means that it is the state which the animal will assume when left to himself that is the very point to be proved and if it does not mean this it can only mean that a state of rest is the simplest state and therefore the most likely to prevail in nature which is one of the fallacies or natural prejudices we have already examined So again of the First Law of Motion that a body once moving will if left to itself continue to move uniformly in a straight line An attempt is made to prove this law by saying that if not the body must deviate either to the right or to the left and that there is no reason why it should do one more than the other But who could know antecedently to experience whether there was a reason or not Might it not be the nature of bodies or of some particular bodies to deviate toward the right or if the supposition is preferred toward the east or south It was long thought that bodies terrestrial ones at least had a natural tendency to deflect downward and there is no shadow of any thing objectionable in the supposition except that it is not true The pretended proof of the law of motion is even more manifestly untenable than that of the law of inertia for it is flagrantly inconsistent it assumes that the continuance of motion in the direction first taken is more natural than deviation either to the right or to the left but denies that one of these can possibly be more natural than the other All these fancies of the possibility of knowing what is natural or not natural by any other means than experience are in truth entirely futile The real and only proof of the laws of motion or of any other law of the universe is experience it is simply that no other suppositions explain or are consistent with the facts of universal nature Geometers have in all ages been open to the imputation of endeavouring to prove the most general facts of the outward world by sophistical reasoning in order to avoid appeals to the senses Archimedes says Professor Playfair established some of the elementary propositions of statics by a process in which he borrows no principle from experiment but establishes his conclusion entirely by reasoning a priori He assumes indeed that equal bodies at the ends of the equal arms of a lever will balance one another and also that a cylinder or parallelopiped of homogeneous matter will be balanced about its centre of magnitude These however are not inferences from experience they are properly speaking conclusions deduced from the principle of the Sufficient Reason And to this day there are few geometers who would not think it far more scientific to establish these or any other premises in this way than to rest their evidence on that familiar experience which in the case in question might have been so safely appealed to Another natural prejudice of most extensive prevalence and which had a great share in producing the errors fallen into by the ancients in their physical inquiries was this That the differences in nature must correspond to our received distinctions that effects which we are accustomed in popular language to call by different names and arrange in different classes must be of different natures and have different causes This prejudice so evidently of the same origin with those already treated of marks more especially the earliest stage of science when it has not yet broken loose from the trammels of everyday phraseology The extraordinary prevalence of the fallacy among the Greek philosophers may be accounted for by their generally knowing no other language than their own from which it was a consequence that their ideas followed the accidental or arbitrary combinations of that language more completely than can happen among the moderns to any but illiterate persons They had great difficulty in distinguishing between things which their language confounded or in putting mentally together things which it distinguished and could hardly combine the objects in nature into any classes but those which were made for them by the popular phrases of their own country or at least could not help fancying those classes to be natural and all others arbitrary and artificial Accordingly scientific investigation among the Greek schools of speculation and their followers in the Middle Ages was little more than a mere sifting and analyzing of the notions attached to common language They thought that by determining the meaning of words they could become acquainted with facts They took for granted says Dr Whewell that philosophy must result from the relations of those notions which are involved in the common use of language and they proceeded to seek it by studying such notions In his next chapter Dr Whewell has so well illustrated and exemplified this error that I shall take the liberty of quoting him at some length The propensity to seek for principles in the common usages of language may be discerned at a very early period Thus we have an example of it in a saying which is reported of Thales the founder of Greek philosophy When he was asked What is the greatest thing’ he replied Place for all other things are in the world but the world is in it’ In Aristotle we have the consummation of this mode of speculation The usual point from which he starts in his inquiries is that we say thus or thus in common language Thus when he has to discuss the question whether there be in any part of the universe a void or space in which there is nothing he inquires first in how many senses we say that one thing is in another He enumerates many of these we say the part is in the whole as the finger is in the hand again we say the species is in the genus as man is included in animal again the government of Greece is in the king and various other senses are described and exemplified but of all these the most proper is when we say a thing is in a vessel and generally in place He next examines what place is and comes to this conclusion that if about a body there be another body including it it is in place and if not not’ A body moves when it changes its place but he adds that if water be in a vessel the vessel being at rest the parts of the water may still move for they are included by each other so that while the whole does not change its place the parts may change their place in a circular order Proceeding then to the question of a void he as usual examines the different senses in which the term is used and adopts as the most proper place without matter with no useful result Again in a question concerning mechanical action he says When a man moves a stone by pushing it with a stick we say both that the man moves the stone and that the stick moves the stone but the latter more properly’ Again we find the Greek philosophers applying themselves to extract their dogmas from the most general and abstract notions which they could detect for example from the conception of the Universe as One or as Many things They tried to determine how far we may or must combine with these conceptions that of a whole of parts of number of limits of place of beginning or end of full or void of rest or motion of cause and effect, and the like The analysis of such conceptions with such a view occupies for instance almost the whole of Aristotle’s Treatise on the Heavens The following paragraph merits particular attention Another mode of reasoning very widely applied in these attempts was the doctrine of contrarieties in which it was assumed that adjectives or substances which are in common language or in some abstract mode of conception opposed to each other must point at some fundamental antithesis in nature which it is important to study Thus Aristotle says that the Pythagoreans from the contrasts which number suggests collected ten principles Limited and Unlimited Odd and Even One and Many Right and Left Male and Female Rest and Motion Straight and Curved Light and Darkness Good and Evil Square and Oblong Aristotle himself deduced the doctrine of four elements and other dogmas by oppositions of the same kind Of the manner in which from premises obtained in this way the ancients attempted to deduce laws of nature an example is given in the same work a few pages further on Aristotle decides that there is no void on such arguments as this In a void there could be no difference of up and down for as in nothing there are no differences so there are none in a privation or negation but a void is merely a privation or negation of matter therefore in a void bodies could not move up and down which it is in their nature to do It is easily seen Dr Whewell very justly adds that such a mode of reasoning elevates the familiar forms of language and the intellectual connections of terms to a supremacy over facts making truth depend upon whether terms are or are not privative and whether we say that bodies fall naturally The propensity to assume that the same relations obtain between objects themselves which obtain between our ideas of them is here seen in the extreme stage of its development For the mode of philosophizing exemplified in the foregoing instances assumes no less than that the proper way of arriving at knowledge of nature is to study nature itself subjectively to apply our observation and analysis not to the facts but to the common notions entertained of the facts Many other equally striking examples may be given of the tendency to assume that things which for the convenience of common life are placed in different classes must differ in every respect Of this nature was the universal and deeplyrooted prejudice of antiquity and the Middle Ages that celestial and terrestrial phenomena must be essentially different and could in no manner or degree depend on the same laws Of the same kind also was the prejudice against which Bacon contended that nothing produced by nature could be successfully imitated by man Calorem solis et ignis toto genere differre ne scilicet homines putent se per opera ignis aliquid simile iis quae in Natura fiunt educere et formare posse and again Compositionem tantum opus Hominis Mistionem vero opus solius Naturae esse ne scilicet homines sperent aliquam ex arte Corporum naturalium generationem aut transformationem The grand distinction in the ancient scientific speculations between natural and violent motions though not without a plausible foundation in the appearances themselves was doubtless greatly recommended to adoption by its conformity to this prejudice From the fundamental error of the scientific inquirers of antiquity we pass by a natural association to a scarcely less fundamental one of their great rival and successor Bacon It has excited the surprise of philosophers that the detailed system of inductive logic which this extraordinary man laboured to construct has been turned to so little direct use by subsequent inquirers having neither continued except in a few of its generalities to be recognized as a theory nor having conducted in practice to any great scientific results But this though not unfrequently remarked has scarcely received any plausible explanation and some indeed have preferred to assert that all rules of induction are useless rather than suppose that Bacon’s rules are grounded on an insufficient analysis of the inductive process Such however will be seen to be the fact as soon as it is considered that Bacon entirely overlooked Plurality of Causes All his rules tacitly imply the assumption so contrary to all we now know of nature that a phenomenon can not have more than one cause When he is inquiring into what he terms the forma calidi aut frigidi gravis aut levis sicci aut humidi and the like he never for an instant doubts that there is some one thing some invariable condition or set of conditions which is present in all cases of heat or cold or whatever other phenomenon he is considering the only difficulty being to find what it is which accordingly he tries to do by a process of elimination rejecting or excluding by negative instances whatever is not the forma or cause in order to arrive at what is But that this forma or cause is one thing and that it is the same in all hot objects he has no more doubt of than another person has that there is always some cause or other In the present state of knowledge it could not be necessary even if we had not already treated so fully of the question to point out how widely this supposition is at variance with the truth It is particularly unfortunate for Bacon that falling into this error he should have fixed almost exclusively upon a class of inquiries in which it was especially fatal namely inquiries into the causes of the sensible qualities of objects For his assumption groundless in every case is false in a peculiar degree with respect to those sensible qualities In regard to scarcely any of them has it been found possible to trace any unity of cause any set of conditions invariably accompanying the quality The conjunctions of such qualities with one another constitute the variety of Kinds in which as already remarked it has not been found possible to trace any law Bacon was seeking for what did not exist The phenomenon of which he sought for the one cause has oftenest no cause at all and when it has depends as far as hitherto ascertained on an unassignable variety of distinct causes And on this rock every one must split who represents to himself as the first and fundamental problem of science to ascertain what is the cause of a given effect rather than what are the effects of a given cause It was shown in an early stage of our inquiry into the nature of Induction how much more ample are the resources which science commands for the latter than for the former inquiry since it is upon the latter only that we can throw any direct light by means of experiment the power of artificially producing an effect implying a previous knowledge of at least one of its causes If we discover the causes of effects it is generally by having previously discovered the effects of causes the greatest skill in devising crucial instances for the former purpose may only end as Bacon’s physical inquiries did in no result at all Was it that his eagerness to acquire the power of producing for man’s benefit effects of practical importance to human life rendering him impatient of pursuing that end by a circuitous route made even him the champion of experiment prefer the direct mode though one of mere observation to the indirect in which alone experiment was possible Or had even Bacon not entirely cleared his mind from the notion of the ancients that rerum cognoscere causas was the sole object of philosophy and that to inquire into the effects of things belonged to servile and mechanical arts It is worth remarking that while the only efficient mode of cultivating speculative science was missed from an undue contempt of manual operations the false speculative views thus engendered gave in their turn a false direction to such practical and mechanical aims as were suffered to exist The assumption universal among the ancients and in the Middle Ages that there were principles of heat and cold dryness and moisture etc led directly to a belief in alchemy in a transmutation of substances a change from one Kind into another Why should it not be possible to make gold Each of the characteristic properties of gold has its forma its essence its set of conditions which if we could discover and learn how to realize we could superinduce that particular property upon any other substance upon wood or iron or lime or clay If then we could effect this with respect to every one of the essential properties of the precious metal we should have converted the other substance into gold Nor did this if once the premises were granted appear to transcend the real powers of mankind For daily experience showed that almost every one of the distinctive sensible properties of any object its consistence its color its taste its smell its shape admitted of being totally changed by fire or water or some other chemical agent The formae of all those qualities seeming therefore to be within human power either to produce or to annihilate not only did the transmutation of substances appear abstractedly possible but the employment of the power at our choice for practical ends seemed by no means hopeless A prejudice universal in the ancient world and from which Bacon was so far from being free that it pervaded and vitiated the whole practical part of his system of logic may with good reason be ranked high in the order of Fallacies of which we are now treating There remains one a priori fallacy or natural prejudice the most deeplyrooted perhaps of all which we have enumerated one which not only reigned supreme in the ancient world but still possesses almost undisputed dominion over many of the most cultivated minds and some of the most remarkable of the numerous instances by which I shall think it necessary to exemplify it will be taken from recent thinkers This is that the conditions of a phenomenon must or at least probably will resemble the phenomenon itself Conformably to what we have before remarked to be of frequent occurrence this fallacy might without much impropriety have been placed in a different class among Fallacies of Generalization for experience does afford a certain degree of countenance to the assumption The cause does in very many cases resemble its effect like produces like Many phenomena have a direct tendency to perpetuate their own existence or to give rise to other phenomena similar to themselves Not to mention forms actually moulded on one another as impressions on wax and the like in which the closest resemblance between the effect and its cause is the very law of the phenomenon all motion tends to continue itself with its own velocity and in its own original direction and the motion of one body tends to set others in motion which is indeed the most common of the modes in which the motions of bodies originate We need scarcely refer to contagion fermentation and the like or to the production of effects by the growth or expansion of a germ or rudiment resembling on a smaller scale the completed phenomenon as in the growth of a plant or animal from an embryo that embryo itself deriving its origin from another plant or animal of the same kind Again the thoughts or reminiscences which are effects of our past sensations resemble those sensations feelings produce similar feelings by way of sympathy acts produce similar acts by involuntary or voluntary imitation With so many appearances in its favour no wonder if a presumption naturally grew up that causes must necessarily resemble their effects and that like could only be produced by like This principle of fallacy has usually presided over the fantastical attempts to influence the course of nature by conjectural means the choice of which was not directed by previous observation and experiment The guess almost always fixed upon some means which possessed features of real or apparent resemblance to the end in view If a charm was wanted as by Ovid’s Medea to prolong life all longlived animals or what were esteemed such were collected and brewed into a broth nec defuit illic Squamea Cinyphii tenuis membrana chelydri Vivacisque jecur cervi quibus insuper addit Ora caputque novem cornicis saecula passae A similar notion was embodied in the celebrated medical theory called the Doctrine of Signatures which is no less says Dr Paris than a belief that every natural substance which possesses any medicinal virtue indicates by an obvious and wellmarked external character the disease for which it is a remedy or the object for which it should be employed This outward character was generally some feature of resemblance real or fantastical either to the effect it was supposed to produce or to the phenomenon over which its power was thought to be exercised Thus the lungs of a fox must be a specific for asthma because that animal is remarkable for its strong powers of respiration Turmeric has a brilliant yellow color which indicates that it has the power of curing the jaundice for the same reason poppies must relieve diseases of the head Agaricus those of the bladder Cassia fistula the affections of the intestines and Aristolochia the disorders of the uterus the polished surface and stony hardness which so eminently characterize the seeds of the Lithospermum officinale common gromwell were deemed a certain indication of their efficacy in calculous and gravelly disorders for a similar reason the roots of the Saxifraga granulata white saxifrage gained reputation in the cure of the same disease and the Euphrasia eyebright acquired fame as an application in complaints of the eye because it exhibits a black spot in its corolla resembling the pupil The bloodstone the Heliotropium of the ancients from the occasional small specks or points of a bloodred color exhibited on its green surface is even at this very day employed in many parts of England and Scotland to stop a bleeding from the nose and nettle tea continues a popular remedy for the cure of Urticaria It is also asserted that some substances bear the signatures of the humours as the petals of the red rose that of the blood and the roots of rhubarb and the flowers of saffron that of the bile The early speculations respecting the chemical composition of bodies were rendered abortive by no circumstance more than by their invariably taking for granted that the properties of the elements must resemble those of the compounds which were formed from them To descend to more modern instances it was long thought and was stoutly maintained by the Cartesians and even by Leibnitz against the Newtonian system nor did Newton himself as we have seen contest the assumption but eluded it by an arbitrary hypothesis that nothing of a physical nature at least could account for motion except previous motion the impulse or impact of some other body It was very long before the scientific world could prevail upon itself to admit attraction and repulsion ie spontaneous tendencies of particles to approach or recede from one another as ultimate laws no more requiring to be accounted for than impulse itself if indeed the latter were not in truth resolvable into the former From the same source arose the innumerable hypotheses devised to explain those classes of motion which appeared more mysterious than others because there was no obvious mode of attributing them to impulse as for example the voluntary motions of the human body Such were the interminable systems of vibrations propagated along the nerves or animal spirits rushing up and down between the muscles and the brain which if the facts could have been proved would have been an important addition to our knowledge of physiological laws but the mere invention or arbitrary supposition of them could not unless by the strongest delusion be supposed to render the phenomena of animal life more comprehensible or less mysterious Nothing however seemed satisfactory but to make out that motion was caused by motion by something like itself If it was not one kind of motion it must be another In like manner it was supposed that the physical qualities of objects must arise from some similar quality or perhaps only some quality bearing the same name in the particles or atoms of which the objects were composed that a sharp taste for example must arise from sharp particles And reversing the inference the effects produced by a phenomenon must it was supposed resemble in their physical attributes the phenomenon itself The influences of the planets were supposed to be analogous to their visible peculiarities Mars being of a red color portended fire and slaughter and the like Passing from physics to metaphysics we may notice among the most remarkable fruits of this a priori fallacy two closely analogous theories employed in ancient and modern times to bridge over the chasm between the world of mind and that of matter the species sensibiles of the Epicureans and the modern doctrine of perception by means of ideas These theories are indeed probably indebted for their existence not solely to the fallacy in question but to that fallacy combined with another natural prejudice already adverted to that a thing can not act where it is not In both doctrines it is assumed that the phenomenon which takes place in us when we see or touch an object and which we regard as an effect of that object or rather of its presence to our organs must of necessity resemble very closely the outward object itself To fulfil this condition the Epicureans supposed that objects were constantly projecting in all directions impalpable images of themselves which entered at the eyes and penetrated to the mind while modern metaphysicians though they rejected this hypothesis agreed in deeming it necessary to suppose that not the thing itself but a mental image or representation of it was the direct object of perception Dr Reid had to employ a world of argument and illustration to familiarize people with the truth that the sensations or impressions on our minds need not necessarily be copies of or bear any resemblance to the causes which produce them in opposition to the natural prejudice which led people to assimilate the action of bodies upon our senses and through them upon our minds to the transfer of a given form from one object to another by actual moulding The works of Dr Reid are even now the most effectual course of study for detaching the mind from the prejudice of which this was an example And the value of the service which he thus rendered to popular philosophy is not much diminished although we may hold with Brown that he went too far in imputing the ideal theory as an actual tenet to the generality of the philosophers who preceded him and especially to Locke and Hume for if they did not themselves consciously fall into the error unquestionably they often led their readers into it The prejudice that the conditions of a phenomenon must resemble the phenomenon is occasionally exaggerated at least verbally into a still more palpable absurdity the conditions of the thing are spoken of as if they were the very thing itself In Bacon’s model inquiry which occupies so great a space in the Novum Organum the inquisitio in formam calidi the conclusion which he favours is that heat is a kind of motion meaning of course not the feeling of heat but the conditions of the feeling meaning therefore only that wherever there is heat there must first be a particular kind of motion but he makes no distinction in his language between these two ideas expressing himself as if heat and the conditions of heat were one and the same thing So the elder Darwin in the beginning of his Zoonomia says The word idea has various meanings in the writers of metaphysics it is here used simply for those notions of external things which our organs of sense bring us acquainted with originally thus far the proposition though vague is unexceptionable in meaning and is defined a contraction a motion or configuration of the fibres which constitute the immediate organ of sense Our notions a configuration of the fibres What kind of logician must he be who thinks that a phenomenon is defined to be the condition on which he supposes it to depend Accordingly he says soon after not that our ideas are caused by or consequent on certain organic phenomena but our ideas are animal motions of the organs of sense And this confusion runs through the four volumes of the Zoonomia the reader never knows whether the writer is speaking of the effect or of its supposed cause of the idea a state of mental consciousness or of the state of the nerves and brain which he considers it to presuppose I have given a variety of instances in which the natural prejudice that causes and their effects must resemble one another has operated in practice so as to give rise to serious errors I shall now go further and produce from writings even of the present or very recent times instances in which this prejudice is laid down as an established principle M Victor Cousin in the last of his celebrated lectures on Locke enunciates the maxim in the following unqualified terms Tout ce qui est vrai de l’effet est vrai de la cause A doctrine to which unless in some peculiar and technical meaning of the words cause and effect it is not to be imagined that any person would literally adhere but he who could so write must be far enough from seeing that the very reverse might be the effect that there is nothing impossible in the supposition that no one property which is true of the effect might be true of the cause Without going quite so far in point of expression Coleridge in his Biographia Literaria affirms as an evident truth that the law of causality holds only between homogeneous things ie things having some common property and therefore can not extend from one world into another its opposite hence as mind and matter have no common property mind can not act upon matter nor matter upon mind What is this but the a priori fallacy of which we are speaking The doctrine like many others of Coleridge is taken from Spinoza in the first book of whose Ethica De Deo it stands as the Third Proposition Quae res nihil commune inter se habent earum una alterius causa esse non potest and is there proved from two socalled axioms equally gratuitous with itself but Spinoza ever systematically consistent pursued the doctrine to its inevitable consequence the materiality of God The same conception of impossibility led the ingenious and subtle mind of Leibnitz to his celebrated doctrine of a preestablished harmony He too thought that mind could not act upon matter nor matter upon mind and that the two therefore must have been arranged by their Maker like two clocks which though unconnected with one another strike simultaneously and always point to the same hour Malebranche’s equally famous theory of Occasional Causes was another form of the same conception instead of supposing the clocks originally arranged to strike together he held that when the one strikes God interposes and makes the other strike in correspondence with it Descartes in like manner whose works are a rich mine of almost every description of a priori fallacy says that the Efficient Cause must at least have all the perfections of the effect and for this singular reason Si enim ponamus aliquid in idea reperiri quod non fuerit in ejus causa hoc igitur habet a nihilo of which it is scarcely a parody to say that if there be pepper in the soup there must be pepper in the cook who made it since otherwise the pepper would be without a cause A similar fallacy is committed by Cicero in his second book De Finibus where speaking in his own person against the Epicureans he charges them with inconsistency in saying that the pleasures of the mind had their origin from those of the body and yet that the former were more valuable as if the effect could surpass the cause Animi voluptas oritur propter voluptatem corporis et major est animi voluptas quam corporis ita fit ut gratulator laetior sit quam is cui gratulatur Even that surely is not an impossibility a person’s good fortune has often given more pleasure to others than it gave to the person himself Descartes with no less readiness applies the same principle the converse way and infers the nature of the effects from the assumption that they must in this or that property or in all their properties resemble their cause To this class belong his speculations and those of so many others after him tending to infer the order of the universe not from observation but by a priori reasoning from supposed qualities of the Godhead This sort of inference was probably never carried to a greater length than it was in one particular instance by Descartes when as a proof of one of his physical principles that the quantity of motion in the universe is invariable he had recourse to the immutability of the Divine Nature Reasoning of a very similar character is however nearly as common now as it was in his time and does duty largely as a means of fencing off disagreeable conclusions Writers have not yet ceased to oppose the theory of divine benevolence to the evidence of physical facts to the principle of population for example And people seem in general to think that they have used a very powerful argument when they have said that to suppose some proposition true would be a reflection on the goodness or wisdom of the Deity Put into the simplest possible terms their argument is If it had depended on me I would not have made the proposition true therefore it is not true Put into other words it stands thus God is perfect therefore what I think perfection must obtain in nature But since in reality every one feels that nature is very far from perfect the doctrine is never applied consistently It furnishes an argument which like many others of a similar character people like to appeal to when it makes for their own side Nobody is convinced by it but each appears to think that it puts religion on his side of the question and that it is a useful weapon of offense for wounding an adversary Although several other varieties of a priori fallacy might probably be added to those here specified these are all against which it seems necessary to give any special caution Our object is to open without attempting or affecting to exhaust the subject Having illustrated therefore this first class of Fallacies at sufficient length I shall proceed to the second From the Fallacies which are properly Prejudices or presumptions antecedent to and superseding proof we pass to those which lie in the incorrect performance of the proving process And as Proof in its widest extent embraces one or more or all of three processes Observation Generalization and Deduction we shall consider in their order the errors capable of being committed in these three operations And first of the first mentioned A fallacy of misobservation may be either negative or positive either Nonobservation or Malobservation It is nonobservation when all the error consists in overlooking or neglecting facts or particulars which ought to have been observed It is malobservation when something is not simply unseen but seen wrong when the fact or phenomenon instead of being recognized for what it is in reality is mistaken for something else Nonobservation may either take place by overlooking instances or by overlooking some of the circumstances of a given instance If we were to conclude that a fortuneteller was a true prophet from not adverting to the cases in which his predictions had been falsified by the event this would be nonobservation of instances but if we overlooked or remained ignorant of the fact that in cases where the predictions had been fulfilled he had been in collusion with some one who had given him the information on which they were grounded this would be nonobservation of circumstances The former case in so far as the act of induction from insufficient evidence is concerned does not fall under this second class of Fallacies but under the third Fallacies of Generalization In every such case however there are two defects or errors instead of one there is the error of treating the insufficient evidence as if it were sufficient which is a Fallacy of the third class and there is the insufficiency itself the not having better evidence which when such evidence or, in other words, when other instances were to be had is Nonobservation and the erroneous inference so far as it is to be attributed to this cause is a Fallacy of the second class It belongs not to our purpose to treat of nonobservation as arising from casual inattention from general slovenliness of mental habits want of due practice in the use of the observing faculties or insufficient interest in the subject The question pertinent to logic is Granting the want of complete competency in the observer on what point is that insufficiency on his part likely to lead him wrong or rather what sorts of instances or of circumstances in any given instance are most likely to escape the notice of observers generally of mankind at large First then it is evident that when the instances on one side of a question are more likely to be remembered and recorded than those on the other especially if there be any strong motive to preserve the memory of the first but not of the latter these last are likely to be overlooked and escape the observation of the mass of mankind This is the recognized explanation of the credit given in spite of reason and evidence to many classes of impostors to quackdoctors and fortunetellers in all ages to the cunning man of modern times and the oracles of old Few have considered the extent to which this fallacy operates in practice even in the teeth of the most palpable negative evidence A striking example of it is the faith which the uneducated portion of the agricultural classes in this and other countries continue to repose in the prophecies as to weather supplied by almanacmakers though every season affords to them numerous cases of completely erroneous prediction but as every season also furnishes some cases in which the prediction is fulfilled this is enough to keep up the credit of the prophet with people who do not reflect on the number of instances requisite for what we have called in our inductive terminology the Elimination of Chance since a certain number of casual coincidences not only may but will happen between any two unconnected events Coleridge in one of the essays in the Friend has illustrated the matter we are now considering in discussing the origin of a proverb which differently worded is to be found in all the languages of Europe viz Fortune favours fools He ascribes it partly to the tendency to exaggerate all effects that seem disproportionate to their visible cause and all circumstances that are in any way strongly contrasted with our notions of the persons under them Omitting some explanations which would refer the error to malobservation or to the other species of nonobservation that of circumstances I take up the quotation further on Unforeseen coincidences may have greatly helped a man yet if they have done for him only what possibly from his own abilities he might have effected for himself his good luck will excite less attention and the instances be less remembered That clever men should attain their objects seems natural and we neglect the circumstances that perhaps produced that success of themselves without the intervention of skill or foresight but we dwell on the fact and remember it as something strange when the same happens to a weak or ignorant man So too though the latter should fail in his undertakings from concurrences that might have happened to the wisest man yet his failure being no more than might have been expected and accounted for from his folly it lays no hold on our attention but fleets away among the other undistinguished waves in which the stream of ordinary life murmurs by us and is forgotten Had it been as true as it was notoriously false that those allembracing discoveries which have shed a dawn of science on the art of chemistry and give no obscure promise of some one great constitutive law in the light of which dwell dominion and the power of prophecy if these discoveries instead of having been as they really were preconcerted by meditation and evolved out of his own intellect had occurred by a set of lucky accidents to the illustrious father and founder of philosophic alchemy if they had presented themselves to Professor Davy exclusively in consequence of his luck in possessing a particular galvanic battery if this battery as far as Davy was concerned had itself been an accident and not as in point of fact it was desired and obtained by him for the purpose of insuring the testimony of experience to his principles and in order to bind down material nature under the inquisition of reason and force from her as by torture unequivocal answers to prepared and preconceived questions yet still they would not have been talked of or described as instances of luck but as the natural results of his admitted genius and known skill But should an accident have disclosed similar discoveries to a mechanic at Birmingham or Sheffield and if the man should grow rich in consequence and partly by the envy of his neighbours and partly with good reason be considered by them as a man below par in the general powers of his understanding then Oh what a lucky fellow Well Fortune does favour fools that’s for certain It is always so’ And forthwith the exclaimer relates half a dozen similar instances Thus accumulating the one sort of facts and never collecting the other we do as poets in their diction and quacks of all denominations do in their reasoning put a part for the whole This passage very happily sets forth the manner in which under the loose mode of induction which proceeds per enumerationem simplicem not seeking for instances of such a kind as to be decisive of the question but generalizing from any which occur or rather which are remembered opinions grow up with the apparent sanction of experience which have no foundation in the laws of nature at all Itaque recte respondit ille we may say with Bacon qui cum suspensa tabula in templo ei monstraretur eorum qui vota solverant quod naufragii periculo elapsi sint atque interrogando premeretur anne tum quidem Deorum numen agnosceret quaesivit denuo At ubi sunt illi depicti qui post vota nuncupata perierunt Eadem ratio est fere omnis superstitionis ut in Astrologicis in Somniis Ominibus Nemesibus et hujusmodi in quibus homines delectati hujusmodi vanitatibus advertunt eventus ubi implentur ast ubi fallunt licet multo frequentius tamen negligunt et praetereunt And he proceeds to say that independently of the love of the marvellous or any other bias in the inclinations there is a natural tendency in the intellect itself to this kind of fallacy since the mind is more moved by affirmative instances though negative ones are of most use in philosophy Is tamen humano intellectui error est proprius et perpetuus ut magis moveatur et excitetur Affirmativis quam Negativis cum rite et ordine aequum se utrique praebere debeat quin contra in omni Axiomate vero constituendo major vis est instantiae negativae But the greatest of all causes of nonobservation is a preconceived opinion This it is which in all ages has made the whole race of mankind and every separate section of it for the most part unobservant of all facts however abundant even when passing under their own eyes which are contradictory to any first appearance or any received tenet It is worth while to recall occasionally to the oblivious memory of mankind some of the striking instances in which opinions that the simplest experiment would have shown to be erroneous continued to be entertained because nobody ever thought of trying that experiment One of the most remarkable of these was exhibited in the Copernican controversy The opponents of Copernicus argued that the earth did not move because if it did a stone let fall from the top of a high tower would not reach the ground at the foot of the tower but at a little distance from it in a contrary direction to the earth’s course in the same manner said they as if a ball is let drop from the masthead while the ship is in full sail it does not fall exactly at the foot of the mast but nearer to the stern of the vessel The Copernicans would have silenced these objectors at once if they had tried dropping a ball from the masthead since they would have found that it does fall exactly at the foot as the theory requires but no they admitted the spurious fact and struggled vainly to make out a difference between the two cases The ball was no part of the ship and the motion forward was not natural either to the ship or to the ball The stone on the other hand let fall from the top of the tower was a part of the earth and therefore the diurnal and annular revolutions which were natural to the earth were also natural to the stone the stone would therefore retain the same motion with the tower and strike the ground precisely at the bottom of it Other examples scarcely less striking are recorded by Dr Whewell where imaginary laws of nature have continued to be received as real merely because no person had steadily looked at facts which almost every one had the opportunity of observing A vague and loose mode of looking at facts very easily observable left men for a long time under the belief that a body ten times as heavy as another falls ten times as fast that objects immersed in water are always magnified without regard to the form of the surface that the magnet exerts an irresistible force that crystal is always found associated with ice and the like These and many others are examples how blind and careless man can be even in observation of the plainest and commonest appearances and they show us that the mere faculties of perception although constantly exercised upon innumerable objects may long fail in leading to any exact knowledge If even on physical facts and these of the most obvious character the observing faculties of mankind can be to this degree the passive slaves of their preconceived impressions we need not be surprised that this should be so lamentably true as all experience attests it to be on things more nearly connected with their stronger feelings on moral social and religious subjects The information which an ordinary traveller brings back from a foreign country as the result of the evidence of his senses is almost always such as exactly confirms the opinions with which he set out He has had eyes and ears for such things only as he expected to see Men read the sacred books of their religion and pass unobserved therein multitudes of things utterly irreconcilable with even their own notions of moral excellence With the same authorities before them different historians alike innocent of intentional misrepresentation see only what is favourable to Protestants or Catholics royalists or republicans Charles I or Cromwell while others having set out with the preconception that extremes must be in the wrong are incapable of seeing truth and justice when these are wholly on one side The influence of a preconceived theory is well exemplified in the superstitions of barbarians respecting the virtues of medicaments and charms The negroes among whom coral as of old among ourselves is worn as an amulet affirm according to Dr Paris that its color is always affected by the state of health of the wearer it becoming paler in disease On a matter open to universal observation a general proposition which has not the smallest vestige of truth is received as a result of experience the preconceived opinion preventing it would seem any observation whatever on the subject For illustration of the first species of nonobservation that of Instances what has now been stated may suffice But there may also be nonobservation of some material circumstances in instances which have not been altogether overlooked nay which may be the very instances on which the whole superstructure of a theory has been founded As in the cases hitherto examined a general proposition was too rashly adopted on the evidence of particulars true indeed but insufficient to support it so in the cases to which we now turn the particulars themselves have been imperfectly observed and the singular propositions on which the generalization is grounded or some at least of those singular propositions are false Such for instance was one of the mistakes committed in the celebrated phlogistic theory a doctrine which accounted for combustion by the extrication of a substance called phlogiston supposed to be contained in all combustible matter The hypothesis accorded tolerably well with superficial appearances the ascent of flame naturally suggests the escape of a substance and the visible residuum of ashes in bulk and weight generally falls extremely short of the combustible material The error was nonobservation of an important portion of the actual residue namely the gaseous products of combustion When these were at last noticed and brought into account it appeared to be a universal law that all substances gain instead of losing weight by undergoing combustion and after the usual attempt to accommodate the old theory to the new fact by means of an arbitrary hypothesis that phlogiston had the quality of positive levity instead of gravity chemists were conducted to the true explanation namely that instead of a substance separated there was on the contrary a substance absorbed Many of the absurd practices which have been deemed to possess medicinal efficacy have been indebted for their reputation to nonobservance of some accompanying circumstance which was the real agent in the cures ascribed to them Thus of the sympathetic powder of Sir Kenelm Digby Whenever any wound had been inflicted this powder was applied to the weapon that had inflicted it which was moreover covered with ointment and dressed two or three times a day The wound itself in the mean time was directed to be brought together and carefully bound up with clean linen rags but above all to be let alone for seven days at the end of which period the bandages were removed when the wound was generally found perfectly united The triumph of the cure was decreed to the mysterious agency of the sympathetic powder which had been so assiduously applied to the weapon whereas it is hardly necessary to observe that the promptness of the cure depended on the total exclusion of air from the wound and upon the sanative operations of nature not having received any disturbance from the officious interference of art The result beyond all doubt furnished the first hint which led surgeons to the improved practice of healing wounds by what is technically called the first intention In all records adds Dr Paris of extraordinary cures performed by mysterious agents there is a great desire to conceal the remedies and other curative means which were simultaneously administered with them thus Oribasius commends in high terms a necklace of Paeony root for the cure of epilepsy but we learn that he always took care to accompany its use with copious evacuations although he assigns to them no share of credit in the cure In later times we have a good specimen of this species of deception presented to us in a work on scrofula by Mr Morley written as we are informed for the sole purpose of restoring the muchinjured character and use of the Vervain in which the author directs the root of this plant to be tied with a yard of white satin ribbon around the neck where it is to remain until the patient is cured but mark during this interval he calls to his aid the most active medicines in the materia medica In other cases the cures really produced by rest regimen and amusement have been ascribed to the medicinal or occasionally to the supernatural means which were put in requisition The celebrated John Wesley while he commemorates the triumph of sulphur and supplication over his bodily infirmity forgets to appreciate the resuscitating influence of four months’ repose from his apostolic labours and such is the disposition of the human mind to place confidence in the operation of mysterious agents that we find him more disposed to attribute his cure to a brown paper plaster of egg and brimstone than to Dr Fothergill’s salutary prescription of country air rest asses’ milk and horse exercise In the following example the circumstance overlooked was of a somewhat different character When the yellow fever raged in America the practitioners trusted exclusively to the copious use of mercury at first this plan was deemed so universally efficacious that in the enthusiasm of the moment it was triumphantly proclaimed that death never took place after the mercury had evinced its effect upon the system all this was very true but it furnished no proof of the efficacy of that metal since the disease in its aggravated form was so rapid in its career that it swept away its victims long before the system could be brought under mercurial influence while in its milder shape it passed off equally well without any assistance from art In these examples the circumstance overlooked was cognizable by the senses In other cases it is one the knowledge of which could only be arrived at by reasoning but the fallacy may still be classed under the head to which for want of a more appropriate name we have given the appellation Fallacies of Nonobservation It is not the nature of the faculties which ought to have been employed but the nonemployment of them which constitutes this Natural Order of Fallacies Wherever the error is negative not positive wherever it consists especially in overlooking in being ignorant or unmindful of some fact which if known and attended to would have made a difference in the conclusion arrived at the error is properly placed in the Class which we are considering In this Class there is not as in all other fallacies there is a positive misestimate of evidence actually had The conclusion would be just if the portion which is seen of the case were the whole of it but there is another portion overlooked which vitiates the result For instance there is a remarkable doctrine which has occasionally found a vent in the public speeches of unwise legislators but which only in one instance that I am aware of has received the sanction of a philosophical writer namely M Cousin who in his preface to the Gorgias of Plato contending that punishment must have some other and higher justification than the prevention of crime makes use of this argument that if punishment were only for the sake of example it would be indifferent whether we punished the innocent or the guilty since the punishment considered as an example is equally efficacious in either case Now we must in order to go along with this reasoning suppose that the person who feels himself under temptation observing somebody punished concludes himself to be in danger of being punished likewise and is terrified accordingly But it is forgotten that if the person punished is supposed to be innocent or even if there be any doubt of his guilt the spectator will reflect that his own danger whatever it may be is not contingent on his guiltiness but threatens him equally if he remains innocent and how therefore is he deterred from guilt by the apprehension of such punishment M Cousin supposes that people will be dissuaded from guilt by whatever renders the condition of the guilty more perilous forgetting that the condition of the innocent also one of the elements in the calculation is in the case supposed made perilous in precisely an equal degree This is a fallacy of overlooking or of nonobservation within the intent of our classification Fallacies of this description are the great stumblingblock to correct thinking in political economy The economical workings of society afford numerous cases in which the effects of a cause consist of two sets of phenomena the one immediate concentrated obvious to all eyes and passing in common apprehension for the whole effect the other widely diffused or lying deeper under the surface and which is exactly contrary to the former Take for instance the common notion so plausible at the first glance of the encouragement given to industry by lavish expenditure A who spends his whole income and even his capital in expensive living is supposed to give great employment to labour B who lives on a small portion and invests the remainder in the funds is thought to give little or no employment For every body sees the gains which are made by A’s tradesmen servants and others while his money is spending B’s savings on the contrary pass into the hands of the person whose stock he purchased who with it pays a debt he owed to some banker who lends it again to some merchant or manufacturer and the capital being laid out in hiring spinners and weavers or carriers and the crews of merchant vessels not only gives immediate employment to at least as much industry as A employs during the whole of his career but coming back with increase by the sale of the goods which have been manufactured or imported forms a fund for the employment of the same and perhaps a greater quantity of labour in perpetuity But the observer does not see and therefore does not consider what becomes of B’s money he does see what is done with A’s he observes the amount of industry which A’s profusion feeds he observes not the far greater quantity which it prevents from being fed and thence the prejudice universal to the time of Adam Smith that prodigality encourages industry and parsimony is a discouragement to it The common argument against free trade was a fallacy of the same nature The purchaser of British silk encourages British industry the purchaser of Lyons silk encourages only French the former conduct is patriotic the latter ought to be prevented by law The circumstance is overlooked that the purchaser of any foreign commodity necessarily causes directly or indirectly the export of an equivalent value of some article of home production beyond what would otherwise be exported either to the same foreign country or to some other which fact though from the complication of the circumstances it can not always be verified by specific observation no observation can possibly be brought to contradict while the evidence of reasoning on which it rests is irrefragable The fallacy is therefore the same as in the preceding case that of seeing a part only of the phenomena and imagining that part to be the whole and may be ranked among Fallacies of Nonobservation To complete the examination of the second of our five classes we have now to speak of Malobservation in which the error does not lie in the fact that something is unseen but that something seen is seen wrong Perception being infallible evidence of whatever is really perceived the error now under consideration can be committed no otherwise than by mistaking for conception what is in fact inference We have formerly shown how intimately the two are blended in almost every thing which is called observation and still more in every Description What is actually on any occasion perceived by our senses being so minute in amount and generally so unimportant a portion of the state of facts which we wish to ascertain or to communicate it would be absurd to say that either in our observations or in conveying their result to others we ought not to mingle inference with fact all that can be said is that when we do so we ought to be aware of what we are doing and to know what part of the assertion rests on consciousness and is therefore indisputable what part on inference and is therefore questionable One of the most celebrated examples of a universal error produced by mistaking an inference for the direct evidence of the senses was the resistance made on the ground of common sense to the Copernican system People fancied they saw the sun rise and set the stars revolve in circles round the pole We now know that they saw no such thing what they really saw was a set of appearances equally reconcilable with the theory they held and with a totally different one It seems strange that such an instance as this of the testimony of the senses pleaded with the most entire conviction in favour of something which was a mere inference of the judgment and as it turned out a false inference should not have opened the eyes of the bigots of common sense and inspired them with a more modest distrust of the competency of mere ignorance to judge the conclusions of cultivated thought In proportion to any person’s deficiency of knowledge and mental cultivation is generally his inability to discriminate between his inferences and the perceptions on which they were grounded Many a marvellous tale many a scandalous anecdote owes its origin to this incapacity The narrator relates not what he saw or heard but the impression which he derived from what he saw or heard and of which perhaps the greater part consisted of inference though the whole is related not as inference but as matter of fact The difficulty of inducing witnesses to restrain within any moderate limits the intermixture of their inferences with the narrative of their perceptions is well known to experienced crossexaminers and still more is this the case when ignorant persons attempt to describe any natural phenomenon The simplest narrative says Dugald Stewart of the most illiterate observer involves more or less of hypothesis nay in general it will be found that in proportion to his ignorance the greater is the number of conjectural principles involved in his statements A village apothecary and if possible in a still greater degree an experienced nurse is seldom able to describe the plainest case without employing a phraseology of which every word is a theory whereas a simple and genuine specification of the phenomena which mark a particular disease a specification unsophisticated by fancy or by preconceived opinions may be regarded as unequivocal evidence of a mind trained by long and successful study to the most difficult of all arts that of the faithful interpretation of nature The universality of the confusion between perceptions and the inferences drawn from them and the rarity of the power to discriminate the one from the other ceases to surprise us when we consider that in the far greater number of instances the actual perceptions of our senses are of no importance or interest to us except as marks from which we infer something beyond them It is not the color and superficial extension perceived by the eye that are important to us but the object of which those visible appearances testify the presence and where the sensation itself is indifferent as it generally is we have no motive to attend particularly to it but acquire a habit of passing it over without distinct consciousness and going on at once to the inference So that to know what the sensation actually was is a study in itself to which painters for example have to train themselves by special and longcontinued discipline and application In things farther removed from the dominion of the outward senses no one who has not great experience in psychological analysis is competent to break this intense association and when such analytic habits do not exist in the requisite degree it is hardly possible to mention any of the habitual judgments of mankind on subjects of a high degree of abstraction from the being of a God and the immortality of the soul down to the multiplication table which are not or have not been considered as matter of direct intuition So strong is the tendency to ascribe an intuitive character to judgments which are mere inferences and often false ones No one can doubt that many a deluded visionary has actually believed that he was directly inspired from Heaven and that the Almighty had conversed with him face to face which yet was only on his part a conclusion drawn from appearances to his senses or feelings in his internal consciousness which afforded no warrant for any such belief A caution therefore against this class of errors is not only needful but indispensable though to determine whether on any of the great questions of metaphysics such errors are actually committed belongs not to this place but as I have so often said to a different science The class of Fallacies of which we are now to speak is the most extensive of all embracing a greater number and variety of unfounded inferences than any of the other classes and which it is even more difficult to reduce to subclasses or species If the attempt made in the preceding books to define the principles of wellgrounded generalization has been successful all generalizations not conformable to those principles might in a certain sense be brought under the present class when however the rules are known and kept in view but a casual lapse committed in the application of them this is a blunder not a fallacy To entitle an error of generalization to the latter epithet it must be committed on principle there must lie in it some erroneous general conception of the inductive process the legitimate mode of drawing conclusions from observation and experiment must be fundamentally misconceived Without attempting any thing so chimerical as an exhaustive classification of all the misconceptions which can exist on the subject let us content ourselves with noting among the cautions which might be suggested a few of the most useful and needful In the first place there are certain kinds of generalization which if the principles already laid down be correct must be groundless experience can not afford the necessary conditions for establishing them by a correct induction Such for instance are all inferences from the order of nature existing on the earth or in the solar system to that which may exist in remote parts of the universe where the phenomena for aught we know may be entirely different or may succeed one another according to different laws or even according to no fixed law at all Such again in matters dependent on causation are all universal negatives all propositions that assert impossibility The nonexistence of any given phenomenon however uniformly experience may as yet have testified to the fact proves at most that no cause adequate to its production has yet manifested itself but that no such causes exist in nature can only be inferred if we are so foolish as to suppose that we know all the forces in nature The supposition would at least be premature while our acquaintance with some even of those which we do know is so extremely recent And however much our knowledge of nature may hereafter be extended it is not easy to see how that knowledge could ever be complete or how if it were we could ever be assured of its being so The only laws of nature which afford sufficient warrant for attributing impossibility even with reference to the existing order of nature and to our own region of the universe are first those of number and extension which are paramount to the laws of the succession of phenomena and not exposed to the agency of counteracting causes and secondly the universal law of causality itself That no valuation in any effect or consequent will take place while the whole of the antecedents remain the same may be affirmed with full assurance But that the addition of some new antecedent might not entirely alter and subvert the accustomed consequent or that antecedents competent to do this do not exist in nature we are in no case empowered positively to conclude It is next to be remarked that all generalizations which profess like the theories of Thales Democritus and others of the early Greek speculators to resolve all things into some one element or like many modern theories to resolve phenomena radically different into the same are necessarily false By radically different phenomena I mean impressions on our senses which differ in quality and not merely in degree On this subject what appeared necessary was said in the chapter on the Limits to the Explanation of Laws of Nature but as the fallacy is even in our own times a common one I shall touch on it somewhat further in this place When we say that the force which retains the planets in their orbits is resolved into gravity or that the force which makes substances combine chemically is resolved into electricity we assert in the one case what is and in the other case what might and probably will ultimately be a legitimate result of induction In both these cases motion is resolved into motion The assertion is that a case of motion which was supposed to be special and to follow a distinct law of its own conforms to and is included in the general law which regulates another class of motions But from these and similar generalizations countenance and currency have been given to attempts to resolve not motion into motion but heat into motion light into motion sensation itself into motion states of consciousness into states of the nervous system as in the ruder forms of the materialist philosophy vital phenomena into mechanical or chemical processes as in some schools of physiology Now I am far from pretending that it may not be capable of proof or that it is not an important addition to our knowledge if proved that certain motions in the particles of bodies are the conditions of the production of heat or light that certain assignable physical modifications of the nerves may be the conditions not only of our sensations or emotions but even of our thoughts that certain mechanical and chemical conditions may in the order of nature be sufficient to determine to action the physiological laws of life All I insist upon in common with every thinker who entertains any clear idea of the logic of science is that it shall not be supposed that by proving these things one step would be made toward a real explanation of heat light or sensation or that the generic peculiarity of those phenomena can be in the least degree evaded by any such discoveries however well established Let it be shown for instance that the most complex series of physical causes and effects succeed one another in the eye and in the brain to produce a sensation of colour rays falling on the eye refracted converging crossing one another making an inverted image on the retina and after this a motion let it be a vibration or a rush of nervous fluid or whatever else you are pleased to suppose along the optic nerve a propagation of this motion to the brain itself and as many more different motions as you choose still at the end of these motions there is something which is not motion there is a feeling or sensation of color Whatever number of motions we may be able to interpolate and whether they be real or imaginary we shall still find at the end of the series a motion antecedent and a color consequent The mode in which any one of the motions produces the next may possibly be susceptible of explanation by some general law of motion but the mode in which the last motion produces the sensation of color can not be explained by any law of motion it is the law of color which is and must always remain a peculiar thing Where our consciousness recognizes between two phenomena an inherent distinction where we are sensible of a difference which is not merely of degree and feel that no adding one of the phenomena to itself would produce the other any theory which attempts to bring either under the laws of the other must be false though a theory which merely treats the one as a cause or condition of the other may possibly be true Among the remaining forms of erroneous generalization several of those most worthy of and most requiring notice have fallen under our examination in former places where in investigating the rules of correct induction we have had occasion to advert to the distinction between it and some common mode of the incorrect In this number is what I have formerly called the natural Induction of uninquiring minds the induction of the ancients which proceeds per enumerationem simplicem This that and the other A are B I can not think of any A which is not B therefore every A is B As a final condemnation of this rude and slovenly mode of generalization I will quote Bacon’s emphatic denunciation of it the most important part as I have more than once ventured to assert of the permanent service rendered by him to philosophy Inductio quae procedit per enumerationem simplicem res puerilis est et precario concludit concludes only by your leave or provisionally et periculo exponitur ab instantia contradictoria et plerumque secundum pauciora quam par est et ex his tantummodo quae praesto sunt pronunciat At Inductio quae ad inventionem et demonstrationem Scientiarum et Artium erit utilis Naturam separare debet per rejectiones et exclusiones debitas ac deinde post negativas tot quot sufficiunt super affirmativas concludere I have already said that the mode of Simple Enumeration is still the common and received method of Induction in whatever relates to man and society Of this a very few instances more by way of memento than of instruction may suffice What for example is to be thought of all the commonsense maxims for which the following may serve as the universal formula Whatsoever has never been will never be As for example negroes have never been as civilized as whites sometimes are therefore it is impossible they should be so Women as a class are supposed not to have hitherto been equal in intellect to men therefore they are necessarily inferior Society can not prosper without this or the other institution eg in Aristotle’s time without slavery in later times without an established priesthood without artificial distinctions of rank etc One poor person in a thousand educated while the nine hundred and ninetynine remain uneducated has usually aimed at raising himself out of his class therefore education makes people dissatisfied with the condition of a labourer Bookish men taken from speculative pursuits and set to work on something they know nothing about have generally been found or thought to do it ill therefore philosophers are unfit for business etc etc All these are inductions by simple enumeration Reasons having some reference to the canons of scientific investigation have been attempted to be given however unsuccessfully for some of these propositions but to the multitude of those who parrot them the enumeratio simplex ex his tantummodo quae praesto sunt pronuncians is the sole evidence Their fallacy consists in this that they are inductions without elimination there has been no real comparison of instances nor even ascertainment of the material facts in any given instance There is also the further error of forgetting that such generalizations even if well established could not be ultimate truths but must be results of laws much more elementary and therefore until deduced from such could at most be admitted as empirical laws holding good within the limits of space and time by which the particular observations that suggested the generalization were bounded This error of placing mere empirical laws and laws in which there is no direct evidence of causation on the same footing of certainty as laws of cause and effect, an error which is at the root of perhaps the greater number of bad inductions is exemplified only in its grossest form in the kind of generalizations to which we have now referred These indeed do not possess even the degree of evidence which pertains to a wellascertained empirical law but admit of refutation on the empirical ground itself without ascending to casual laws A little reflection indeed will show that mere negations can only form the ground of the lowest and least valuable kind of empirical law A phenomenon has never been noticed this only proves that the conditions of that phenomenon have not yet occurred in experience but does not prove that they may not occur hereafter There is a better kind of empirical law than this namely when a phenomenon which is observed presents within the limits of observation a series of gradations in which a regularity or something like a mathematical law is perceptible from which therefore something may be rationally presumed as to those terms of the series which are beyond the limits of observation But in negation there are no gradations and no series the generalizations therefore which deny the possibility of any given condition of man and society merely because it has never yet been witnessed can not possess this higher degree of validity even as empirical laws What is more the minuter examination which that higher order of empirical laws presupposes being applied to the subjectmatter of these not only does not confirm but actually refutes them For in reality the past history of Man and Society instead of exhibiting them as immovable unchangeable incapable of ever presenting new phenomena shows them on the contrary to be in many most important particulars not only changeable but actually undergoing a progressive change The empirical law therefore best expressive in most cases of the genuine result of observation would be not that such and such a phenomenon will continue unchanged but that it will continue to change in some particular manner Accordingly while almost all generalizations relating to Man and Society antecedent to the last fifty or sixty years have erred in the gross way which we have attempted to characterize namely by implicitly assuming that nature and society will forever revolve in the same orbit and exhibit essentially the same phenomena which is also the vulgar error of the ostentatiously practical the votaries of socalled common sense in our day especially in Great Britain the more thinking minds of the present age having applied a more minute analysis to the past records of our race have for the most part adopted a contrary opinion that the human species is in a state of necessary progression and that from the terms of the series which are past we may infer positively those which are yet to come Of this doctrine considered as a philosophical tenet we shall have occasion to speak more fully in the concluding Book If not in all its forms free from error it is at least free from the gross and error which we previously exemplified But in all except the most eminently philosophical minds it is infected with precisely the same kind of fallacy as that is For we must remember that even this other and better generalization the progressive change in the condition of the human species is after all but an empirical law to which too it is not difficult to point out exceedingly large exceptions and even if these could be got rid of either by disputing the facts or by explaining and limiting the theory the general objection remains valid against the supposed law as applicable to any other than what in our third book were termed Adjacent Cases For not only is it no ultimate but not even a causal law Changes do indeed take place in human affairs but every one of those changes depends on determinate causes the progressiveness of the species is not a cause but a summary expression for the general result of all the causes So soon as by a quite different sort of induction it shall be ascertained what causes have produced these successive changes from the beginning of history in so far as they have really taken place and by what causes of a contrary tendency they have been occasionally checked or entirely counteracted we may then be prepared to predict the future with reasonable foresight we may be in possession of the real law of the future and may be able to declare on what circumstances the continuance of the same onward movement will eventually depend But this it is the error of many of the more advanced thinkers in the present age to overlook and to imagine that the empirical law collected from a mere comparison of the condition of our species at different past times is a real law is the law of its changes not only past but also to come The truth is that the causes on which the phenomena of the moral world depend are in every age and almost in every country combined in some different proportion so that it is scarcely to be expected that the general result of them all should conform very closely in its details at least to any uniformly progressive series And all generalizations which affirm that mankind have a tendency to grow better or worse richer or poorer more cultivated or more barbarous that population increases faster than subsistence or subsistence than population that inequality of fortune has a tendency to increase or to break down and the like propositions of considerable value as empirical laws within certain but generally rather narrow limits are in reality true or false according to times and circumstances What we have said of empirical generalizations from times past to times still to come holds equally true of similar generalizations from present times to times past when persons whose acquaintance with moral and social facts is confined to their own age take the men and the things of that age for the type of men and things in general and apply without scruple to the interpretation of the events of history the empirical laws which represent sufficiently for daily guidance the common phenomena of human nature at that time and in that particular state of society If examples are wanted almost every historical work until a very recent period abounded in them The same may be said of those who generalize empirically from the people of their own country to the people of other countries as if human beings felt judged and acted everywhere in the same manner In the foregoing instances the distinction is confounded between empirical laws which express merely the customary order of the succession of effects and the laws of causation on which the effects depend There may however be incorrect generalization when this mistake is not committed when the investigation takes its proper direction that of causes and the result erroneously obtained purports to be a really causal law The most vulgar form of this fallacy is that which is commonly called post hoc ergo propter hoc or cum hoc ergo propter hoc As when it was inferred that England owed her industrial preeminence to her restrictions on commerce as when the old school of financiers and some speculative writers maintained that the national debt was one of the causes of national prosperity as when the excellence of the Church of the Houses of Lords and Commons of the procedure of the law courts etc were inferred from the mere fact that the country had prospered under them In such cases as these if it can be rendered probable by other evidence that the supposed causes have some tendency to produce the effect ascribed to them the fact of its having been produced though only in one instance is of some value as a verification by specific experience but in itself it goes scarcely any way at all toward establishing such a tendency since admitting the effect a hundred other antecedents could show an equally strong title of that kind to be considered as the cause In these examples we see bad generalization a posteriori or empiricism properly so called causation inferred from casual conjunction without either due elimination or any presumption arising from known properties of the supposed agent But bad generalization a priori is fully as common which is properly called false theory conclusions drawn by way of deduction from properties of some one agent which is known or supposed to be present all other coexisting agents being overlooked As the former is the error of sheer ignorance so the latter is especially that of semiinstructed minds and is mainly committed in attempting to explain complicated phenomena by a simpler theory than their nature admits of As when one school of physicians sought for the universal principle of all disease in lentor and morbid viscidity of the blood and imputing most bodily derangements to mechanical obstructions thought to cure them by mechanical remedies while another the chemical school acknowledged no source of disease but the presence of some hostile acid or alkali or some deranged condition in the chemical composition of the fluid or solid parts and conceived therefore that all remedies must act by producing chemical changes in the body We find Tournefort busily engaged in testing every vegetable juice in order to discover in it some traces of an acid or alkaline ingredient which might confer upon it medicinal activity The fatal errors into which such an hypothesis was liable to betray the practitioner received an awful illustration in the history of the memorable fever that raged at Leyden in the year 1699 and which consigned twothirds of the population of that city to an untimely grave an event which in a great measure depended upon the Professor Sylvius de la Boe who having just embraced the chemical doctrines of Van Helmont assigned the origin of the distemper to a prevailing acid and declared that its cure could alone only be effected by the copious administration of absorbent and testaceous medicines These aberrations in medical theory have their exact parallels in politics All the doctrines which ascribe absolute goodness to particular forms of government particular social arrangements and even to particular modes of education without reference to the state of civilization and the various distinguishing characters of the society for which they are intended are open to the same objection that of assuming one class of influencing circumstances to be the paramount rulers of phenomena which depend in an equal or greater degree on many others But on these considerations it is the less necessary that we should now dwell as they will occupy our attention more largely in the concluding Book The last of the modes of erroneous generalization to which I shall advert is that to which we may give the name of False Analogies This Fallacy stands distinguished from those already treated of by the peculiarity that it does not even simulate a complete and conclusive induction but consists in the misapplication of an argument which is at best only admissible as an inconclusive presumption where real proof is unattainable An argument from analogy is an inference that what is true in a certain case is true in a case known to be somewhat similar but not known to be exactly parallel that is to be similar in all the material circumstances An object has the property B another object is not known to have that property but resembles the first in a property A not known to be connected with B and the conclusion to which the analogy points is that this object has the property B also As for example that the planets are inhabited because the earth is so The planets resemble the earth in describing elliptical orbits round the sun in being attracted by it and by one another in being nearly spherical revolving on their axes etc and as we have now reason to believe from the revelations of the spectroscope are composed in great part at least of similar materials but it is not known that any of these properties or all of them together are the conditions on which the possession of inhabitants is dependent or are marks of those conditions Nevertheless so long as we do not know what the conditions are they may be connected by some law of nature with those common properties and to the extent of that possibility the planets are more likely to be inhabited than if they did not resemble the earth at all This nonassignable and generally small increase of probability beyond what would otherwise exist is all the evidence which a conclusion can derive from analogy For if we have the slightest reason to suppose any real connection between the two properties A and B the argument is no longer one of analogy If it had been ascertained I purposely put an absurd supposition that there was a connection by causation between the fact of revolving on an axis and the existence of animated beings or if there were any reasonable ground for even suspecting such a connection a probability would arise of the existence of inhabitants in the planets which might be of any degree of strength up to a complete induction but we should then infer the fact from the ascertained or presumed law of causation and not from the analogy of the earth The name analogy however is sometimes employed by extension to denote those arguments of an inductive character but not amounting to a real induction which are employed to strengthen the argument drawn from a simple resemblance Though A the property common to the two cases can not be shown to be the cause or effect of B the analogical reasoner will endeavour to show that there is some less close degree of connection between them that A is one of a set of conditions from which when all united B would result or is an occasional effect of some cause which has been known also to produce B and the like Any of which things if shown would render the existence of B by so much more probable than if there had not been even that amount of known connection between B and A Now an error or fallacy of analogy may occur in two ways Sometimes it consists in employing an argument of either of the above kinds with correctness indeed but overrating its probative force This very common aberration is sometimes supposed to be particularly incident to persons distinguished for their imagination but in reality it is the characteristic intellectual vice of those whose imaginations are barren either from want of exercise natural defect or the narrowness of their range of ideas To such minds objects present themselves clothed in but few properties and as therefore few analogies between one object and another occur to them they almost invariably overrate the degree of importance of those few while one whose fancy takes a wider range perceives and remembers so many analogies tending to conflicting conclusions that he is much less likely to lay undue stress on any of them We always find that those are the greatest slaves to metaphorical language who have but one set of metaphors But this is only one of the modes of error in the employment of arguments of analogy There is another more properly deserving the name of fallacy namely when resemblance in one point is inferred from resemblance in another point though there is not only no evidence to connect the two circumstances by way of causation but the evidence tends positively to disconnect them This is properly the Fallacy of False Analogies As a first instance we may cite that favourite argument in defence of absolute power drawn from the analogy of paternal government in a family which government however much in need of control is not and can not be controlled by the children themselves while they remain children Paternal government says the argument works well therefore despotic government in a state will work well I waive as not pertinent in this place all that could be said in qualification of the alleged excellence of paternal government However this might be the argument from the family to the state would not the less proceed on a false analogy implying that the beneficial working of parental government depends in the family on the only point which it has in common with political despotism namely irresponsibility Whereas it depends when real not on that but on two other circumstances of the case the affection of the parent for the children and the superiority of the parent in wisdom and experience neither of which properties can be reckoned on or are at all likely to exist between a political despot and his subjects and when either of these circumstances fails even in the family and the influence of the irresponsibility is allowed to work uncorrected the result is any thing but good government This therefore is a false analogy Another example is the not uncommon dictum that bodies politic have youth maturity old age and death like bodies natural that after a certain duration of prosperity they tend spontaneously to decay This also is a false analogy because the decay of the vital powers in an animated body can be distinctly traced to the natural progress of those very changes of structure which in their earlier stages constitutes its growth to maturity while in the body politic the progress of those changes can not generally speaking have any effect but the still further continuance of growth it is the stoppage of that progress and the commencement of retrogression that alone would constitute decay Bodies politic die but it is of disease or violent death they have no old age The following sentence from Hooker’s Ecclesiastical Polity is an instance of a false analogy from physical bodies to what are called bodies politic As there could be in natural bodies no motion of any thing unless there were some which moveth all things and continueth immovable even so in politic societies there must be some unpunishable or else no man shall suffer punishment There is a double fallacy here for not only the analogy but the premise from which it is drawn is untenable The notion that there must be something immovable which moves all other things is the old scholastic error of a primum mobile The following instance I quote from Archbishop Whately’s Rhetoric It would be admitted that a great and permanent diminution in the quantity of some useful commodity such as corn or coal or iron throughout the world would be a serious and lasting loss and again that if the fields and coalmines yielded regularly double quantities with the same labour we should be so much the richer hence it might be inferred that if the quantity of gold and silver in the world were diminished onehalf or were doubled like results would follow the utility of these metals for the purposes of coin being very great Now there are many points of resemblance and many of difference between the precious metals on the one hand and corn coal etc on the other but the important circumstance to the supposed argument is that the utility of gold and silver as coin which is far the chief depends on their value which is regulated by their scarcity or rather to speak strictly by the difficulty of obtaining them whereas if corn and coal were ten times as abundant ie more easily obtained a bushel of either would still be as useful as now But if it were twice as easy to procure gold as it is a sovereign would be twice as large if only half as easy it would be of the size of a halfsovereign and this besides the trifling circumstance of the cheapness or dearness of gold ornaments would be all the difference The analogy therefore fails in the point essential to the argument The same author notices after Bishop Copleston the case of False Analogy which consists in inferring from the similarity in many respects between the metropolis of a country and the heart of the animal body that the increased size of the metropolis is a disease Some of the false analogies on which systems of physics were confidently grounded in the time of the Greek philosophers are such as we now call fanciful not that the resemblances are not often real but that it is long since any one has been inclined to draw from them the inferences which were then drawn Such for instance are the curious speculations of the Pythagoreans on the subject of numbers Finding that the distances of the planets bore or seemed to bear to one another a proportion not varying much from that of the divisions of the monochord they inferred from it the existence of an inaudible music that of the spheres as if the music of a harp had depended solely on the numerical proportions and not on the material nor even on the existence of any material any strings at all It has been similarly imagined that certain combinations of numbers which were found to prevail in some natural phenomena must run through the whole of nature as that there must be four elements because there are four possible combinations of hot and cold wet and dry that there must be seven planets because there were seven metals and even because there were seven days of the week Kepler himself thought that there could be only six planets because there were only five regular solids With these we may class the reasonings so common in the speculations of the ancients founded on a supposed perfection in nature meaning by nature the customary order of events as they take place of themselves without human interference This also is a rude guess at an analogy supposed to pervade all phenomena however dissimilar Since what was thought to be perfection appeared to obtain in some phenomena it was inferred in opposition to the plainest evidence to obtain in all We always suppose that which is better to take place in nature if it be possible says Aristotle and the vaguest and most heterogeneous qualities being confounded together under the notion of being better there was no limit to the wildness of the inferences Thus because the heavenly bodies were perfect they must move in circles and uniformly For they the Pythagoreans would not allow says Geminus of any such disorder among divine and eternal things as that they should sometimes move quicker and sometimes slower and sometimes stand still for no one would tolerate such anomaly in the movements even of a man who was decent and orderly The occasions of life however are often reasons for men going quicker or slower but in the incorruptible nature of the stars it is not possible that any cause can be alleged of quickness or slowness It is seeking an argument of analogy very far to suppose that the stars must observe the rules of decorum in gait and carriage prescribed for themselves by the longbearded philosophers satirized by Lucian As late as the Copernican controversy it was urged as an argument in favour of the true theory of the solar system that it placed the fire the noblest element in the centre of the universe This was a remnant of the notion that the order of nature must be perfect and that perfection consisted in conformity to rules of precedency in dignity either real or conventional Again reverting to numbers certain numbers were perfect therefore those numbers must obtain in the great phenomena of nature Six was a perfect number that is equal to the sum of all its factors an additional reason why there must be exactly six planets The Pythagoreans on the other hand attributed perfection to the number ten but agreed in thinking that the perfect number must be somehow realized in the heavens and knowing only of nine heavenly bodies to make up the enumeration they asserted that there was an antichthon or counterearth on the other side of the sun invisible to us Even Huygens was persuaded that when the number of the heavenly bodies had reached twelve it could not admit of any further increase Creative power could not go beyond that sacred number Some curious instances of false analogy are to be found in the arguments of the Stoics to prove the equality of all crimes and the equal wretchedness of all who had not realized their idea of perfect virtue Cicero toward the end of his Fourth Book De Finibus states some of these as follows Ut inquit in fidibus plurimis si nulla earum ita contenta numeris sit ut concentum servare possit omnes aeque incontentae sunt sic peccata quia discrepant aeque discrepant paria sunt igitur To which Cicero himself aptly answers aeque contingit omnibus fidibus ut incontentae sint illud non continuo ut aeque incontentae The Stoic resumes Ut enim inquit gubernator aeque peccat si palearum navem evertit et si auri item aeque peccat qui parentem et qui servum injuria verberat assuming that because the magnitude of the interest at stake makes no difference in the mere defect of skill it can make none in the moral defect a false analogy Again Quis ignorat si plures ex alto emergere velint propius fore eos quidem ad respirandum qui ad summam jam aquam appropinquant sed nihilo magis respirare posse quam eos qui sunt in profundo Nihil ergo adjuvat procedere et progredi in virtute quominus miserrimus sit antequam ad eam pervenerit quoniam in aqua nihil adjuvat et quoniam catuli qui jam despecturi sunt caeci aeque et ii qui modo nati Platonem quoque necesse est quoniam nondum videbat sapientiam aeque caecum animo ac Phalarim fuisse Cicero in his own person combats these false analogies by other analogies tending to an opposite conclusion Ista similia non sunt Cato Illa sunt similia hebes acies est cuipiam oculorum corpore alius languescit hi curatione adhibita levantur in dies alter valet plus quotidie alter videt Hi similes sunt omnibus qui virtuti student levantur vitiis levantur erroribus In these and all other arguments drawn from remote analogies and from metaphors which are cases of analogy it is apparent especially when we consider the extreme facility of raising up contrary analogies and conflicting metaphors that so far from the metaphor or analogy proving any thing the applicability of the metaphor is the very thing to be made out It has to be shown that in the two cases asserted to be analogous the same law is really operating that between the known resemblance and the inferred one there is some connection by means of causation Cicero and Cato might have bandied opposite analogies forever it rested with each of them to prove by just induction or at least to render probable that the case resembled the one set of analogous cases and not the other in the circumstances on which the disputed question really hinged Metaphors for the most part therefore assume the proposition which they are brought to prove their use is to aid the apprehension of it to make clearly and vividly comprehended what it is that the person who employs the metaphor is proposing to make out and sometimes also by what media he proposes to do so For an apt metaphor though it can not prove often suggests the proof For instance when D’Alembert I believe remarked that in certain governments only two creatures find their way to the highest places the eagle and the serpent the metaphor not only conveys with great vividness the assertion intended but contributes toward substantiating it by suggesting in a lively manner the means by which the two opposite characters thus typified effect their rise When it is said that a certain person misunderstands another because the lesser of two objects can not comprehend the greater the application of what is true in the literal sense of the word comprehend to its metaphorical sense points to the fact which is the ground and justification of the assertion viz that one mind can not thoroughly understand another unless it can contain it in itself that is unless it possesses all that is contained in the other When it is urged as an argument for education that if the soil is left uncultivated weeds will spring up the metaphor though no proof but a statement of the thing to be proved states it in terms which by suggesting a parallel case put the mind upon the track of the real proof For the reason why weeds grow in an uncultivated soil is that the seeds of worthless products exist everywhere and can germinate and grow in almost all circumstances while the reverse is the case with those which are valuable and this being equally true of mental products this mode of conveying an argument independently of its rhetorical advantages has a logical value since it not only suggests the grounds of the conclusion but points to another case in which those grounds have been found or at least deemed to be sufficient On the other hand when Bacon who is equally conspicuous in the use and abuse of figurative illustration says that the stream of time has brought down to us only the least valuable part of the writings of the ancients as a river carries froth and straws floating on its surface while more weighty objects sink to the bottom this even if the assertion illustrated by it were true would be no good illustration there being no parity of cause The levity by which substances float on a stream and the levity which is synonymous with worthlessness have nothing in common except the name and to show how little value there is in the metaphor we need only change the word into buoyancy to turn the semblance of argument involved in Bacon’s illustration against himself A metaphor then is not to be considered as an argument but as an assertion that an argument exists that a parity subsists between the case from which the metaphor is drawn and that to which it is applied This parity may exist though the two cases be apparently very remote from one another the only resemblance existing between them may be a resemblance of relations an analogy in Ferguson’s and Archbishop Whately’s sense as in the preceding instance in which an illustration from agriculture was applied to mental cultivation To terminate the subject of Fallacies of Generalization it remains to be said that the most fertile source of them is bad classification bringing together in one group and under one name things which have no common properties or none but such as are too unimportant to allow general propositions of any considerable value to be made respecting the class The misleading effect is greatest when a word which in common use expresses some definite fact is extended by slight links of connection to cases in which that fact does not exist but some other or others only slightly resembling it Thus Bacon in speaking of the Idola or Fallacies arising from notions temere et inaequaliter ˆ rebus abstractae exemplifies them by the notion of Humidum or Wet so familiar in the physics of antiquity and of the Middle Ages Invenietur verbum istud Humidum nihil aliud quam nota confusa diversarum actionum quae nullam constantiam aut reductionem patiuntur Significat enim et quod circa aliud corpus facile se circumfundit et quod in se est indeterminabile nec consistere potest et quod facile cedit undique et quod facile se dividit et dispergit et quod facile se unit et colligit et quod facile fluit et in motu ponitur et quod alteri corpori facile adhaeret idque madefacit et quod facile reducitur in liquidum sive colliquatur cum antea consisteret Itaque quum ad hujus nominis praedicationem et impositionem ventum sit si alia accipias flamma humida est si alia accipias aer humidus non est si alia pulvis minutus humidus est si alia vitrum humidum est ut facile appareat istam notionem ex aqua tantum et communibus et vulgaribus liquoribus absque ulla debita verificatione temere abstractam esse Bacon himself is not exempt from a similar accusation when inquiring into the nature of heat where he occasionally proceeds like one who seeking for the cause of hardness after examining that quality in iron flint and diamond should expect to find that it is something which can be traced also in hard water a hard knot and a hard heart The word in the Greek philosophy and the words Generation and Corruption both then and long afterward denoted such a multitude of heterogeneous phenomena that any attempt at philosophizing in which those words were used was almost as necessarily abortive as if the word hard had been taken to denote a class including all the things mentioned above for instance which properly signified motion was taken to denote not only all motion but even all change being recognized as one of the modes of The effect was to connect with every form of or change ideas drawn from motion in the proper and literal sense and which had no real connection with any other kind of than that Aristotle and Plato laboured under a continual embarrassment from this misuse of terms But if we proceed further in this direction we shall encroach upon the Fallacy of Ambiguity which belongs to a different class the last in order of our classification Fallacies of Confusion We have now in our progress through the classes of Fallacies arrived at those to which in the common books of logic the appellation is in general exclusively appropriated those which have their seat in the ratiocinative or deductive part of the investigation of truth Of these fallacies it is the less necessary for us to insist at any length as they have been most satisfactorily treated in a work familiar to almost all in this country at least who feel any interest in these speculations Archbishop Whately’s Logic Against the more obvious forms of this class of fallacies the rules of the syllogism are a complete protection Not as we have so often said that ratiocination can not be good unless it be in the form of a syllogism but that by showing it in that form we are sure to discover if it be bad or at least if it contain any fallacy of this class Among Fallacies of Ratiocination we ought perhaps to include the errors committed in processes which have the appearance only not the reality of an inference from premises the fallacies connected with the conversion and aequipollency of propositions I believe errors of this description to be far more frequently committed than is generally supposed or than their extreme obviousness might seem to admit of For example the simple conversion of a universal affirmative proposition All A are B therefore all B are A I take to be a very common form of error though committed like many other fallacies oftener in the silence of thought than in express words for it can scarcely be clearly enunciated without being detected And so with another form of fallacy not substantially different from the preceding the erroneous conversion of an hypothetical proposition The proper converse of an hypothetical proposition is this If the consequent be false the antecedent is false but this If the consequent be true the antecedent is true by no means holds good but is an error corresponding to the simple conversion of a universal affirmative Yet hardly any thing is more common than for people in their private thoughts to draw this inference As when the conclusion is accepted which it so often is for proof of the premises That the premises can not be true if the conclusion is false is the unexceptionable foundation of the legitimate mode of reasoning called reductio ad absurdum But people continually think and express themselves as if they also believed that the premises can not be false if the conclusion is true The truth or supposed truth of the inferences which follow from a doctrine often enables it to find acceptance in spite of gross absurdities in it How many philosophical systems which had scarcely any intrinsic recommendation have been received by thoughtful men because they were supposed to lend additional support to religion morality some favourite view of politics or some other cherished persuasion not merely because their wishes were thereby enlisted on its side but because its leading to what they deemed sound conclusions appeared to them a strong presumption in favour of its truth though the presumption when viewed in its true light amounted only to the absence of that particular evidence of falsehood which would have resulted from its leading by correct inference to something already known to be false Again the very frequent error in conduct of mistaking reverse of wrong for right is the practical form of a logical error with respect to the Opposition of Propositions It is committed for want of the habit of distinguishing the contrary of a proposition from the contradictory of it and of attending to the logical canon that contrary propositions though they can not both be true may both be false If the error were to express itself in words it would run distinctly counter to this canon It generally however does not so express itself and to compel it to do so is the most effectual method of detecting and exposing it Among Fallacies of Ratiocination are to be ranked in the first place all the cases of vicious syllogism laid down in the books These generally resolve themselves into having more than three terms to the syllogism either avowedly or in the covert mode of an undistributed middle term or an illicit process of one of the two extremes It is not indeed very easy fully to convict an argument of falling under any one of these vicious cases in particular for the reason already more than once referred to that the premises are seldom formally set out if they were the fallacy would impose upon nobody and while they are not it is almost always to a certain degree optional in what manner the suppressed link shall be filled up The rules of the syllogism are rules for compelling a person to be aware of the whole of what he must undertake to defend if he persists in maintaining his conclusion He has it almost always in his power to make his syllogism good by introducing a false premise and hence it is scarcely ever possible decidedly to affirm that any argument involves a bad syllogism but this detracts nothing from the value of the syllogistic rules since it is by them that a reasoner is compelled distinctly to make his election what premises he is prepared to maintain The election made there is generally so little difficulty in seeing whether the conclusion follows from the premises set out that we might without much logical impropriety have merged this fourth class of fallacies in the fifth or Fallacies of Confusion Perhaps however the commonest and certainly the most dangerous fallacies of this class are those which do not lie in a single syllogism but slip in between one syllogism and another in a chain of argument and are committed by changing the premises A proposition is proved or an acknowledged truth laid down in the first part of an argumentation and in the second a further argument is founded not on the same proposition but on some other resembling it sufficiently to be mistaken for it Instances of this fallacy will be found in almost all the argumentative discourses of imprecise thinkers and we need only here advert to one of the obscurer forms of it recognized by the schoolmen as the fallacy ˆ dicto secundum quid ad dictum simpliciter This is committed when in the premises a proposition is asserted with a qualification and the qualification lost sight of in the conclusion or oftener when a limitation or condition though not asserted is necessary to the truth of the proposition but is forgotten when that proposition comes to be employed as a premise Many of the bad arguments in vogue belong to this class of error The premise is some admitted truth some common maxim the reasons or evidence for which have been forgotten or are not thought of at the time but if they had been thought of would have shown the necessity of so limiting the premise that it would no longer have supported the conclusion drawn from it Of this nature is the fallacy in what is called by Adam Smith and others the Mercantile Theory in Political Economy That theory sets out from the common maxim that whatever brings in money enriches or that every one is rich in proportion to the quantity of money he obtains From this it is concluded that the value of any branch of trade or of the trade of the country altogether consists in the balance of money it brings in that any trade which carries more money out of the country than it draws into it is a losing trade that therefore money should be attracted into the country and kept there by prohibitions and bounties and a train of similar corollaries All for want of reflecting that if the riches of an individual are in proportion to the quantity of money he can command it is because that is the measure of his power of purchasing money’s worth and is therefore subject to the proviso that he is not debarred from employing his money in such purchases The premise therefore is only true secundum quid but the theory assumes it to be true absolutely and infers that increase of money is increase of riches even when produced by means subversive of the condition under which alone money can be riches A second instance is the argument by which it used to be contended before the commutation of tithe that tithes fell on the landlord and were a deduction from rent because the rent of tithefree land was always higher than that of land of the same quality and the same advantages of situation subject to tithe Whether it be true or not that a tithe falls on rent a treatise on Logic is not the place to examine but it is certain that this is no proof of it Whether the proposition be true or false tithefree land must by the necessity of the case pay a higher rent For if tithes do not fall on rent it must be because they fall on the consumer because they raise the price of agricultural produce But if the produce be raised in price the farmer of tithefree as well as the farmer of tithed land gets the benefit To the latter the rise is but a compensation for the tithe he pays to the first who pays none it is clear gain and therefore enables him and if there be freedom of competition forces him to pay so much more rent to his landlord The question remains to what class of fallacies this belongs The premise is that the owner of tithed land receives less rent than the owner of tithefree land the conclusion is that therefore he receives less than he himself would receive if tithe were abolished But the premise is only true conditionally the owner of tithed land receives less than what the owner of tithefree land is enabled to receive when other lands are tithed while the conclusion is applied to a state of circumstances in which that condition fails and in which by consequence the premise will not be true The fallacy therefore is ˆ dicto secundum quid ad dictum simpliciter A third example is the opposition sometimes made to legitimate interferences of government in the economical affairs of society grounded on a misapplication of the maxim that an individual is a better judge than the government of what is for his own pecuniary interest This objection was urged to Mr Wakefield’s principle of colonization the concentration of the settlers by fixing such a price on unoccupied land as may preserve the most desirable proportion between the quantity of land in culture and the laboring population Against this it was argued that if individuals found it for their advantage to occupy extensive tracts of land they being better judges of their own interest than the legislature which can only proceed on general rules ought not to be restrained from doing so But in this argument it was forgotten that the fact of a person’s taking a large tract of land is evidence only that it is his interest to take as much as other people but not that it might not be for his interest to content himself with less if he could be assured that other people would do so too an assurance which nothing but a government regulation can give If all other people took much and he only a little he would reap none of the advantages derived from the concentration of the population and the consequent possibility of procuring labour for hire but would have placed himself without equivalent in a situation of voluntary inferiority The proposition therefore that the quantity of land which people will take when left to themselves is that which is most for their interest to take is true only secundum quid it is only their interest while they have no guarantee for the conduct of one another But the arrangement disregards the limitation and takes the proposition for true simpliciter One of the conditions oftenest dropped when what would otherwise be a true proposition is employed as a premise for proving others is the condition of time It is a principle of political economy that prices profits wages etc always find their level but this is often interpreted as if it meant that they are always or generally at their level while the truth is as Coleridge epigrammatically expresses it that they are always finding their level which might be taken as a paraphrase or ironical definition of a storm Under the same head of fallacy ˆ dicto secundum quid ad dictum simpliciter might be placed all the errors which are vulgarly called misapplications of abstract truths that is where a principle true as the common expression is in the abstract that is all modifying causes being supposed absent is reasoned on as if it were true absolutely and no modifying circumstance could ever by possibility exist This very common form of error it is not requisite that we should exemplify here as it will be particularly treated of hereafter in its application to the subjects on which it is most frequent and most fatal those of politics and society Under this fifth and last class it is convenient to arrange all those fallacies in which the source of error is not so much a false estimate of the probative force of known evidence as an indistinct indefinite and fluctuating conception of what the evidence is At the head of these stands that multitudinous body of fallacious reasonings in which the source of error is the ambiguity of terms when something which is true if a word be used in a particular sense is reasoned on as if it were true in another sense In such a case there is not a malestimation of evidence because there is not properly any evidence to the point at all there is evidence but to a different point which from a confused apprehension of the meaning of the terms used is supposed to be the same This error will naturally be oftener committed in our ratiocinations than in our direct inductions because in the former we are deciphering our own or other people’s notes while in the latter we have the things themselves present either to the senses or to the memory Except indeed when the induction is not from individual cases to a generality but from generalities to a still higher generalization in that case the fallacy of ambiguity may affect the inductive process as well as the ratiocinative It occurs in ratiocination in two ways when the middle term is ambiguous or when one of the terms of the syllogism is taken in one sense in the premises and in another sense in the conclusion Some good exemplifications of this fallacy are given by Archbishop Whately One case says he which may be regarded as coming under the head of Ambiguous Middle is what I believe logical writers mean by Fallacia Figurae Dictionis’ the fallacy built on the grammatical structure of language from men’s usually taking for granted that paronymous or conjugate words ie those belonging to each other as the substantive adjective verb etc of the same root have a precisely corresponding meaning which is by no means universally the case Such a fallacy could not indeed be even exhibited in strict logical form which would preclude even the attempt at it since it has two middle terms in sound as well as sense But nothing is more common in practice than to vary continually the terms employed with a view to grammatical convenience nor is there any thing unfair in such a practice as long as the meaning is preserved unaltered eg murder should be punished with death this man is a murderer therefore he deserves to die’ etc Here we proceed on the assumption in this case just that to commit murder and to be a murderer to deserve death and to be one who ought to die are respectively equivalent expressions and it would frequently prove a heavy inconvenience to be debarred this kind of liberty but the abuse of it gives rise to the Fallacy in question eg projectors are unfit to be trusted this man has formed a project therefore he is unfit to be trusted here the sophist proceeds on the hypothesis that he who forms a project must be a projector whereas the bad sense that commonly attaches to the latter word is not at all implied in the former This fallacy may often be considered as lying not in the Middle but in one of the terms of the Conclusion so that the conclusion drawn shall not be in reality at all warranted by the premises though it will appear to be so by means of the grammatical affinity of the words eg to be acquainted with the guilty is a presumption of guilt this man is so acquainted therefore we may presume that he is guilty this argument proceeds on the supposition of an exact correspondence between presume and presumption which however does not really exist for presumption’ is commonly used to express a kind of slight suspicion whereas to presume’ amounts to actual belief There are innumerable instances of a noncorrespondence in paronymous words similar to that above instanced as between art and artful design and designing faith and faithful etc and the more slight the variation of the meaning the more likely is the fallacy to be successful for when the words have become so widely removed in sense as pity’ and pitiful’ every one would perceive such a fallacy nor would it be employed but in jest The present Fallacy is nearly allied to or rather perhaps may be regarded as a branch of that founded on etymology viz when a term is used at one time in its customary and at another in its etymological sense Perhaps no example of this can be found that is more extensively and mischievously employed than in the case of the word representative assuming that its right meaning must correspond exactly with the strict and original sense of the verb represent’ the sophist persuades the multitude that a member of the House of Commons is bound to be guided in all points by the opinion of his constituents and in short to be merely their spokesman whereas law and custom which in this case may be considered as fixing the meaning of the term require no such thing but enjoin the representative to act according to the best of his own judgment and on his own responsibility The following are instances of great practical importance in which arguments are habitually founded on a verbal ambiguity The mercantile public are frequently led into this fallacy by the phrase scarcity of money In the language of commerce money has two meanings currency or the circulating medium and capital seeking investment especially investment on loan In this last sense the word is used when the money market is spoken of and when the value of money is said to be high or low the rate of interest being meant The consequence of this ambiguity is that as soon as scarcity of money in the latter of these senses begins to be felt as soon as there is difficulty of obtaining loans and the rate of interest is high it is concluded that this must arise from causes acting upon the quantity of money in the other and more popular sense that the circulating medium must have diminished in quantity or ought to be increased I am aware that independently of the double meaning of the term there are in the facts themselves some peculiarities giving an apparent support to this error but the ambiguity of the language stands on the very threshold of the subject and intercepts all attempts to throw light upon it Another ambiguous expression which continually meets us in the political controversies of the present time especially in those which relate to organic changes is the phrase influence of property which is sometimes used for the influence of respect for superior intelligence or gratitude for the kind offices which persons of large property have it so much in their power to bestow at other times for the influence of fear fear of the worst sort of power which large property also gives to its possessor the power of doing mischief to dependents To confound these two is the standing fallacy of ambiguity brought against those who seek to purify the electoral system from corruption and intimidation Persuasive influence acting through the conscience of the voter and carrying his heart and mind with it is beneficial therefore it is pretended coercive influence which compels him to forget that he is a moral agent or to act in opposition to his moral convictions ought not to be placed under restraint Another word which is often turned into an instrument of the fallacy of ambiguity is Theory In its most proper acceptation theory means the completed result of philosophical induction from experience In that sense there are erroneous as well as true theories for induction may be incorrectly performed but theory of some sort is the necessary result of knowing any thing of a subject and having put one’s knowledge into the form of general propositions for the guidance of practice In this the proper sense of the word Theory is the explanation of practice In another and a more vulgar sense theory means any mere fiction of the imagination endeavouring to conceive how a thing may possibly have been produced instead of examining how it was produced In this sense only are theory and theorists unsafe guides but because of this ridicule or discredit is attempted to be attached to theory in its proper sense that is to legitimate generalization the end and aim of all philosophy and a conclusion is represented as worthless just because that has been done which if done correctly constitutes the highest worth that a principle for the guidance of practice can possess namely to comprehend in a few words the real law on which a phenomenon depends or some property or relation which is universally true of it The Church is sometimes understood to mean the clergy alone sometimes the whole body of believers or at least of communicants The declamations respecting the inviolability of church property are indebted for the greater part of their apparent force to this ambiguity The clergy being called the church are supposed to be the real owners of what is called church property whereas they are in truth only the managing members of a much larger body of proprietors and enjoy on their own part a mere usufruct not extending beyond a life interest The following is a Stoical argument taken from Cicero De Finibus book the third Quod est bonum omne laudabile est Quod autem laudabile est omne honestum est Bonum igitur quod est honestum est Here the ambiguous word is laudabile which in the minor premise means any thing which mankind are accustomed on good grounds to admire or value as beauty for instance or good fortune but in the major it denotes exclusively moral qualities In much the same manner the Stoics endeavoured logically to justify as philosophical truths their figurative and rhetorical expressions of ethical sentiment as that the virtuous man is alone free alone beautiful alone a king etc Whoever has virtue has Good because it has been previously determined not to call any thing else good but again Good necessarily includes freedom beauty and even kingship all these being good things therefore whoever has virtue has all these The following is an argument of Descartes to prove in his a priori manner the being of a God The conception says he of an infinite Being proves the real existence of such a being For if there is not really any such being I must have made the conception but if I could make it I can also unmake it which evidently is not true therefore there must be externally to myself an archetype from which the conception was derived In this argument which it may be observed would equally prove the real existence of ghosts and of witches the ambiguity is in the pronoun I by which in one place is to be understood my will in another the laws of my nature If the conception existing as it does in my mind had no original without the conclusion would unquestionably follow that I made it that is the laws of my nature must have somehow evolved it but that my will made it would not follow Now when Descartes afterward adds that I can not unmake the conception he means that I can not get rid of it by an act of my will which is true but is not the proposition required I can as much unmake this conception as I can any other no conception which I have once had can I ever dismiss by mere volition but what some of the laws of my nature have produced other laws or those same laws in other circumstances may and often do subsequently efface Analogous to this are some of the ambiguities in the freewill controversy which as they will come under special consideration in the concluding Book I only mention memoriae causa In that discussion too the word I is often shifted from one meaning to another at one time standing for my volitions at another time for the actions which are the consequences of them or the mental dispositions from which they proceed The latter ambiguity is exemplified in an argument of Coleridge in his Aids to Reflection in support of the freedom of the will It is not true he says that a man is governed by motives the man makes the motive not the motive the man the proof being that what is a strong motive to one man is no motive at all to another The premise is true but only amounts to this that different persons have different degrees of susceptibility to the same motive as they have also to the same intoxicating liquid which however does not prove that they are free to be drunk or not drunk whatever quantity of the fluid they may drink What is proved is that certain mental conditions in the person himself must cooperate in the production of the act with the external inducement but those mental conditions also are the effect of causes and there is nothing in the argument to prove that they can arise without a cause that a spontaneous determination of the will without any cause at all ever takes place as the freewill doctrine supposes The double use in the freewill controversy of the word Necessity which sometimes stands only for Certainty at other times for Compulsion sometimes for what can not be prevented at other times only for what we have reason to be assured will not we shall have occasion hereafter to pursue to some of its ulterior consequences A most important ambiguity both in common and in metaphysical language is thus pointed out by Archbishop Whately in the Appendix to his Logic Same as well as One Identical and other words derived from them is used frequently in a sense very different from its primary one as applicable to a single object being employed to denote great similarity When several objects are undistinguishably alike one single description will apply equally to any of them and thence they are said to be all of one and the same nature appearance etc As eg when we say this house is built of the same stone with such another’ we only mean that the stones are undistinguishable in their qualities not that the one building was pulled down and the other constructed with the materials Whereas sameness in the primary sense does not even necessarily imply similarity for if we say of any man that he is greatly altered since such a time we understand and indeed imply by the very expression that he is one person though different in several qualities It is worth observing also that Same in the secondary sense admits according to popular usage of degrees we speak of two things being nearly the same but not entirely personal identity does not admit of degrees Nothing perhaps has contributed more to the error of Realism than inattention to this ambiguity When several persons are said to have one and the same opinion thought or idea many men overlooking the true simple statement of the case which is that they are all thinking alike look for something more abstruse and mystical and imagine there must be some One Thing in the primary sense though not an individual which is present at once in the mind of each of these persons and thence readily sprung Plato’s theory of Ideas each of which was according to him one real eternal object existing entire and complete in each of the individual objects that are known by one name It is indeed not a matter of inference but of authentic history that Plato’s doctrine of Ideas and the Aristotelian doctrine in this respect similar to the Platonic of substantial forms and second substances grew up in the precise way here pointed out from the supposed necessity of finding in things which were said to have the same nature or the same qualities something which was the same in the very sense in which a man is the same as himself All the idle speculations respecting and similar abstractions so common in the ancient and in some modern schools of thought sprang from the same source The Aristotelian logicians saw however one case of the ambiguity and provided against it with their peculiar felicity in the invention of technical language when they distinguished things which differed both specie and numero from those which differed numero tantum that is which were exactly alike in some particular respect at least but were distinct individuals An extension of this distinction to the two meanings of the word Same namely things which are the same specie tantum and a thing which is the same numero as well as specie would have prevented the confusion which has been a source of so much darkness and such an abundance of positive error in metaphysical philosophy One of the most singular examples of the length to which a thinker of eminence may be led away by an ambiguity of language is afforded by this very case I refer to the famous argument by which Bishop Berkeley flattered himself that he had forever put an end to skepticism atheism and irreligion It is briefly as follows I thought of a thing yesterday I ceased to think of it I think of it again today I had therefore in my mind yesterday an idea of the object I have also an idea of it today this idea is evidently not another but the very same idea Yet an intervening time elapsed in which I had it not Where was the idea during this interval It must have been somewhere it did not cease to exist otherwise the idea I had yesterday could not be the same idea no more than the man I see alive today can be the same whom I saw yesterday if the man has died in the mean while Now an idea can not be conceived to exist anywhere except in a mind and hence there must exist a Universal Mind in which all ideas have their permanent residence during the intervals of their conscious presence in our own minds It is evident that Berkeley here confounded sameness numero with sameness specie that is with exact resemblance and assumed the former where there was only the latter not perceiving that when we say we have the same thought today which we had yesterday we do not mean the same individual thought but a thought exactly similar as we say that we have the same illness which we had last year meaning only the same sort of illness In one remarkable instance the scientific world was divided into two furiously hostile parties by an ambiguity of language affecting a branch of science which more completely than most others enjoys the advantage of a precise and welldefined terminology I refer to the famous dispute respecting the vis viva the history of which is given at large in Professor Playfair’s Dissertation The question was whether the force of a moving body was proportional its mass being given to its velocity simply or to the square of its velocity and the ambiguity was in the word Force One of the effects says Playfair produced by a moving body is proportional to the square of the velocity while another is proportional to the velocity simply from whence clearer thinkers were subsequently led to establish a double measure of the efficiency of a moving power one being called vis viva and the other momentum About the facts both parties were from the first agreed the only question was with which of the two effects the term force should be or could most conveniently be associated But the disputants were by no means aware that this was all they thought that force was one thing the production of effects another and the question by which set of effects the force which produced both the one and the other should be measured was supposed to be a question not of terminology but of fact The ambiguity of the word Infinite is the real fallacy in the amusing logical puzzle of Achilles and the Tortoise a puzzle which has been too hard for the ingenuity or patience of many philosophers and which no less a thinker than Sir William Hamilton considered as insoluble as a sound argument though leading to a palpable falsehood The fallacy as Hobbes hinted lies in the tacit assumption that whatever is infinitely divisible is infinite but the following solution to the invention of which I have no claim is more precise and satisfactory The argument is let Achilles run ten times as fast as the tortoise yet if the tortoise has the start Achilles will never overtake him For suppose them to be at first separated by an interval of a thousand feet when Achilles has run these thousand feet the tortoise will have got on a hundred when Achilles has run those hundred the tortoise will have run ten and so on forever therefore Achilles may run forever without overtaking the tortoise Now the forever in the conclusion means for any length of time that can be supposed but in the premises ever does not mean any length of time it means any number of subdivisions of time It means that we may divide a thousand feet by ten and that quotient again by ten and so on as often as we please that there never needs be an end to the subdivisions of the distance nor consequently to those of the time in which it is performed But an unlimited number of subdivisions may be made of that which is itself limited The argument proves no other infinity of duration than may be embraced within five minutes As long as the five minutes are not expired what remains of them may be divided by ten and again by ten as often as we like which is perfectly compatible with their being only five minutes altogether It proves in short that to pass through this finite space requires a time which is infinitely divisible but not an infinite time the confounding of which distinction Hobbes had already seen to be the gist of the fallacy The following ambiguities of the word right in addition to the obvious and familiar one of a right and the adjective right are extracted from a forgotten paper of my own in a periodical Speaking morally you are said to have a right to do a thing if all persons are morally bound not to hinder you from doing it But in another sense to have a right to do a thing is the opposite of having no right to do it ie of being under a moral obligation to forbear doing it In this sense to say that you have a right to do a thing means that you may do it without any breach of duty on your part that other persons not only ought not to hinder you but have no cause to think worse of you for doing it This is a perfectly distinct proposition from the preceding The right which you have by virtue of a duty incumbent upon other persons is obviously quite a different thing from a right consisting in the absence of any duty incumbent upon yourself Yet the two things are perpetually confounded Thus a man will say he has a right to publish his opinions which may be true in this sense that it would be a breach of duty in any other person to interfere and prevent the publication but he assumes thereupon that in publishing his opinions he himself violates no duty which may either be true or false depending as it does on his having taken due pains to satisfy himself first that the opinions are true and next that their publication in this manner and at this particular juncture will probably be beneficial to the interests of truth on the whole The second ambiguity is that of confounding a right of any kind with a right to enforce that right by resisting or punishing a violation of it People will say for example that they have a right to good government which is undeniably true it being the moral duty of their governors to govern them well But in granting this you are supposed to have admitted their right or liberty to turn out their governors and perhaps to punish them for having failed in the performance of this duty which far from being the same thing is by no means universally true but depends on an immense number of varying circumstances requiring to be conscientiously weighed before adopting or acting on such a resolution This last example is like others which have been cited a case of fallacy within fallacy it involves not only the second of the two ambiguities pointed out but the first likewise One not unusual form of the Fallacy of Ambiguous Terms is known technically as the Fallacy of Composition and Division when the same term is collective in the premises distributive in the conclusion or vic versa or when the middle term is collective in one premise distributive in the other As if one were to say I quote from Archbishop Whately All the angles of a triangle are equal to two right angles A B C is an angle of a triangle therefore A B C is equal to two right angles There is no fallacy more common or more likely to deceive than the one now before us The form in which it is most usually employed is to establish some truth separately concerning each single member of a certain class and thence to infer the same of the whole collectively As in the argument one sometimes hears to prove that the world could do without great men If Columbus it is said had never lived America would still have been discovered at most only a few years later if Newton had never lived some other person would have discovered the law of gravitation and so forth Most true these things would have been done but in all probability not till some one had again been found with the qualities of Columbus or Newton Because any one great man might have had his place supplied by other great men the argument concludes that all great men could have been dispensed with The term great men is distributive in the premises and collective in the conclusion Such also is the fallacy which probably operates on most adventurers in lotteries eg the gaining of a high prize is no uncommon occurrence and what is no uncommon occurrence may reasonably be expected therefore the gaining of a high prize may reasonably be expected’ the conclusion when applied to the individual as in practice it is must be understood in the sense of reasonably expected by a certain individual’ therefore for the major premise to be true the middle term must be understood to mean no uncommon occurrence to some one particular person’ whereas for the minor which has been placed first to be true you must understand it of no uncommon occurrence to some one or other’ and thus you will have the Fallacy of Composition This is a Fallacy with which men are extremely apt to deceive themselves for when a multitude of particulars are presented to the mind many are too weak or too indolent to take a comprehensive view of them but confine their attention to each single point by turns and then decide infer and act accordingly eg the imprudent spendthrift finding that he is able to afford this or that or the other expense forgets that all of them together will ruin him The debauchee destroys his health by successive acts of intemperance because no one of those acts would be of itself sufficient to do him any serious harm A sick person reasons with himself one and another and another of my symptoms do not prove that I have a fatal disease and practically concludes that all taken together do not prove it We have now sufficiently exemplified one of the principal Genera in this Order of Fallacies where the source of error being the ambiguity of terms the premises are verbally what is required to support the conclusion but not really so In the second great Fallacy of Confusion they are neither verbally nor really sufficient though from their multiplicity and confused arrangement and still oftener from defect of memory they are not seen to be what they are The fallacy I mean is that of Petitio Principii or begging the question including the more complex and not uncommon variety of it which is termed Reasoning in a Circle Petitio Principii as defined by Archbishop Whately is the fallacy in which the premise either appears manifestly to be the same as the conclusion or is actually proved from the conclusion or is such as would naturally and properly so be proved By the last clause I presume is meant that it is not susceptible of any other proof for otherwise there would be no fallacy To deduce from a proposition propositions from which it would itself more naturally be deduced is often an allowable deviation from the usual didactic order or at most what by an adaptation of a phrase familiar to mathematicians may be called a logical inelegance The employment of a proposition to prove that on which it is itself dependent for proof by no means implies the degree of mental imbecility which might at first be supposed The difficulty of comprehending how this fallacy could possibly be committed disappears when we reflect that all persons even the instructed hold a great number of opinions without exactly recollecting how they came by them Believing that they have at some former time verified them by sufficient evidence but having forgotten what the evidence was they may easily be betrayed into deducing from them the very propositions which are alone capable of serving as premises for their establishment As if says Archbishop Whately one should attempt to prove the being of a God from the authority of Holy Writ which might easily happen to one with whom both doctrines as fundamental tenets of his religious creed stand on the same ground of familiar and traditional belief Arguing in a circle however is a stronger case of the fallacy and implies more than the mere passive reception of a premise by one who does not remember how it is to be proved It implies an actual attempt to prove two propositions reciprocally from one another and is seldom resorted to at least in express terms by any person in his own speculations but is committed by those who being hard pressed by an adversary are forced into giving reasons for an opinion of which when they began to argue they had not sufficiently considered the grounds As in the following example from Archbishop Whately Some mechanicians attempt to prove what they ought to lay down as a probable but doubtful hypothesis that every particle of matter gravitates equally why’ because those bodies which contain more particles ever gravitate more strongly ie are heavier’ but it may be urged those which are heaviest are not always more bulky’ no but they contain more particles though more closely condensed’ how do you know that’ because they are heavier’ how does that prove it’ because all particles of matter gravitating equally that mass which is specifically the heavier must needs have the more of them in the same space’ It appears to me that the fallacious reasoner in his private thoughts would not be likely to proceed beyond the first step He would acquiesce in the sufficiency of the reason first given bodies which contain more particles are heavier It is when he finds this questioned and is called upon to prove it without knowing how that he tries to establish his premise by supposing proved what he is attempting to prove by it The most effectual way in fact of exposing a petitio principii when circumstances allow of it is by challenging the reasoner to prove his premises which if he attempts to do he is necessarily driven into arguing in a circle It is not uncommon however for thinkers and those not of the lowest description to be led even in their own thoughts not indeed into formally proving each of two propositions from the other but into admitting propositions which can only be so proved In the preceding example the two together form a complete and consistent though hypothetical explanation of the facts concerned And the tendency to mistake mutual coherency for truth to trust one’s safety to a strong chain though it has no point of support is at the bottom of much which when reduced to the strict forms of argumentation can exhibit itself no otherwise than as reasoning in a circle All experience bears testimony to the enthralling effect of neat concatenation in a system of doctrines and the difficulty with which people admit the persuasion that any thing which holds so well together can possibly fall Since every case where a conclusion which can only be proved from certain premises is used for the proof of those premises is a case of petitio principii that fallacy includes a very great proportion of all incorrect reasoning It is necessary for completing our view of the fallacy to exemplify some of the disguises under which it is accustomed to mask itself and to escape exposure A proposition would not be admitted by any person in his senses as a corollary from itself unless it were expressed in language which made it seem different One of the commonest modes of so expressing it is to present the proposition itself in abstract terms as a proof of the same proposition expressed in concrete language This is a very frequent mode not only of pretended proof but of pretended explanation and is parodied when Molière Le Malade Imaginaire makes one of his absurd physicians say Mihi a docto doctore Demandatur causam et rationem quare Opium facit dormire A quoi respondeo Quia est in eo Virtus dormitiva Cujus est natura Sensus assoupire The words Nature and Essence are grand instruments of this mode of begging the question as in the wellknown argument of the scholastic theologians that the mind thinks always because the essence of the mind is to think Locke had to point out that if by essence is here meant some property which must manifest itself by actual exercise at all times the premise is a direct assumption of the conclusion while if it only means that to think is the distinctive property of a mind there is no connection between the premise and the conclusion since it is not necessary that a distinctive property should be perpetually in action The following is one of the modes in which these abstract terms Nature and Essence are used as instruments of this fallacy Some particular properties of a thing are selected more or less arbitrarily to be termed its nature or essence and when this has been done these properties are supposed to be invested with a kind of indefeasibleness to have become paramount to all the other properties of the thing and incapable of being prevailed over or counteracted by them As when Aristotle in a passage already cited decides that there is no void on such arguments as this in a void there could be no difference of up and down for as in nothing there are no differences so there are none in a privation or negation but a void is merely a privation or negation of matter therefore in a void bodies could not move up and down which it is in their nature to do In other words it is in the nature of bodies to move up and down ergo any physical fact which supposes them not so to move can not be authentic This mode of reasoning by which a bad generalization is made to overrule all facts which contradict it is Petitio Principii in one of its most palpable forms None of the modes of assuming what should be proved are in more frequent use than what are termed by Bentham questionbegging appellatives names which beg the question under the disguise of stating it The most potent of these are such as have a laudatory or vituperative character For instance in politics the word Innovation The dictionary meaning of this term being merely a change to something new it is difficult for the defenders even of the most salutary improvement to deny that it is an innovation yet the word having acquired in common usage a vituperative connotation in addition to its dictionary meaning the admission is always construed as a large concession to the disadvantage of the thing proposed The following passage from the argument in refutation of the Epicureans in the second book of Cicero De Finibus affords a fine example of this sort of fallacy Et quidem illud ipsum non nimium probo et tantum patior philosophum loqui de cupiditatibus finiendis An potest cupiditas finiri tollenda est atque extrahenda radicitus Quis est enim in quo sit cupiditas quin recte cupidus dici possit Ergo et avarus erit sed finite adulter verum habebit modum et luxuriosus eodem modo Qualis ista philosophia est quae non interitum afferat pravitatis sed sit contenta mediocritate vitiorum The question was whether certain desires when kept within bounds are vices or not and the argument decides the point by applying to them a word cupiditas which implies vice It is shown however in the remarks which follow that Cicero did not intend this as a serious argument but as a criticism on what he deemed an inappropriate expression Rem ipsam prorsus probo elegantiam desidero Appellet haec desideria naturae cupiditatis nomen servet alio etc But many persons both ancient and modern have employed this or something equivalent to it as a real and conclusive argument We may remark that the passage respecting cupiditas and cupidus is also an example of another fallacy already noticed that of Paronymous Terms Many more of the arguments of the ancient moralists and especially of the Stoics fall within the definition of Petitio Principii In the De Finibus for example which I continue to quote as being probably the best extant exemplification at once of the doctrines and the methods of the schools of philosophy existing at that time of what value as arguments are such pleas as those of Cato in the third book That if virtue were not happiness it could not be a thing to boast of That if death or pain were evils it would be impossible not to fear them and it could not therefore be laudable to despise them etc In one way of viewing these arguments they may be regarded as appeals to the authority of the general sentiment of mankind which had stamped its approval upon certain actions and characters by the phrases referred to but that such could have been the meaning intended is very unlikely considering the contempt of the ancient philosophers for vulgar opinion In any other sense they are clear cases of Petitio Principii since the word laudable and the idea of boasting imply principles of conduct and practical maxims can only be proved from speculative truths namely from the properties of the subjectmatter and can not therefore be employed to prove those properties As well might it be argued that a government is good because we ought to support it or that there is a God because it is our duty to pray to him It is assumed by all the disputants in the De Finibus as the foundation of the inquiry into the summum bonum that sapiens semper beatus est Not simply that wisdom gives the best chance of happiness or that wisdom consists in knowing what happiness is and by what things it is promoted these propositions would not have been enough for them but that the sage always is and must of necessity be happy The idea that wisdom could be consistent with unhappiness was always rejected as inadmissible the reason assigned by one of the interlocutors near the beginning of the third book being that if the wise could be unhappy there was little use in pursuing wisdom But by unhappiness they did not mean pain or suffering to that it was granted that the wisest person was liable in common with others he was happy because in possessing wisdom he had the most valuable of all possessions the most to be sought and prized of all things and to possess the most valuable thing was to be the most happy By laying it down therefore at the commencement of the inquiry that the sage must be happy the disputed question respecting the summum bonum was in fact begged with the further assumption that pain and suffering so far as they can coexist with wisdom are not unhappiness and are no evil The following are additional instances of Petitio Principii under more or less of disguise Plato in the Sophistes attempts to prove that things may exist which are incorporeal by the argument that justice and wisdom are incorporeal and justice and wisdom must be something Here if by something be meant as Plato did in fact mean a thing capable of existing in and by itself and not as a quality of some other thing he begs the question in asserting that justice and wisdom must be something if he means any thing else his conclusion is not proved This fallacy might also be classed under ambiguous middleterm something in the one premise meaning some substance in the other merely some object of thought whether substance or attribute It was formerly an argument employed in proof of what is now no longer a popular doctrine the infinite divisibility of matter that every portion of matter however small must at least have an upper and an under surface Those who used this argument did not see that it assumed the very point in dispute the impossibility of arriving at a minimum of thickness for if there be a minimum its upper and under surface will of course be one it will be itself a surface and no more The argument owes its very considerable plausibility to this that the premise does actually seem more obvious than the conclusion though really identical with it As expressed in the premise the proposition appeals directly and in concrete language to the incapacity of the human imagination for conceiving a minimum Viewed in this light it becomes a case of the a priori fallacy or natural prejudice that whatever can not be conceived can not exist Every fallacy of Confusion it is almost unnecessary to repeat will if cleared up become a fallacy of some other sort and it will be found of deductive or ratiocinative fallacies generally that when they mislead there is mostly as in this case a fallacy of some other description lurking under them by virtue of which chiefly it is that the verbal juggle which is the outside or body of this kind of fallacy passes undetected Euler’s Algebra a book otherwise of great merit but full to overflowing of logical errors in respect to the foundation of the science contains the following argument to prove that minus multiplied by minus gives plus a doctrine the opprobrium of all mere mathematicians and which Euler had not a glimpse of the true method of proving He says minus multiplied by minus can not give minus for minus multiplied by plus gives minus and minus multiplied by minus can not give the same product as minus multiplied by plus Now one is obliged to ask why minus multiplied by minus must give any product at all and if it does why its product can not be the same as that of minus multiplied by plus for this would seem at the first glance not more absurd than that minus by minus should give the same as plus by plus the proposition which Euler prefers to it The premise requires proof as much as the conclusion nor can it be proved except by that more comprehensive view of the nature of multiplication and of algebraic processes in general which would also supply a far better proof of the mysterious doctrine which Euler is here endeavouring to demonstrate A striking instance of reasoning in a circle is that of some ethical writers who first take for their standard of moral truth what being the general they deem to be the natural or instinctive sentiments and perceptions of mankind and then explain away the numerous instances of divergence from their assumed standard by representing them as cases in which the perceptions are unhealthy Some particular mode of conduct or feeling is affirmed to be unnatural why because it is abhorrent to the universal and natural sentiments of mankind Finding no such sentiment in yourself you question the fact and the answer is if your antagonist is polite that you are an exception a peculiar case But neither say you do I find in the people of some other country or of some former age any such feeling of abhorrence ay but their feelings were sophisticated and unhealthy One of the most notable specimens of reasoning in a circle is the doctrine of Hobbes Rousseau and others which rests the obligations by which human beings are bound as members of society on a supposed social compact I waive the consideration of the fictitious nature of the compact itself but when Hobbes through the whole Leviathan elaborately deduces the obligation of obeying the sovereign not from the necessity or utility of doing so but from a promise supposed to have been made by our ancestors on renouncing savage life and agreeing to establish political society it is impossible not to retort by the question Why are we bound to keep a promise made for us by others or why bound to keep a promise at all No satisfactory ground can be assigned for the obligation except the mischievous consequences of the absence of faith and mutual confidence among mankind We are therefore brought round to the interests of society as the ultimate ground of the obligation of a promise and yet those interests are not admitted to be a sufficient justification for the existence of government and law Without a promise it is thought that we should not be bound to that which is implied in all modes of living in society namely to yield a general obedience to the laws therein established and so necessary is the promise deemed that if none has actually been made some additional safety is supposed to be given to the foundations of society by feigning one Two principal subdivisions of the class of Fallacies of Confusion having been disposed of there remains a third in which the confusion is not as in the Fallacy of Ambiguity in misconceiving the import of the premises nor as in Petitio Principii in forgetting what the premises are but in mistaking the conclusion which is to be proved This is the fallacy of Ignoratio Elenchi in the widest sense of the phrase also called by Archbishop Whately the Fallacy of Irrelevant Conclusion His examples and remarks are highly worthy of citation Various kinds of propositions are according to the occasion substituted for the one of which proof is required sometimes the particular for the universal sometimes a proposition with different terms and various are the contrivances employed to effect and to conceal this substitution and to make the conclusion which the sophist has drawn answer practically the same purpose as the one he ought to have established We say practically the same purpose’ because it will very often happen that some emotion will be excited some sentiment impressed on the mind by a dexterous employment of this fallacy such as shall bring men into the disposition requisite for your purpose though they may not have assented to or even stated distinctly in their own minds the proposition which it was your business to establish Thus if a sophist has to defend one who has been guilty of some serious offense which he wishes to extenuate though he is unable distinctly to prove that it is not such yet if he can succeed in making the audience laugh at some casual matter he has gained practically the same point So also if any one has pointed out the extenuating circumstances in some particular case of offense so as to show that it differs widely from the generality of the same class the sophist if he finds himself unable to disprove these circumstances may do away the force of them by simply referring the action to that very class which no one can deny that it belongs to and the very name of which will excite a feeling of disgust sufficient to counteract the extenuation eg let it be a case of peculation and that many mitigating circumstances have been brought forward which can not be denied the sophistical opponent will reply Well but after all the man is a rogue and there is an end of it’ now in reality this was by hypothesis never the question and the mere assertion of what was never denied ought not in fairness to be regarded as decisive but practically the odiousness of the word arising in great measure from the association of those very circumstances which belong to most of the class but which we have supposed to be absent in this particular instance excites precisely that feeling of disgust which in effect destroys the force of the defence In like manner we may refer to this head all cases of improper appeal to the passions and every thing else which is mentioned by Aristotle as extraneous to the matter in hand ¹ Again instead of proving that this prisoner has committed an atrocious fraud’ you prove that the fraud he is accused of is atrocious instead of proving as in the wellknown tale of Cyrus and the two coats that the taller boy had a right to force the other boy to exchange coats with him you prove that the exchange would have been advantageous to both instead of proving that the poor ought to be relieved in this way rather than in that you prove that the poor ought to be relieved instead of proving that the irrational agent whether a brute or a madman can never be deterred from any act by apprehension of punishment as for instance a dog from sheepbiting by fear of being beaten you prove that the beating of one dog does not operate as an example to other dogs etc It is evident that Ignoratio Elenchi may be employed as well for the apparent refutation of your opponent’s proposition as for the apparent establishment of your own for it is substantially the same thing to prove what was not denied or to disprove what was not asserted The latter practice is not less common and it is more offensive because it frequently amounts to a personal affront in attributing to a person opinions etc which he perhaps holds in abhorrence Thus when in a discussion one party vindicates on the ground of general expediency a particular instance of resistance to government in a case of intolerable oppression the opponent may gravely maintain that we ought not to do evil that good may come’ a proposition which of course had never been denied the point in dispute being whether resistance in this particular case were doing evil or not’ Or again by way of disproving the assertion of the right of private judgment in religion one may hear a grave argument to prove that it is impossible every one can be right in his judgment’ The works of controversial writers are seldom free from this fallacy The attempts for instance to disprove the population doctrines of Malthus have been mostly cases of ignoratio elenchi Malthus has been supposed to be refuted if it could be shown that in some countries or ages population has been nearly stationary as if he had asserted that population always increases in a given ratio or had not expressly declared that it increases only in so far as it is not restrained by prudence or kept down by poverty and disease Or perhaps a collection of facts is produced to prove that in some one country the people are better off with a dense population than they are in another country with a thin one or that the people have become more numerous and better off at the same time As if the assertion were that a dense population could not possibly be well off as if it were not part of the very doctrine and essential to it that where there is a more abundant production there may be a greater population without any increase of poverty or even with a diminution of it The favourite argument against Berkeley’s theory of the nonexistence of matter and the most popularly effective next to a grin an argument moreover which is not confined to coxcombs nor to men like Samuel Johnson whose greatly overrated ability certainly did not lie in the direction of metaphysical speculation but is the stock argument of the Scotch school of metaphysicians is a palpable Ignoratio Elenchi The argument is perhaps as frequently expressed by gesture as by words and one of its commonest forms consists in knocking a stick against the ground This short and easy confutation overlooks the fact that in denying matter Berkeley did not deny any thing to which our senses bear witness and therefore can not be answered by any appeal to them His skepticism related to the supposed substratum or hidden cause of the appearances perceived by our senses the evidence of which whatever may be thought of its conclusiveness is certainly not the evidence of sense And it will always remain a signal proof of the want of metaphysical profundity of Reid Stewart and I am sorry to add of Brown that they should have persisted in asserting that Berkeley if he believed his own doctrine was bound to walk into the kennel or run his head against a post As if persons who do not recognize an occult cause of their sensations could not possibly believe that a fixed order subsists among the sensations themselves Such a want of comprehension of the distinction between a thing and its sensible manifestation or in metaphysical language between the noumenon and the phenomenon would be impossible to even the dullest disciple of Kant or Coleridge It would be easy to add a greater number of examples of this fallacy as well as of the others which I have attempted to characterize But a more copious exemplification does not seem to be necessary and the intelligent reader will have little difficulty in adding to the catalogue from his own reading and experience We shall therefore here close our exposition of the general principles of logic and proceed to the supplementary inquiry which is necessary to complete our design Si l’homme peut prdire avec une assurance presque entire les phnomnes dont il conna”t les lois si lors mme qu’elles lui sont inconnues il peut d’aprs l’exprience prvoir avec une grande probabilit les vnements de l’avenir pourquoi regarderaiton comme une entreprise chimrique celle de tracer avec quelque vraisemblance le tableau des destines futures de l’espce humaine d’aprs les rsultats de son histoire Le seul fondement de croyance dans les sciences naturelles est cette ide que les lois gnrales connues ou ignores qui rglent les phnomnes de l’univers sont ncessaires et constantes et par quelle raison ce principe seraitil moins vrai pour le dveloppement des facults intellectuelles et morales de l’homme que pour les autres oprations de la nature Enfin puisque des opinions formes d’aprs l’exprience sont la seule rgle de la conduite des hommes les plus sages pourquoi interdiraiton au philosophe d’appuyer ses conjectures sur cette mme base pourvu qu’il ne leur attribue pas une certitude suprieure ˆ celle qui peut na”tre du nombre de la constance de l’exactitude des observations CONDORCET Esquisse d’un Tableau Historique des Progrs de l’Esprit Humain Principles of Evidence and Theories of Method are not to be constructed a priori The laws of our rational faculty like those of every other natural agency are only learned by seeing the agent at work The earlier achievements of science were made without the conscious observance of any Scientific Method and we should never have known by what process truth is to be ascertained if we had not previously ascertained many truths But it was only the easier problems which could be thus resolved natural sagacity when it tried its strength against the more difficult ones either failed altogether or if it succeeded here and there in obtaining a solution had no sure means of convincing others that its solution was correct In scientific investigation as in all other works of human skill the way of obtaining the end is seen as it were instinctively by superior minds in some comparatively simple case and is then by judicious generalization adapted to the variety of complex cases We learn to do a thing in difficult circumstances by attending to the manner in which we have spontaneously done the same thing in easier ones This truth is exemplified by the history of the various branches of knowledge which have successively in the ascending order of their complication assumed the character of sciences and will doubtless receive fresh confirmation from those of which the final scientific constitution is yet to come and which are still abandoned to the uncertainties of vague and popular discussion Although several other sciences have emerged from this state at a comparatively recent date none now remain in it except those which relate to man himself the most complex and most difficult subject of study on which the human mind can be engaged Concerning the physical nature of man as an organized being though there is still much uncertainty and much controversy which can only be terminated by the general acknowledgment and employment of stricter rules of induction than are commonly recognized there is however a considerable body of truths which all who have attended to the subject consider to be fully established nor is there now any radical imperfection in the method observed in the department of science by its most distinguished modern teachers But the laws of Mind and in even a greater degree those of Society are so far from having attained a similar state of even partial recognition that it is still a controversy whether they are capable of becoming subjects of science in the strict sense of the term and among those who are agreed on this point there reigns the most irreconcilable diversity on almost every other Here therefore if anywhere the principles laid down in the preceding Books may be expected to be useful If on matters so much the most important with which human intellect can occupy itself a more general agreement is ever to exist among thinkers if what has been pronounced the proper study of mankind is not destined to remain the only subject which Philosophy can not succeed in rescuing from Empiricism the same process through which the laws of many simpler phenomena have by general acknowledgment been placed beyond dispute must be consciously and deliberately applied to those more difficult inquiries If there are some subjects on which the results obtained have finally received the unanimous assent of all who have attended to the proof and others on which mankind have not yet been equally successful on which the most sagacious minds have occupied themselves from the earliest date and have never succeeded in establishing any considerable body of truths so as to be beyond denial or doubt it is by generalizing the methods successfully followed in the former inquiries and adapting them to the latter that we may hope to remove this blot on the face of science The remaining chapters are an endeavour to facilitate this most desirable object In attempting this I am not unmindful how little can be done toward it in a mere treatise on Logic or how vague and unsatisfactory all precepts of Method must necessarily appear when not practically exemplified in the establishment of a body of doctrine Doubtless the most effectual mode of showing how the sciences of Ethics and Politics may be constructed would be to construct them a task which it needs scarcely be said I am not about to undertake But even if there were no other examples the memorable one of Bacon would be sufficient to demonstrate that it is sometimes both possible and useful to point out the way though without being one’s self prepared to adventure far into it And if more were to be attempted this at least is not a proper place for the attempt In substance whatever can be done in a work like this for the Logic of the Moral Sciences has been or ought to have been accomplished in the five preceding Books to which the present can be only a kind of supplement or appendix since the methods of investigation applicable to moral and social science must have been already described if I have succeeded in enumerating and characterizing those of science in general It remains however to examine which of those methods are more especially suited to the various branches of moral inquiry under what peculiar facilities or difficulties they are there employed how far the unsatisfactory state of those inquiries is owing to a wrong choice of methods how far to want of skill in the application of right ones and what degree of ultimate success may be attained or hoped for by a better choice or more careful employment of logical processes appropriate to the case In other words whether moral sciences exist or can exist to what degree of perfection they are susceptible of being carried and by what selection or adaptation of the methods brought to view in the previous part of this work that degree of perfection is attainable At the threshold of this inquiry we are met by an objection which if not removed would be fatal to the attempt to treat human conduct as a subject of science Are the actions of human beings like all other natural events subject to invariable laws Does that constancy of causation which is the foundation of every scientific theory of successive phenomena really obtain among them This is often denied and for the sake of systematic completeness if not from any very urgent practical necessity the question should receive a deliberate answer in this place We shall devote to the subject a chapter apart The question whether the law of causality applies in the same strict sense to human actions as to other phenomena is the celebrated controversy concerning the freedom of the will which from at least as far back as the time of Pelagius has divided both the philosophical and the religious world The affirmative opinion is commonly called the doctrine of Necessity as asserting human volitions and actions to be necessary and inevitable The negative maintains that the will is not determined like other phenomena by antecedents but determines itself that our volitions are not properly speaking the effects of causes or at least have no causes which they uniformly and implicitly obey I have already made it sufficiently apparent that the former of these opinions is that which I consider the true one but the misleading terms in which it is often expressed and the indistinct manner in which it is usually apprehended have both obstructed its reception and perverted its influence when received The metaphysical theory of freewill as held by philosophers for the practical feeling of it common in a greater or less degree to all mankind is in no way inconsistent with the contrary theory was invented because the supposed alternative of admitting human actions to be necessary was deemed inconsistent with every one’s instinctive consciousness as well as humiliating to the pride and even degrading to the moral nature of man Nor do I deny that the doctrine as sometimes held is open to these imputations for the misapprehension in which I shall be able to show that they originate unfortunately is not confined to the opponents of the doctrine but is participated in by many perhaps we might say by most of its supporters Correctly conceived the doctrine called Philosophical Necessity is simply this that given the motives which are present to an individual’s mind and given likewise the character and disposition of the individual the manner in which he will act might be unerringly inferred that if we knew the person thoroughly and knew all the inducements which are acting upon him we could foretell his conduct with as much certainty as we can predict any physical event This proposition I take to be a mere interpretation of universal experience a statement in words of what every one is internally convinced of No one who believed that he knew thoroughly the circumstances of any case and the characters of the different persons concerned would hesitate to foretell how all of them would act Whatever degree of doubt he may in fact feel arises from the uncertainty whether he really knows the circumstances or the character of some one or other of the persons with the degree of accuracy required but by no means from thinking that if he did know these things there could be any uncertainty what the conduct would be Nor does this full assurance conflict in the smallest degree with what is called our feeling of freedom We do not feel ourselves the less free because those to whom we are intimately known are well assured how we shall will to act in a particular case We often on the contrary regard the doubt what our conduct will be as a mark of ignorance of our character and sometimes even resent it as an imputation The religious metaphysicians who have asserted the freedom of the will have always maintained it to be consistent with divine foreknowledge of our actions and if with divine then with any other foreknowledge We may be free and yet another may have reason to be perfectly certain what use we shall make of our freedom It is not therefore the doctrine that our volitions and actions are invariable consequents of our antecedent states of mind that is either contradicted by our consciousness or felt to be degrading But the doctrine of causation when considered as obtaining between our volitions and their antecedents is almost universally conceived as involving more than this Many do not believe and very few practically feel that there is nothing in causation but invariable certain and unconditional sequence There are few to whom mere constancy of succession appears a sufficiently stringent bond of union for so peculiar a relation as that of cause and effect. Even if the reason repudiates the imagination retains the feeling of some more intimate connection of some peculiar tie or mysterious constraint exercised by the antecedent over the consequent Now this it is which considered as applying to the human will conflicts with our consciousness and revolts our feelings We are certain that in the case of our volitions there is not this mysterious constraint We know that we are not compelled as by a magical spell to obey any particular motive We feel that if we wished to prove that we have the power of resisting the motive we could do so that wish being it needs scarcely be observed a new antecedent and it would be humiliating to our pride and what is of more importance paralyzing to our desire of excellence if we thought otherwise But neither is any such mysterious compulsion now supposed by the best philosophical authorities to be exercised by any other cause over its effect Those who think that causes draw their effects after them by a mystical tie are right in believing that the relation between volitions and their antecedents is of another nature But they should go farther and admit that this is also true of all other effects and their antecedents If such a tie is considered to be involved in the word Necessity the doctrine is not true of human actions but neither is it then true of inanimate objects It would be more correct to say that matter is not bound by necessity than that mind is so That the freewill metaphysicians being mostly of the school which rejects Hume’s and Brown’s analysis of Cause and Effect, should miss their way for want of the light which that analysis affords can not surprise us The wonder is that the necessitarians who usually admit that philosophical theory should in practice equally lose sight of it The very same misconception of the doctrine called Philosophical Necessity which prevents the opposite party from recognizing its truth I believe to exist more or less obscurely in the minds of most necessitarians however they may in words disavow it I am much mistaken if they habitually feel that the necessity which they recognize in actions is but uniformity of order and capability of being predicted They have a feeling as if there were at bottom a stronger tie between the volitions and their causes as if when they asserted that the will is governed by the balance of motives they meant something more cogent than if they had only said that whoever knew the motives and our habitual susceptibilities to them could predict how we should will to act They commit in opposition to their own scientific system the very same mistake which their adversaries commit in obedience to theirs and in consequence do really in some instances suffer those depressing consequences which their opponents erroneously impute to the doctrine itself I am inclined to think that this error is almost wholly an effect of the associations with a word and that it would be prevented by forbearing to employ for the expression of the simple fact of causation so extremely inappropriate a term as Necessity That word in its other acceptations involves much more than mere uniformity of sequence it implies irresistibleness Applied to the will it only means that the given cause will be followed by the effect subject to all possibilities of counteraction by other causes but in common use it stands for the operation of those causes exclusively which are supposed too powerful to be counteracted at all When we say that all human actions take place of necessity we only mean that they will certainly happen if nothing prevents when we say that dying of want to those who can not get food is a necessity we mean that it will certainly happen whatever may be done to prevent it The application of the same term to the agencies on which human actions depend as is used to express those agencies of nature which are really uncontrollable can not fail when habitual to create a feeling of uncontrollableness in the former also This however is a mere illusion There are physical sequences which we call necessary as death for want of food or air there are others which though as much cases of causation as the former are not said to be necessary as death from poison which an antidote or the use of the stomachpump will sometimes avert It is apt to be forgotten by people’s feelings even if remembered by their understandings that human actions are in this last predicament they are never except in some cases of mania ruled by any one motive with such absolute sway that there is no room for the influence of any other The causes therefore on which action depends are never uncontrollable and any given effect is only necessary provided that the causes tending to produce it are not controlled That whatever happens could not have happened otherwise unless something had taken place which was capable of preventing it no one surely needs hesitate to admit But to call this by the name Necessity is to use the term in a sense so different from its primitive and familiar meaning from that which it bears in the common occasions of life as to amount almost to a play upon words The associations derived from the ordinary sense of the term will adhere to it in spite of all we can do and though the doctrine of Necessity as stated by most who hold it is very remote from fatalism it is probable that most necessitarians are fatalists more or less in their feelings A fatalist believes or half believes for nobody is a consistent fatalist not only that whatever is about to happen will be the infallible result of the causes which produce it which is the true necessitarian doctrine but moreover that there is no use in struggling against it that it will happen however we may strive to prevent it Now a necessitarian believing that our actions follow from our characters and that our characters follow from our organization our education and our circumstances is apt to be with more or less of consciousness on his part a fatalist as to his own actions and to believe that his nature is such or that his education and circumstances have so moulded his character that nothing can now prevent him from feeling and acting in a particular way or at least that no effort of his own can hinder it In the words of the sect which in our own day has most perseveringly inculcated and most perversely misunderstood this great doctrine his character is formed for him and not by him therefore his wishing that it had been formed differently is of no use he has no power to alter it But this is a grand error He has to a certain extent a power to alter his character Its being in the ultimate resort formed for him is not inconsistent with its being in part formed by him as one of the intermediate agents His character is formed by his circumstances including among these his particular organization but his own desire to mould it in a particular way is one of those circumstances and by no means one of the least influential We can not indeed directly will to be different from what we are But neither did those who are supposed to have formed our characters directly will that we should be what we are Their will had no direct power except over their own actions They made us what they did make us by willing not the end but the requisite means and we when our habits are not too inveterate can by similarly willing the requisite means make ourselves different If they could place us under the influence of certain circumstances we in like manner can place ourselves under the influence of other circumstances We are exactly as capable of making our own character if we will as others are of making it for us Yes answers the Owenite but these words if we will surrender the whole point since the will to alter our own character is given us not by any efforts of ours but by circumstances which we can not help it comes to us either from external causes or not at all Most true if the Owenite stops here he is in a position from which nothing can expel him Our character is formed by us as well as for us but the wish which induces us to attempt to form it is formed for us and how Not in general by our organization nor wholly by our education but by our experience experience of the painful consequences of the character we previously had or by some strong feeling of admiration or aspiration accidentally aroused But to think that we have no power of altering our character and to think that we shall not use our power unless we desire to use it are very different things and have a very different effect on the mind A person who does not wish to alter his character can not be the person who is supposed to feel discouraged or paralyzed by thinking himself unable to do it The depressing effect of the fatalist doctrine can only be felt where there is a wish to do what that doctrine represents as impossible It is of no consequence what we think forms our character when we have no desire of our own about forming it but it is of great consequence that we should not be prevented from forming such a desire by thinking the attainment impracticable and that if we have the desire we should know that the work is not so irrevocably done as to be incapable of being altered And indeed if we examine closely we shall find that this feeling of our being able to modify our own character if we wish is itself the feeling of moral freedom which we are conscious of A person feels morally free who feels that his habits or his temptations are not his masters but he theirs who even in yielding to them knows that he could resist that were he desirous of altogether throwing them off there would not be required for that purpose a stronger desire than he knows himself to be capable of feeling It is of course necessary to render our consciousness of freedom complete that we should have succeeded in making our character all we have hitherto attempted to make it for if we have wished and not attained we have to that extent not power over our own character we are not free Or at least we must feel that our wish if not strong enough to alter our character is strong enough to conquer our character when the two are brought into conflict in any particular case of conduct And hence it is said with truth that none but a person of confirmed virtue is completely free The application of so improper a term as Necessity to the doctrine of cause and effect in the matter of human character seems to me one of the most signal instances in philosophy of the abuse of terms and its practical consequences one of the most striking examples of the power of language over our associations The subject will never be generally understood until that objectionable term is dropped The freewill doctrine by keeping in view precisely that portion of the truth which the word Necessity puts out of sight namely the power of the mind to cooperate in the formation of its own character has given to its adherents a practical feeling much nearer to the truth than has generally I believe existed in the minds of necessitarians The latter may have had a stronger sense of the importance of what human beings can do to shape the characters of one another but the freewill doctrine has I believe fostered in its supporters a much stronger spirit of selfculture There is still one fact which requires to be noticed in addition to the existence of a power of selfformation before the doctrine of the causation of human actions can be freed from the confusion and misapprehensions which surround it in many minds When the will is said to be determined by motives a motive does not mean always or solely the anticipation of a pleasure or of a pain I shall not here inquire whether it be true that in the commencement all our voluntary actions are mere means consciously employed to obtain some pleasure or avoid some pain It is at least certain that we gradually through the influence of association come to desire the means without thinking of the end the action itself becomes an object of desire and is performed without reference to any motive beyond itself Thus far it may still be objected that the action having through association become pleasurable we are as much as before moved to act by the anticipation of a pleasure namely the pleasure of the action itself But granting this the matter does not end here As we proceed in the formation of habits and become accustomed to will a particular act or a particular course of conduct because it is pleasurable we at last continue to will it without any reference to its being pleasurable Although from some change in us or in our circumstances we have ceased to find any pleasure in the action or perhaps to anticipate any pleasure as the consequence of it we still continue to desire the action and consequently to do it In this manner it is that habits of hurtful excess continue to be practiced although they have ceased to be pleasurable and in this manner also it is that the habit of willing to persevere in the course which he has chosen does not desert the moral hero even when the reward however real which he doubtless receives from the consciousness of welldoing is any thing but an equivalent for the sufferings he undergoes or the wishes which he may have to renounce A habit of willing is commonly called a purpose and among the causes of our volitions and of the actions which flow from them must be reckoned not only likings and aversions but also purposes It is only when our purposes have become independent of the feelings of pain or pleasure from which they originally took their rise that we are said to have a confirmed character A character says Novalis is a completely fashioned will and the will once so fashioned may be steady and constant when the passive susceptibilities of pleasure and pain are greatly weakened or materially changed With the corrections and explanations now given the doctrine of the causation of our volitions by motives and of motives by the desirable objects offered to us combined with our particular susceptibilities of desire may be considered I hope as sufficiently established for the purposes of this treatise It is a common notion or at least it is implied in many common modes of speech that the thoughts feelings and actions of sentient beings are not a subject of science in the same strict sense in which this is true of the objects of outward nature This notion seems to involve some confusion of ideas which it is necessary to begin by clearing up Any facts are fitted in themselves to be a subject of science which follow one another according to constant laws although those laws may not have been discovered nor even be discoverable by our existing resources Take for instance the most familiar class of meteorological phenomena those of rain and sunshine Scientific inquiry has not yet succeeded in ascertaining the order of antecedence and consequence among these phenomena so as to be able at least in our regions of the earth to predict them with certainty or even with any high degree of probability Yet no one doubts that the phenomena depend on laws and that these must be derivative laws resulting from known ultimate laws those of heat electricity vaporization and elastic fluids Nor can it be doubted that if we were acquainted with all the antecedent circumstances we could even from those more general laws predict saving difficulties of calculation the state of the weather at any future time Meteorology therefore not only has in itself every natural requisite for being but actually is a science though from the difficulty of observing the facts on which the phenomena depend a difficulty inherent in the peculiar nature of those phenomena the science is extremely imperfect and were it perfect might probably be of little avail in practice since the data requisite for applying its principles to particular instances would rarely be procurable A case may be conceived of an intermediate character between the perfection of science and this its extreme imperfection It may happen that the greater causes those on which the principal part of the phenomena depends are within the reach of observation and measurement so that if no other causes intervened a complete explanation could be given not only of the phenomena in general but of all the variations and modifications which it admits of But inasmuch as other perhaps many other causes separately insignificant in their effects cooperate or conflict in many or in all cases with those greater causes the effect accordingly presents more or less of aberration from what would be produced by the greater causes alone Now if these minor causes are not so constantly accessible or not accessible at all to accurate observation the principal mass of the effect may still as before be accounted for and even predicted but there will be variations and modifications which we shall not be competent to explain thoroughly and our predictions will not be fulfilled accurately but only approximately It is thus for example with the theory of the tides No one doubts that Tidology as Dr Whewell proposes to call it is really a science As much of the phenomena as depends on the attraction of the sun and moon is completely understood and may in any even unknown part of the earth’s surface be foretold with certainty and the far greater part of the phenomena depends on those causes But circumstances of a local or casual nature such as the configuration of the bottom of the ocean the degree of confinement from shores the direction of the wind etc influence in many or in all places the height and time of the tide and a portion of these circumstances being either not accurately knowable not precisely measurable or not capable of being certainly foreseen the tide in known places commonly varies from the calculated result of general principles by some difference that we can not explain and in unknown ones may vary from it by a difference that we are not able to foresee or conjecture Nevertheless not only is it certain that these variations depend on causes and follow their causes by laws of unerring uniformity not only therefore is tidology a science like meteorology but it is what hitherto at least meteorology is not a science largely available in practice General laws may be laid down respecting the tides predictions may be founded on those laws and the result will in the main though often not with complete accuracy correspond to the predictions And this is what is or ought to be meant by those who speak of sciences which are not exact sciences Astronomy was once a science without being an exact science It could not become exact until not only the general course of the planetary motions but the perturbations also were accounted for and referred to their causes It has become an exact science because its phenomena have been brought under laws comprehending the whole of the causes by which the phenomena are influenced whether in a great or only in a trifling degree whether in all or only in some cases and assigning to each of those causes the share of effect which really belongs to it But in the theory of the tides the only laws as yet accurately ascertained are those of the causes which affect the phenomenon in all cases and in a considerable degree while others which affect it in some cases only or if in all only in a slight degree have not been sufficiently ascertained and studied to enable us to lay down their laws still less to deduce the completed law of the phenomenon by compounding the effects of the greater with those of the minor causes Tidology therefore is not yet an exact science not from any inherent incapacity of being so but from the difficulty of ascertaining with complete precision the real derivative uniformities By combining however the exact laws of the greater causes and of such of the minor ones as are sufficiently known with such empirical laws or such approximate generalizations respecting the miscellaneous variations as can be obtained by specific observation we can lay down general propositions which will be true in the main and on which with allowance for the degree of their probable inaccuracy we may safely ground our expectations and our conduct The science of human nature is of this description It falls far short of the standard of exactness now realized in Astronomy but there is no reason that it should not be as much a science as Tidology is or as Astronomy was when its calculations had only mastered the main phenomena but not the perturbations The phenomena with which this science is conversant being the thoughts feelings and actions of human beings it would have attained the ideal perfection of a science if it enabled us to foretell how an individual would think feel or act throughout life with the same certainty with which astronomy enables us to predict the places and the occultations of the heavenly bodies It needs scarcely be stated that nothing approaching to this can be done The actions of individuals could not be predicted with scientific accuracy were it only because we can not foresee the whole of the circumstances in which those individuals will be placed But further even in any given combination of present circumstances no assertion which is both precise and universally true can be made respecting the manner in which human beings will think feel or act This is not however because every person’s modes of thinking feeling and acting do not depend on causes nor can we doubt that if in the case of any individual our data could be complete we even now know enough of the ultimate laws by which mental phenomena are determined to enable us in many cases to predict with tolerable certainty what in the greater number of supposable combinations of circumstances his conduct or sentiments would be But the impressions and actions of human beings are not solely the result of their present circumstances but the joint result of those circumstances and of the characters of the individuals and the agencies which determine human character are so numerous and diversified nothing which has happened to the person throughout life being without its portion of influence that in the aggregate they are never in any two cases exactly similar Hence even if our science of human nature were theoretically perfect that is if we could calculate any character as we can calculate the orbit of any planet from given data still as the data are never all given nor ever precisely alike in different cases we could neither make positive predictions nor lay down universal propositions Inasmuch however as many of those effects which it is of most importance to render amenable to human foresight and control are determined like the tides in an incomparably greater degree by general causes than by all partial causes taken together depending in the main on those circumstances and qualities which are common to all mankind or at least to large bodies of them and only in a small degree on the idiosyncrasies of organization or the peculiar history of individuals it is evidently possible with regard to all such effects to make predictions which will almost always be verified and general propositions which are almost always true And whenever it is sufficient to know how the great majority of the human race or of some nation or class of persons will think feel and act these propositions are equivalent to universal ones For the purposes of political and social science this is sufficient As we formerly remarked an approximate generalization is in social inquiries for most practical purposes equivalent to an exact one that which is only probable when asserted of individual human beings indiscriminately selected being certain when affirmed of the character and collective conduct of masses It is no disparagement therefore to the science of Human Nature that those of its general propositions which descend sufficiently into detail to serve as a foundation for predicting phenomena in the concrete are for the most part only approximately true But in order to give a genuinely scientific character to the study it is indispensable that these approximate generalizations which in themselves would amount only to the lowest kind of empirical laws should be connected deductively with the laws of nature from which they result should be resolved into the properties of the causes on which the phenomena depend In other words the science of Human Nature may be said to exist in proportion as the approximate truths which compose a practical knowledge of mankind can be exhibited as corollaries from the universal laws of human nature on which they rest whereby the proper limits of those approximate truths would be shown and we should be enabled to deduce others for any new state of circumstances in anticipation of specific experience The proposition now stated is the text on which the two succeeding chapters will furnish the comment What the Mind is as well as what Matter is or any other question respecting Things in themselves as distinguished from their sensible manifestations it would be foreign to the purposes of this treatise to consider Here as throughout our inquiry we shall keep clear of all speculations respecting the mind’s own nature and shall understand by the laws of mind those of mental Phenomena of the various feelings or states of consciousness of sentient beings These according to the classification we have uniformly followed consist of Thoughts Emotions Volitions and Sensations the last being as truly states of Mind as the three former It is usual indeed to speak of sensations as states of body not of mind But this is the common confusion of giving one and the same name to a phenomenon and to the approximate cause or conditions of the phenomenon The immediate antecedent of a sensation is a state of body but the sensation itself is a state of mind If the word Mind means any thing it means that which feels Whatever opinion we hold respecting the fundamental identity or diversity of matter and mind in any case the distinction between mental and physical facts between the internal and the external world will always remain as a matter of classification and in that classification sensations like all other feelings must be ranked as mental phenomena The mechanism of their production both in the body itself and in what is called outward nature is all that can with any propriety be classed as physical The phenomena of mind then are the various feelings of our nature both those improperly called physical and those peculiarly designated as mental and by the laws of mind I mean the laws according to which those feelings generate one another All states of mind are immediately caused either by other states of mind or by states of body When a state of mind is produced by a state of mind I call the law concerned in the case a law of Mind When a state of mind is produced directly by a state of body the law is a law of Body and belongs to physical science With regard to those states of mind which are called sensations all are agreed that these have for their immediate antecedents states of body Every sensation has for its proximate cause some affection of the portion of our frame called the nervous system whether this affection originates in the action of some external object or in some pathological condition of the nervous organization itself The laws of this portion of our nature the varieties of our sensations and the physical conditions on which they proximately depend manifestly belong to the province of Physiology Whether the remainder of our mental states are similarly dependent on physical conditions is one of the vexatae questiones in the science of human nature It is still disputed whether our thoughts emotions and volitions are generated through the intervention of material mechanism whether we have organs of thought and of emotion in the same sense in which we have organs of sensation Many eminent physiologists hold the affirmative These contend that a thought for example is as much the result of nervous agency as a sensation that some particular state of our nervous system in particular of that central portion of it called the brain invariably precedes and is presupposed by every state of our consciousness According to this theory one state of mind is never really produced by another all are produced by states of body When one thought seems to call up another by association it is not really a thought which recalls a thought the association did not exist between the two thoughts but between the two states of the brain or nerves which preceded the thoughts one of those states recalls the other each being attended in its passage by the particular state of consciousness which is consequent on it On this theory the uniformities of succession among states of mind would be mere derivative uniformities resulting from the laws of succession of the bodily states which cause them There would be no original mental laws no Laws of Mind in the sense in which I use the term at all and mental science would be a mere branch though the highest and most recondite branch of the science of physiology M Comte accordingly claims the scientific cognizance of moral and intellectual phenomena exclusively for physiologists and not only denies to Psychology or Mental Philosophy properly so called the character of a science but places it in the chimerical nature of its objects and pretensions almost on a par with astrology But after all has been said which can be said it remains incontestable that there exist uniformities of succession among states of mind and that these can be ascertained by observation and experiment Further that every mental state has a nervous state for its immediate antecedent and proximate cause though extremely probable can not hitherto be said to be proved in the conclusive manner in which this can be proved of sensations and even were it certain yet every one must admit that we are wholly ignorant of the characteristics of these nervous states we know not and at present have no means of knowing in what respect one of them differs from another and our only mode of studying their successions or coexistences must be by observing the successions and coexistences of the mental states of which they are supposed to be the generators or causes The successions therefore which obtain among mental phenomena do not admit of being deduced from the physiological laws of our nervous organization and all real knowledge of them must continue for a long time at least if not always to be sought in the direct study by observation and experiment of the mental successions themselves Since therefore the order of our mental phenomena must be studied in those phenomena and not inferred from the laws of any phenomena more general there is a distinct and separate Science of Mind The relations indeed of that science to the science of physiology must never be overlooked or undervalued It must by no means be forgotten that the laws of mind may be derivative laws resulting from laws of animal life and that their truth therefore may ultimately depend on physical conditions and the influence of physiological states or physiological changes in altering or counteracting the mental successions is one of the most important departments of psychological study But on the other hand to reject the resource of psychological analysis and construct the theory of the mind solely on such data as physiology at present affords seems to me as great an error in principle and an even more serious one in practice Imperfect as is the science of mind I do not scruple to affirm that it is in a considerably more advanced state than the portion of physiology which corresponds to it and to discard the former for the latter appears to me an infringement of the true canons of inductive philosophy which must produce and which does produce erroneous conclusions in some very important departments of the science of human nature The subject then of Psychology is the uniformities of succession the laws whether ultimate or derivative according to which one mental state succeeds another is caused by or at least is caused to follow another Of these laws some are general others more special The following are examples of the most general laws First Whenever any state of consciousness has once been excited in us no matter by what cause an inferior degree of the same state of consciousness a state of consciousness resembling the former but inferior in intensity is capable of being reproduced in us without the presence of any such cause as excited it at first Thus if we have once seen or touched an object we can afterward think of the object though it be absent from our sight or from our touch If we have been joyful or grieved at some event we can think of or remember our past joy or grief though no new event of a happy or painful nature has taken place When a poet has put together a mental picture of an imaginary object a Castle of Indolence a Una or a Hamlet he can afterward think of the ideal object he has created without any fresh act of intellectual combination This law is expressed by saying in the language of Hume that every mental impression has its idea Secondly These ideas or secondary mental states are excited by our impressions or by other ideas according to certain laws which are called Laws of Association Of these laws the first is that similar ideas tend to excite one another The second is that when two impressions have been frequently experienced or even thought of either simultaneously or in immediate succession then whenever one of these impressions or the idea of it recurs it tends to excite the idea of the other The third law is that greater intensity in either or both of the impressions is equivalent in rendering them excitable by one another to a greater frequency of conjunction These are the laws of ideas on which I shall not enlarge in this place but refer the reader to works professedly psychological in particular to Mr James Mill’s Analysis of the Phenomena of the Human Mind where the principal laws of association along with many of their applications are copiously exemplified and with a masterly hand These simple or elementary Laws of Mind have been ascertained by the ordinary methods of experimental inquiry nor could they have been ascertained in any other manner But a certain number of elementary laws having thus been obtained it is a fair subject of scientific inquiry how far those laws can be made to go in explaining the actual phenomena It is obvious that complex laws of thought and feeling not only may but must be generated from these simple laws And it is to be remarked that the case is not always one of Composition of Causes the effect of concurring causes is not always precisely the sum of the effects of those causes when separate nor even always an effect of the same kind with them Reverting to the distinction which occupies so prominent a place in the theory of induction the laws of the phenomena of mind are sometimes analogous to mechanical but sometimes also to chemical laws When many impressions or ideas are operating in the mind together there sometimes takes place a process of a similar kind to chemical combination When impressions have been so often experienced in conjunction that each of them calls up readily and instantaneously the ideas of the whole group those ideas sometimes melt and coalesce into one another and appear not several ideas but one in the same manner as when the seven prismatic colours are presented to the eye in rapid succession the sensation produced is that of white But as in this last case it is correct to say that the seven colours when they rapidly follow one another generate white but not that they actually are white so it appears to me that the Complex Idea formed by the blending together of several simpler ones should when it really appears simple that is when the separate elements are not consciously distinguishable in it be said to result from or be generated by the simple ideas not to consist of them Our idea of an orange really consists of the simple ideas of a certain color a certain form a certain taste and smell etc because we can by interrogating our consciousness perceive all these elements in the idea But we can not perceive in so apparently simple a feeling as our perception of the shape of an object by the eye all that multitude of ideas derived from other senses without which it is well ascertained that no such visual perception would ever have had existence nor in our idea of Extension can we discover those elementary ideas of resistance derived from our muscular frame in which it has been conclusively shown that the idea originates These therefore are cases of mental chemistry in which it is proper to say that the simple ideas generate rather than that they compose the complex ones With respect to all the other constituents of the mind its beliefs its abstruser conceptions its sentiments emotions and volitions there are some among whom are Hartley and the author of the Analysis who think that the whole of these are generated from simple ideas of sensation by a chemistry similar to that which we have just exemplified These philosophers have made out a great part of their case but I am not satisfied that they have established the whole of it They have shown that there is such a thing as mental chemistry that the heterogeneous nature of a feeling A considered in relation to B and C is no conclusive argument against its being generated from B and C Having proved this they proceed to show that where A is found B and C were or may have been present and why therefore they ask should not A have been generated from B and C But even if this evidence were carried to the highest degree of completeness which it admits of if it were shown which hitherto it has not in all cases been that certain groups of associated ideas not only might have been but actually were present whenever the more recondite mental feeling was experienced this would amount only to the Method of Agreement and could not prove causation until confirmed by the more conclusive evidence of the Method of Difference If the question be whether Belief is a mere case of close association of ideas it would be necessary to examine experimentally if it be true that any ideas whatever provided they are associated with the required degree of closeness give rise to belief If the inquiry be into the origin of moral feelings the feeling for example of moral reprobation it is necessary to compare all the varieties of actions or states of mind which are ever morally disapproved and see whether in all these cases it can be shown or reasonably surmised that the action or state of mind had become connected by association in the disapproving mind with some particular class of hateful or disgusting ideas and the method employed is thus far that of Agreement But this is not enough Supposing this proved we must try further by the Method of Difference whether this particular kind of hateful or disgusting ideas when it becomes associated with an action previously indifferent will render that action a subject of moral disapproval If this question can be answered in the affirmative it is shown to be a law of the human mind that an association of that particular description is the generating cause of moral reprobation That all this is the case has been rendered extremely probable but the experiments have not been tried with the degree of precision necessary for a complete and absolutely conclusive induction It is further to be remembered that even if all which this theory of mental phenomena contends for could be proved we should not be the more enabled to resolve the laws of the more complex feelings into those of the simpler ones The generation of one class of mental phenomena from another whenever it can be made out is a highly interesting fact in psychological chemistry but it no more supersedes the necessity of an experimental study of the generated phenomenon than a knowledge of the properties of oxygen and sulphur enables us to deduce those of sulphuric acid without specific observation and experiment Whatever therefore may be the final issue of the attempt to account for the origin of our judgments our desires or our volitions from simpler mental phenomena it is not the less imperative to ascertain the sequences of the complex phenomena themselves by special study in conformity to the canons of Induction Thus in respect to Belief psychologists will always have to inquire what beliefs we have by direct consciousness and according to what laws one belief produces another what are the laws in virtue of which one thing is recognized by the mind either rightly or erroneously as evidence of another thing In regard to Desire they will have to examine what objects we desire naturally and by what causes we are made to desire things originally indifferent or even disagreeable to us and so forth It may be remarked that the general laws of association prevail among these more intricate states of mind in the same manner as among the simpler ones A desire an emotion an idea of the higher order of abstraction even our judgments and volitions when they have become habitual are called up by association according to precisely the same laws as our simple ideas In the course of these inquiries it will be natural and necessary to examine how far the production of one state of mind by another is influenced by any assignable state of body The commonest observation shows that different minds are susceptible in very different degrees to the action of the same psychological causes The idea for example of a given desirable object will excite in different minds very different degrees of intensity of desire The same subject of meditation presented to different minds will excite in them very unequal degrees of intellectual action These differences of mental susceptibility in different individuals may be first original and ultimate facts or secondly they may be consequences of the previous mental history of those individuals or thirdly and lastly they may depend on varieties of physical organization That the previous mental history of the individuals must have some share in producing or in modifying the whole of their mental character is an inevitable consequence of the laws of mind but that differences of bodily structure also cooperate is the opinion of all physiologists confirmed by common experience It is to be regretted that hitherto this experience being accepted in the gross without due analysis has been made the groundwork of empirical generalizations most detrimental to the progress of real knowledge It is certain that the natural differences which really exist in the mental predispositions or susceptibilities of different persons are often not unconnected with diversities in their organic constitution But it does not therefore follow that these organic differences must in all cases influence the mental phenomena directly and immediately They often affect them through the medium of their psychological causes For example the idea of some particular pleasure may excite in different persons even independently of habit or education very different strengths of desire and this may be the effect of their different degrees or kinds of nervous susceptibility but these organic differences we must remember will render the pleasurable sensation itself more intense in one of these persons than in the other so that the idea of the pleasure will also be an intenser feeling and will by the operation of mere mental laws excite an intenser desire without its being necessary to suppose that the desire itself is directly influenced by the physical peculiarity As in this so in many cases such differences in the kind or in the intensity of the physical sensations as must necessarily result from differences of bodily organization will of themselves account for many differences not only in the degree but even in the kind of the other mental phenomena So true is this that even different qualities of mind different types of mental character will naturally be produced by mere differences of intensity in the sensations generally as is well pointed out in the able essay on Dr Priestley by Mr Martineau mentioned in a former chapter The sensations which form the elements of all knowledge are received either simultaneously or successively when several are received simultaneously as the smell the taste the color the form etc of a fruit their association together constitutes our idea of an object when received successively their association makes up the idea of an event Any thing then which favours the associations of synchronous ideas will tend to produce a knowledge of objects a perception of qualities while any thing which favours association in the successive order will tend to produce a knowledge of events of the order of occurrences and of the connection of cause and effect: in other words in the one case a perceptive mind with a discriminate feeling of the pleasurable and painful properties of things a sense of the grand and the beautiful will be the result in the other a mind attentive to the movements and phenomena a ratiocinative and philosophic intellect Now it is an acknowledged principle that all sensations experienced during the presence of any vivid impression become strongly associated with it and with each other and does it not follow that the synchronous feelings of a sensitive constitution ie the one which has vivid impressions will be more intimately blended than in a differently formed mind If this suggestion has any foundation in truth it leads to an inference not unimportant that where nature has endowed an individual with great original susceptibility he will probably be distinguished by fondness for natural history a relish for the beautiful and great and moral enthusiasm where there is but a mediocrity of sensibility a love of science of abstract truth with a deficiency of taste and of fervor is likely to be the result We see from this example that when the general laws of mind are more accurately known and above all more skilfully applied to the detailed explanation of mental peculiarities they will account for many more of those peculiarities than is ordinarily supposed Unfortunately the reaction of the last and present generation against the philosophy of the eighteenth century has produced a very general neglect of this great department of analytical inquiry of which consequently the recent progress has been by no means proportional to its early promise The majority of those who speculate on human nature prefer dogmatically to assume that the mental differences which they perceive or think they perceive among human beings are ultimate facts incapable of being either explained or altered rather than take the trouble of fitting themselves by the requisite processes of thought for referring those mental differences to the outward causes by which they are for the most part produced and on the removal of which they would cease to exist The German school of metaphysical speculation which has not yet lost its temporary predominance in European thought has had this among many other injurious influences and at the opposite extreme of the psychological scale no writer either of early or of recent date is chargeable in a higher degree with this aberration from the true scientific spirit than M Comte It is certain that in human beings at least differences in education and in outward circumstances are capable of affording an adequate explanation of by far the greatest portion of character and that the remainder may be in great part accounted for by physical differences in the sensations produced in different individuals by the same external or internal cause There are however some mental facts which do not seem to admit of these modes of explanation Such to take the strongest case are the various instincts of animals and the portion of human nature which corresponds to those instincts No mode has been suggested even by way of hypothesis in which these can receive any satisfactory or even plausible explanation from psychological causes alone and there is great reason to think that they have as positive and even as direct and immediate a connection with physical conditions of the brain and nerves as any of our mere sensations have A supposition which it is perhaps not superfluous to add in no way conflicts with the indisputable fact that these instincts may be modified to any extent or entirely conquered in human beings and to no inconsiderable extent even in some of the domesticated animals by other mental influences and by education Whether organic causes exercise a direct influence over any other classes of mental phenomena is hitherto as far from being ascertained as is the precise nature of the organic conditions even in the case of instincts The physiology however of the brain and nervous system is in a state of such rapid advance and is continually bringing forth such new and interesting results that if there be really a connection between mental peculiarities and any varieties cognizable by our senses in the structure of the cerebral and nervous apparatus the nature of that connection is now in a fair way of being found out The latest discoveries in cerebral physiology appear to have proved that any such connection which may exist is of a radically different character from that contended for by Gall and his followers and that whatever may hereafter be found to be the true theory of the subject phrenology at least is untenable The laws of mind as characterized in the preceding chapter compose the universal or abstract portion of the philosophy of human nature and all the truths of common experience constituting a practical knowledge of mankind must to the extent to which they are truths be results or consequences of these Such familiar maxims when collected a posteriori from observation of life occupy among the truths of the science the place of what in our analysis of Induction have so often been spoken of under the title of Empirical Laws An Empirical Law it will be remembered is a uniformity whether of succession or of coexistence which holds true in all instances within our limits of observation but is not of a nature to afford any assurance that it would hold beyond those limits either because the consequent is not really the effect of the antecedent but forms part along with it of a chain of effects flowing from prior causes not yet ascertained or because there is ground to believe that the sequence though a case of causation is resolvable into simpler sequences and depending therefore on a concurrence of several natural agencies is exposed to an unknown multitude of possibilities of counteraction In other words an empirical law is a generalization of which not content with finding it true we are obliged to ask why is it true knowing that its truth is not absolute but dependent on some more general conditions and that it can only be relied on in so far as there is ground of assurance that those conditions are realized Now the observations concerning human affairs collected from common experience are precisely of this nature Even if they were universally and exactly true within the bounds of experience which they never are still they are not the ultimate laws of human action they are not the principles of human nature but results of those principles under the circumstances in which mankind have happened to be placed When the Psalmist said in his haste that all men are liars he enunciated what in some ages and countries is borne out by ample experience but it is not a law of man’s nature to lie though it is one of the consequences of the laws of human nature that lying is nearly universal when certain external circumstances exist universally especially circumstances productive of habitual distrust and fear When the character of the old is asserted to be cautious and of the young impetuous this again is but an empirical law for it is not because of their youth that the young are impetuous nor because of their age that the old are cautious It is chiefly if not wholly because the old during their many years of life have generally had much experience of its various evils and having suffered or seen others suffer much from incautious exposure to them have acquired associations favourable to circumspection while the young as well from the absence of similar experience as from the greater strength of the inclinations which urge them to enterprise engage themselves in it more readily Here then is the explanation of the empirical law here are the conditions which ultimately determine whether the law holds good or not If an old man has not been oftener than most young men in contact with danger and difficulty he will be equally incautious if a youth has not stronger inclinations than an old man he probably will be as little enterprising The empirical law derives whatever truth it has from the causal laws of which it is a consequence If we know those laws we know what are the limits to the derivative law while if we have not yet accounted for the empirical law if it rests only on observation there is no safety in applying it far beyond the limits of time place and circumstance in which the observations were made The really scientific truths then are not these empirical laws but the causal laws which explain them The empirical laws of those phenomena which depend on known causes and of which a general theory can therefore be constructed have whatever may be their value in practice no other function in science than that of verifying the conclusions of theory Still more must this be the case when most of the empirical laws amount even within the limits of observation only to approximate generalizations This however is not so much as is sometimes supposed a peculiarity of the sciences called moral It is only in the simplest branches of science that empirical laws are ever exactly true and not always in those Astronomy for example is the simplest of all the sciences which explain in the concrete the actual course of natural events The causes or forces on which astronomical phenomena depend are fewer in number than those which determine any other of the great phenomena of nature Accordingly as each effect results from the conflict of but few causes a great degree of regularity and uniformity might be expected to exist among the effects and such is really the case they have a fixed order and return in cycles But propositions which should express with absolute correctness all the successive positions of a planet until the cycle is completed would be of almost unmanageable complexity and could be obtained from theory alone The generalizations which can be collected on the subject from direct observation even such as Kepler’s law are mere approximations the planets owing to their perturbations by one another do not move in exact ellipses Thus even in astronomy perfect exactness in the mere empirical laws is not to be looked for much less then in more complex subjects of inquiry The same example shows how little can be inferred against the universality or even the simplicity of the ultimate laws from the impossibility of establishing any but approximate empirical laws of the effects The laws of causation according to which a class of phenomena are produced may be very few and simple and yet the effects themselves may be so various and complicated that it shall be impossible to trace any regularity whatever completely through them For the phenomena in question may be of an eminently modifiable character insomuch that innumerable circumstances are capable of influencing the effect although they may all do it according to a very small number of laws Suppose that all which passes in the mind of man is determined by a few simple laws still if those laws be such that there is not one of the facts surrounding a human being or of the events which happen to him that does not influence in some mode or degree his subsequent mental history and if the circumstances of different human beings are extremely different it will be no wonder if very few propositions can be made respecting the details of their conduct or feelings which will be true of all mankind Now without deciding whether the ultimate laws of our mental nature are few or many it is at least certain that they are of the above description It is certain that our mental states and our mental capacities and susceptibilities are modified either for a time or permanently by every thing which happens to us in life Considering therefore how much these modifying causes differ in the case of any two individuals it would be unreasonable to expect that the empirical laws of the human mind the generalizations which can be made respecting the feelings or actions of mankind without reference to the causes that determine them should be any thing but approximate generalizations They are the common wisdom of common life and as such are invaluable especially as they are mostly to be applied to cases not very dissimilar to those from which they were collected But when maxims of this sort collected from Englishmen come to be applied to Frenchmen or when those collected from the present day are applied to past or future generations they are apt to be very much at fault Unless we have resolved the empirical law into the laws of the causes on which it depends and ascertained that those causes extend to the case which we have in view there can be no reliance placed in our inferences For every individual is surrounded by circumstances different from those of every other individual every nation or generation of mankind from every other nation or generation and none of these differences are without their influence in forming a different type of character There is indeed also a certain general resemblance but peculiarities of circumstances are continually constituting exceptions even to the propositions which are true in the great majority of cases Although however there is scarcely any mode of feeling or conduct which is in the absolute sense common to all mankind and though the generalizations which assert that any given variety of conduct or feeling will be found universally however nearly they may approximate to truth within given limits of observation will be considered as scientific propositions by no one who is at all familiar with scientific investigation yet all modes of feeling and conduct met with among mankind have causes which produce them and in the propositions which assign those causes will be found the explanation of the empirical laws and the limiting principle of our reliance on them Human beings do not all feel and act alike in the same circumstances but it is possible to determine what makes one person in a given position feel or act in one way another in another how any given mode of feeling and conduct compatible with the general laws physical and mental of human nature has been or may be formed In other words mankind have not one universal character but there exist universal laws of the Formation of Character And since it is by these laws combined with the facts of each particular case that the whole of the phenomena of human action and feeling are produced it is on these that every rational attempt to construct the science of human nature in the concrete and for practical purposes must proceed The laws then of the formation of character being the principal object of scientific inquiry into human nature it remains to determine the method of investigation best fitted for ascertaining them And the logical principles according to which this question is to be decided must be those which preside over every other attempt to investigate the laws of very complex phenomena For it is evident that both the character of any human being and the aggregate of the circumstances by which that character has been formed are facts of a high order of complexity Now to such cases we have seen that the Deductive Method setting out from general laws and verifying their consequences by specific experience is alone applicable The grounds of this great logical doctrine have formerly been stated and its truth will derive additional support from a brief examination of the specialties of the present case There are only two modes in which laws of nature can be ascertained deductively and experimentally including under the denomination of experimental inquiry observation as well as artificial experiment Are the laws of the formation of character susceptible of a satisfactory investigation by the method of experimentation Evidently not because even if we suppose unlimited power of varying the experiment which is abstractedly possible though no one but an Oriental despot has that power or if he had would probably be disposed to exercise it a still more essential condition is wanting the power of performing any of the experiments with scientific accuracy The instances requisite for the prosecution of a directly experimental inquiry into the formation of character would be a number of human beings to bring up and educate from infancy to mature age And to perform any one of these experiments with scientific propriety it would be necessary to know and record every sensation or impression received by the young pupil from a period long before it could speak including its own notions respecting the sources of all those sensations and impressions It is not only impossible to do this completely but even to do so much of it as should constitute a tolerable approximation One apparently trivial circumstance which eluded our vigilance might let in a train of impressions and associations sufficient to vitiate the experiment as an authentic exhibition of the effects flowing from given causes No one who has sufficiently reflected on education is ignorant of this truth and whoever has not will find it most instructively illustrated in the writings of Rousseau and Helvetius on that great subject Under this impossibility of studying the laws of the formation of character by experiments purposely contrived to elucidate them there remains the resource of simple observation But if it be impossible to ascertain the influencing circumstances with any approach to completeness even when we have the shaping of them ourselves much more impossible is it when the cases are further removed from our observation and altogether out of our control Consider the difficulty of the very first step of ascertaining what actually is the character of the individual in each particular case that we examine There is hardly any person living concerning some essential part of whose character there are not differences of opinion even among his intimate acquaintances and a single action or conduct continued only for a short time goes a very little way toward ascertaining it We can only make our observations in a rough way and en masse not attempting to ascertain completely in any given instance what character has been formed and still less by what causes but only observing in what state of previous circumstances it is found that certain marked mental qualities or deficiencies oftenest exist These conclusions besides that they are mere approximate generalizations deserve no reliance even as such unless the instances are sufficiently numerous to eliminate not only chance but every assignable circumstance in which a number of the cases examined may happen to have resembled one another So numerous and various too are the circumstances which form individual character that the consequence of any particular combination is hardly ever some definite and strongly marked character always found where that combination exists and not otherwise What is obtained even after the most extensive and accurate observation is merely a comparative result as for example that in a given number of Frenchmen taken indiscriminately there will be found more persons of a particular mental tendency and fewer of the contrary tendency than among an equal number of Italians or English similarly taken or thus of a hundred Frenchmen and an equal number of Englishmen fairly selected and arranged according to the degree in which they possess a particular mental characteristic each number 1 2 3 etc of the one series will be found to possess more of that characteristic than the corresponding number of the other Since therefore the comparison is not one of kinds but of ratios and degrees and since in proportion as the differences are slight it requires a greater number of instances to eliminate chance it can not often happen to any one to know a sufficient number of cases with the accuracy requisite for making the sort of comparison last mentioned less than which however would not constitute a real induction Accordingly there is hardly one current opinion respecting the characters of nations classes or descriptions of persons which is universally acknowledged as indisputable And finally if we could even obtain by way of experiment a much more satisfactory assurance of these generalizations than is really possible they would still be only empirical laws They would show indeed that there was some connection between the type of character formed and the circumstances existing in the case but not what the precise connection was nor to which of the peculiarities of those circumstances the effect was really owing They could only therefore be received as results of causation requiring to be resolved into the general laws of the causes until the determination of which we could not judge within what limits the derivative laws might serve as presumptions in cases yet unknown or even be depended on as permanent in the very cases from which they were collected The French people had or were supposed to have a certain national character but they drive out their royal family and aristocracy alter their institutions pass through a series of extraordinary events for the greater part of a century and at the end of that time their character is found to have undergone important changes A long list of mental and moral differences are observed or supposed to exist between men and women but at some future and it may be hoped not distant period equal freedom and an equally independent social position come to be possessed by both and their differences of character are either removed or totally altered But if the differences which we think we observe between French and English or between men and women can be connected with more general laws if they be such as might be expected to be produced by the differences of government former customs and physical peculiarities in the two nations and by the diversities of education occupations personal independence and social privileges and whatever original differences there may be in bodily strength and nervous sensibility between the two sexes then indeed the coincidence of the two kinds of evidence justifies us in believing that we have both reasoned rightly and observed rightly Our observation though not sufficient as proof is ample as verification And having ascertained not only the empirical laws but the causes of the peculiarities we need be under no difficulty in judging how far they may be expected to be permanent or by what circumstances they would be modified or destroyed Since then it is impossible to obtain really accurate propositions respecting the formation of character from observation and experiment alone we are driven perforce to that which even if it had not been the indispensable would have been the most perfect mode of investigation and which it is one of the principal aims of philosophy to extend namely that which tries its experiments not on the complex facts but on the simple ones of which they are compounded and after ascertaining the laws of the causes the composition of which gives rise to the complex phenomena then considers whether these will not explain and account for the approximate generalizations which have been framed empirically respecting the sequences of those complex phenomena The laws of the formation of character are in short derivative laws resulting from the general laws of mind and are to be obtained by deducing them from those general laws by supposing any given set of circumstances and then considering what according to the laws of mind will be the influence of those circumstances on the formation of character A science is thus formed to which I would propose to give the name of Ethology or the Science of Character from a word more nearly corresponding to the term character as I here use it than any other word in the same language The name is perhaps etymologically applicable to the entire science of our mental and moral nature but if as is usual and convenient we employ the name Psychology for the science of the elementary laws of mind Ethology will serve for the ulterior science which determines the kind of character produced in conformity to those general laws by any set of circumstances physical and moral According to this definition Ethology is the science which corresponds to the art of education in the widest sense of the term including the formation of national or collective character as well as individual It would indeed be vain to expect however completely the laws of the formation of character might be ascertained that we could know so accurately the circumstances of any given case as to be able positively to predict the character that would be produced in that case But we must remember that a degree of knowledge far short of the power of actual prediction is often of much practical value There may be great power of influencing phenomena with a very imperfect knowledge of the causes by which they are in any given instance determined It is enough that we know that certain means have a tendency to produce a given effect and that others have a tendency to frustrate it When the circumstances of an individual or of a nation are in any considerable degree under our control we may by our knowledge of tendencies be enabled to shape those circumstances in a manner much more favourable to the ends we desire than the shape which they would of themselves assume This is the limit of our power but within this limit the power is a most important one This science of Ethology may be called the Exact Science of Human Nature for its truths are not like the empirical laws which depend on them approximate generalizations but real laws It is however as in all cases of complex phenomena necessary to the exactness of the propositions that they should be hypothetical only and affirm tendencies not facts They must not assert that something will always or certainly happen but only that such and such will be the effect of a given cause so far as it operates uncounteracted It is a scientific proposition that bodily strength tends to make men courageous not that it always makes them so that an interest on one side of a question tends to bias the judgment not that it invariably does so that experience tends to give wisdom not that such is always its effect These propositions being assertive only of tendencies are not the less universally true because the tendencies may be frustrated While on the one hand Psychology is altogether or principally a science of observation and experiment Ethology as I have conceived it is as I have already remarked altogether deductive The one ascertains the simple laws of Mind in general the other traces their operation in complex combinations of circumstances Ethology stands to Psychology in a relation very similar to that in which the various branches of natural philosophy stand to mechanics The principles of Ethology are properly the middle principles the axiomata media as Bacon would have said of the science of mind as distinguished on the one hand from the empirical laws resulting from simple observation and on the other from the highest generalizations And this seems a suitable place for a logical remark which though of general application is of peculiar importance in reference to the present subject Bacon has judiciously observed that the axiomata media of every science principally constitute its value The lowest generalizations until explained by and resolved into the middle principles of which they are the consequences have only the imperfect accuracy of empirical laws while the most general laws are too general and include too few circumstances to give sufficient indication of what happens in individual cases where the circumstances are almost always immensely numerous In the importance therefore which Bacon assigns in every science to the middle principles it is impossible not to agree with him But I conceive him to have been radically wrong in his doctrine respecting the mode in which these axiomata media should be arrived at though there is no one proposition laid down in his works for which he has been more extravagantly eulogized He enunciates as a universal rule that induction should proceed from the lowest to the middle principles and from those to the highest never reversing that order and consequently leaving no room for the discovery of new principles by way of deduction at all It is not to be conceived that a man of his sagacity could have fallen into this mistake if there had existed in his time among the sciences which treat of successive phenomena one single instance of a deductive science such as mechanics astronomy optics acoustics etc now are In those sciences it is evident that the higher and middle principles are by no means derived from the lowest but the reverse In some of them the very highest generalizations were those earliest ascertained with any scientific exactness as for example in mechanics the laws of motion Those general laws had not indeed at first the acknowledged universality which they acquired after having been successfully employed to explain many classes of phenomena to which they were not originally seen to be applicable as when the laws of motion were employed in conjunction with other laws to explain deductively the celestial phenomena Still the fact remains that the propositions which were afterward recognized as the most general truths of the science were of all its accurate generalizations those earliest arrived at Bacon’s greatest merit can not therefore consist as we are so often told that it did in exploding the vicious method pursued by the ancients of flying to the highest generalizations first and deducing the middle principles from them since this is neither a vicious nor an exploded but the universally accredited method of modern science and that to which it owes its greatest triumphs The error of ancient speculation did not consist in making the largest generalizations first but in making them without the aid or warrant of rigorous inductive methods and applying them deductively without the needful use of that important part of the Deductive Method termed Verification The order in which truths of the various degrees of generality should be ascertained can not I apprehend be prescribed by any unbending rule I know of no maxim which can be laid down on the subject but to obtain those first in respect to which the conditions of a real induction can be first and most completely realized Now wherever our means of investigation can reach causes without stopping at the empirical laws of the effects the simplest cases being those in which fewest causes are simultaneously concerned will be most amenable to the inductive process and these are the cases which elicit laws of the greatest comprehensiveness In every science therefore which has reached the stage at which it becomes a science of causes it will be usual as well as desirable first to obtain the highest generalizations and then deduce the more special ones from them Nor can I discover any foundation for the Baconian maxim so much extolled by subsequent writers except this That before we attempt to explain deductively from more general laws any new class of phenomena it is desirable to have gone as far as is practicable in ascertaining the empirical laws of those phenomena so as to compare the results of deduction not with one individual instance after another but with general propositions expressive of the points of agreement which have been found among many instances For if Newton had been obliged to verify the theory of gravitation not by deducing from it Kepler’s laws but by deducing all the observed planetary positions which had served Kepler to establish those laws the Newtonian theory would probably never have emerged from the state of an hypothesis The applicability of these remarks to the special case under consideration can not admit of question The science of the formation of character is a science of causes The subject is one to which those among the canons of induction by which laws of causation are ascertained can be rigorously applied It is therefore both natural and advisable to ascertain the simplest which are necessarily the most general laws of causation first and to deduce the middle principles from them In other words Ethology the deductive science is a system of corollaries from Psychology the experimental science Of these the earlier alone has been as yet really conceived or studied as a science the other Ethology is still to be created But its creation has at length become practicable The empirical laws destined to verify its deductions have been formed in abundance by every successive age of humanity and the premises for the deductions are now sufficiently complete Excepting the degree of uncertainty which still exists as to the extent of the natural differences of individual minds and the physical circumstances on which these may be dependent considerations which are of secondary importance when we are considering mankind in the average or en masse I believe most competent judges will agree that the general laws of the different constituent elements of human nature are even now sufficiently understood to render it possible for a competent thinker to deduce from those laws with a considerable approach to certainty the particular type of character which would be formed in mankind generally by any assumed set of circumstances A science of Ethology founded on the laws of Psychology is therefore possible though little has yet been done and that little not at all systematically toward forming it The progress of this important but most imperfect science will depend on a double process first that of deducing theoretically the ethological consequences of particular circumstances of position and comparing them with the recognized results of common experience and secondly the reverse operation increased study of the various types of human nature that are to be found in the world conducted by persons not only capable of analyzing and recording the circumstances in which these types severally prevail but also sufficiently acquainted with psychological laws to be able to explain and account for the characteristics of the type by the peculiarities of the circumstances the residuum alone when there proves to be any being set down to the account of congenital predispositions For the experimental or a posteriori part of this process the materials are continually accumulating by the observation of mankind So far as thought is concerned the great problem of Ethology is to deduce the requisite middle principles from the general laws of Psychology The subject to be studied is the origin and sources of all those qualities in human beings which are interesting to us either as facts to be produced to be avoided or merely to be understood and the object is to determine from the general laws of mind combined with the general position of our species in the universe what actual or possible combinations of circumstances are capable of promoting or of preventing the production of those qualities A science which possesses middle principles of this kind arranged in the order not of causes but of the effects which it is desirable to produce or to prevent is duly prepared to be the foundation of the corresponding Art And when Ethology shall be thus prepared practical education will be the mere transformation of those principles into a parallel system of precepts and the adaptation of these to the sum total of the individual circumstances which exist in each particular case It is hardly necessary again to repeat that as in every other deductive science verification a posteriori must proceed pari passu with deduction a priori The inference given by theory as to the type of character which would be formed by any given circumstances must be tested by specific experience of those circumstances whenever obtainable and the conclusions of the science as a whole must undergo a perpetual verification and correction from the general remarks afforded by common experience respecting human nature in our own age and by history respecting times gone by The conclusions of theory can not be trusted unless confirmed by observation nor those of observation unless they can be affiliated to theory by deducing them from the laws of human nature and from a close analysis of the circumstances of the particular situation It is the accordance of these two kinds of evidence separately taken the consilience of a priori reasoning and specific experience which forms the only sufficient ground for the principles of any science so immersed in matter dealing with such complex and concrete phenomena as Ethology Next after the science of individual man comes the science of man in society of the actions of collective masses of mankind and the various phenomena which constitute social life If the formation of individual character is already a complex subject of
because the number of concurrent causes all exercising more or less influence on the total effect is greater in the proportion in which a nation or the species at large exposes a larger surface to the operation of agents psychological and physical than any single individual If it was necessary to prove in opposition to an existing prejudice that the simpler of the two is capable of being a subject of science the prejudice is likely to be yet stronger against the possibility of giving a scientific character to the study of Politics and of the phenomena of Society It is accordingly but of yesterday that the conception of a political or social science has existed anywhere but in the mind of here and there an insulated thinker generally very ill prepared for its realization though the subject itself has of all others engaged the most general attention and been a theme of interested and earnest discussions almost from the beginning of recorded time The condition indeed of politics as a branch of knowledge was until very lately and has scarcely even yet ceased to be that which Bacon animadverted on as the natural state of the sciences while their cultivation is abandoned to practitioners not being carried on as a branch of speculative inquiry but only with a view to the exigencies of daily practice and the fructifera experimenta therefore being aimed at almost to the exclusion of the lucifera Such was medical investigation before physiology and natural history began to be cultivated as branches of general knowledge The only questions examined were what diet is wholesome or what medicine will cure some given disease without any previous systematic inquiry into the laws of nutrition and of the healthy and morbid action of the different organs on which laws the effect of any diet or medicine must evidently depend And in politics the questions which engaged general attention were similar Is such an enactment or such a form of government beneficial or the reverse either universally or to some particular community without any previous inquiry into the general conditions by which the operation of legislative measures or the effects produced by forms of government are determined Students in politics thus attempted to study the pathology and therapeutics of the social body before they had laid the necessary foundation in its physiology to cure disease without understanding the laws of health And the result was such as it must always be when persons even of ability attempt to deal with the complex questions of a science before its simpler and more elementary truths have been established No wonder that when the phenomena of society have so rarely been contemplated in the point of view characteristic of science the philosophy of society should have made little progress should contain few general propositions sufficiently precise and certain for common inquirers to recognize in them a scientific character The vulgar notion accordingly is that all pretension to lay down general truths on politics and society is quackery that no universality and no certainty are attainable in such matters What partly excuses this common notion is that it is really not without foundation in one particular sense A large proportion of those who have laid claim to the character of philosophic politicians have attempted not to ascertain universal sequences but to frame universal precepts They have imagined some one form of government or system of laws to fit all cases a pretension well meriting the ridicule with which it is treated by practitioners and wholly unsupported by the analogy of the art to which from the nature of its subject that of politics must be the most nearly allied No one now supposes it possible that one remedy can cure all diseases or even the same disease in all constitutions and habits of body It is not necessary even to the perfection of a science that the corresponding art should possess universal or even general rules The phenomena of society might not only be completely dependent on known causes but the mode of action of all those causes might be reducible to laws of considerable simplicity and yet no two cases might admit of being treated in precisely the same manner So great might be the variety of circumstances on which the results in different cases depend that the art might not have a single general precept to give except that of watching the circumstances of the particular case and adapting our measures to the effects which according to the principles of the science result from those circumstances But although in so complicated a class of subjects it is impossible to lay down practical maxims of universal application it does not follow that the phenomena do not conform to universal laws All phenomena of society are phenomena of human nature generated by the action of outward circumstances upon masses of human beings and if therefore the phenomena of human thought feeling and action are subject to fixed laws the phenomena of society can not but conform to fixed laws the consequence of the preceding There is indeed no hope that these laws though our knowledge of them were as certain and as complete as it is in astronomy would enable us to predict the history of society like that of the celestial appearances for thousands of years to come But the difference of certainty is not in the laws themselves it is in the data to which these laws are to be applied In astronomy the causes influencing the result are few and change little and that little according to known laws we can ascertain what they are now and thence determine what they will be at any epoch of a distant future The data therefore in astronomy are as certain as the laws themselves The circumstances on the contrary which influence the condition and progress of society are innumerable and perpetually changing and though they all change in obedience to causes and therefore to laws the multitude of the causes is so great as to defy our limited powers of calculation Not to say that the impossibility of applying precise numbers to facts of such a description would set an impassable limit to the possibility of calculating them beforehand even if the powers of the human intellect were otherwise adequate to the task But as before remarked an amount of knowledge quite insufficient for prediction may be most valuable for guidance The science of society would have attained a very high point of perfection if it enabled us in any given condition of social affairs in the condition for instance of Europe or any European country at the present time to understand by what causes it had in any and every particular been made what it was whether it was tending to any and to what changes what effects each feature of its existing state was likely to produce in the future and by what means any of those effects might be prevented modified or accelerated or a different class of effects superinduced There is nothing chimerical in the hope that general laws sufficient to enable us to answer these various questions for any country or time with the individual circumstances of which we are well acquainted do really admit of being ascertained and that the other branches of human knowledge which this undertaking presupposes are so far advanced that the time is ripe for its commencement Such is the object of the Social Science That the nature of what I consider the true method of the science may be made more palpable by first showing what that method is not it will be expedient to characterize briefly two radical misconceptions of the proper mode of philosophizing on society and government one or other of which is either explicitly or more often unconsciously entertained by almost all who have meditated or argued respecting the logic of politics since the notion of treating it by strict rules and on Baconian principles has been current among the more advanced thinkers These erroneous methods if the word method can be applied to erroneous tendencies arising from the absence of any sufficiently distinct conception of method may be termed the Experimental or Chemical mode of investigation and the Abstract or Geometrical mode We shall begin with the former The laws of the phenomena of society are and can be nothing but the laws of the actions and passions of human beings united together in the social state Men however in a state of society are still men their actions and passions are obedient to the laws of individual human nature Men are not when brought together converted into another kind of substance with different properties as hydrogen and oxygen are different from water or as hydrogen oxygen carbon and azote are different from nerves muscles and tendons Human beings in society have no properties but those which are derived from and may be resolved into the laws of the nature of individual man In social phenomena the Composition of Causes is the universal law Now the method of philosophizing which may be termed chemical overlooks this fact and proceeds as if the nature of man as an individual were not concerned at all or were concerned in a very inferior degree in the operations of human beings in society All reasoning in political or social affairs grounded on principles of human nature is objected to by reasoners of this sort under such names as abstract theory For the direction of their opinions and conduct they profess to demand in all cases without exception specific experience This mode of thinking is not only general with practitioners in politics and with that very numerous class who on a subject which no one however ignorant thinks himself incompetent to discuss profess to guide themselves by common sense rather than by science but is often countenanced by persons with greater pretensions to instruction persons who having sufficient acquaintance with books and with the current ideas to have heard that Bacon taught mankind to follow experience and to ground their conclusions on facts instead of metaphysical dogmas think that by treating political facts in as directly experimental a method as chemical facts they are showing themselves true Baconians and proving their adversaries to be mere syllogizers and schoolmen As however the notion of the applicability of experimental methods to political philosophy can not coexist with any just conception of these methods themselves the kind of arguments from experience which the chemical theory brings forth as its fruits and which form the staple in this country especially of parliamentary and hustings oratory are such as at no time since Bacon would have been admitted to be valid in chemistry itself or in any other branch of experimental science They are such as these that the prohibition of foreign commodities must conduce to national wealth because England has flourished under it or because countries in general which have adopted it have flourished that our laws or our internal administration or our constitution are excellent for a similar reason and the eternal arguments from historical examples from Athens or Rome from the fires in Smithfield or the French Revolution I will not waste time in contending against modes of argumentation which no person with the smallest practice in estimating evidence could possibly be betrayed into which draw conclusions of general application from a single unanalysed instance or arbitrarily refer an effect to some one among its antecedents without any process of elimination or comparison of instances It is a rule both of justice and of good sense to grapple not with the absurdest but with the most reasonable form of a wrong opinion We shall suppose our inquirer acquainted with the true conditions of experimental investigation and competent in point of acquirements for realizing them so far as they can be realized He shall know as much of the facts of history as mere erudition can teach as much as can be proved by testimony without the assistance of any theory and if those mere facts properly collated can fulfil the conditions of a real induction he shall be qualified for the task But that no such attempt can have the smallest chance of success has been abundantly shown in the tenth chapter of the Third Book We there examined whether effects which depend on a complication of causes can be made the subject of a true induction by observation and experiment and concluded on the most convincing grounds that they can not Since of all effects none depend on so great a complication of causes as social phenomena we might leave our case to rest in safety on that previous showing But a logical principle as yet so little familiar to the ordinary run of thinkers requires to be insisted on more than once in order to make the due impression and the present being the case which of all others exemplifies it the most strongly there will be advantage in restating the grounds of the general maxim as applied to the specialties of the class of inquiries now under consideration The first difficulty which meets us in the attempt to apply experimental methods for ascertaining the laws of social phenomena is that we are without the means of making artificial experiments Even if we could contrive experiments at leisure and try them without limit we should do so under immense disadvantage both from the impossibility of ascertaining and taking note of all the facts of each case and because those facts being in a perpetual state of change before sufficient time had elapsed to ascertain the result of the experiment some material circumstances would always have ceased to be the same But it is unnecessary to consider the logical objections which would exist to the conclusiveness of our experiments since we palpably never have the power of trying any We can only watch those which nature produces or which are produced for other reasons We can not adapt our logical means to our wants by varying the circumstances as the exigencies of elimination may require If the spontaneous instances formed by contemporary events and by the successions of phenomena recorded in history afford a sufficient variation of circumstances an induction from specific experience is attainable otherwise not The question to be resolved is therefore whether the requisites for induction respecting the causes of political effects or the properties of political agents are to be met with in history including under the term contemporary history And in order to give fixity to our conceptions it will be advisable to suppose this question asked in reference to some special subject of political inquiry or controversy such as that frequent topic of debate in the present century the operation of restrictive and prohibitory commercial legislation upon national wealth Let this then be the scientific question to be investigated by specific experience In order to apply to the case the most perfect of the methods of experimental inquiry the Method of Difference we require to find two instances which tally in every particular except the one which is the subject of inquiry If two nations can be found which are alike in all natural advantages and disadvantages whose people resemble each other in every quality physical and moral spontaneous and acquired whose habits usages opinions laws and institutions are the same in all respects except that one of them has a more protective tariff or in other respects interferes more with the freedom of industry if one of these nations is found to be rich and the other poor or one richer than the other this will be an experimentum crucis a real proof by experience which of the two systems is most favourable to national riches But the supposition that two such instances can be met with is manifestly absurd Nor is such a concurrence even abstractedly possible Two nations which agreed in every thing except their commercial policy would agree also in that Differences of legislation are not inherent and ultimate diversities are not properties of Kinds They are effects of preexisting causes If the two nations differ in this portion of their institutions it is from some difference in their position and thence in their apparent interests or in some portion or other of their opinions habits and tendencies which opens a view of further differences without any assignable limit capable of operating on their industrial prosperity as well as on every other feature of their condition in more ways than can be enumerated or imagined There is thus a demonstrated impossibility of obtaining in the investigations of the social science the conditions required for the most conclusive form of inquiry by specific experience In the absence of the direct we may next try as in other cases the supplementary resource called in a former place the Indirect Method of Difference which instead of two instances differing in nothing but the presence or absence of a given circumstance compares two classes of instances respectively agreeing in nothing but the presence of a circumstance on the one side and its absence on the other To choose the most advantageous case conceivable a case far too advantageous to be ever obtained suppose that we compare one nation which has a restrictive policy with two or more nations agreeing in nothing but in permitting free trade We need not now suppose that either of these nations agrees with the first in all its circumstances one may agree with it in some of its circumstances and another in the remainder And it may be argued that if these nations remain poorer than the restrictive nation it can not be for want either of the first or of the second set of circumstances but it must be for want of the protective system If we might say the restrictive nation had prospered from the one set of causes the first of the freetrade nations would have prospered equally if by reason of the other the second would but neither has therefore the prosperity was owing to the restrictions This will be allowed to be a very favourable specimen of an argument from specific experience in politics and if this be inconclusive it would not be easy to find another preferable to it Yet that it is inconclusive scarcely requires to be pointed out Why must the prosperous nation have prospered from one cause exclusively National prosperity is always the collective result of a multitude of favourable circumstances and of these the restrictive nation may unite a greater number than either of the others though it may have all of those circumstances in common with either one or the other of them Its prosperity may be partly owing to circumstances common to it with one of those nations and partly with the other while they having each of them only half the number of favourable circumstances have remained inferior So that the closest imitation which can be made in the social science of a legitimate induction from direct experience gives but a specious semblance of conclusiveness without any real value The Method of Difference in either of its forms being thus completely out of the question there remains the Method of Agreement But we are already aware of how little value this method is in cases admitting Plurality of Causes and social phenomena are those in which the plurality prevails in the utmost possible extent Suppose that the observer makes the luckiest hit which could be given by any conceivable combination of chances that he finds two nations which agree in no circumstance whatever except in having a restrictive system and in being prosperous or a number of nations all prosperous which have no antecedent circumstances common to them all but that of having a restrictive policy It is unnecessary to go into the consideration of the impossibility of ascertaining from history or even from contemporary observation that such is really the fact that the nations agree in no other circumstance capable of influencing the case Let us suppose this impossibility vanquished and the fact ascertained that they agree only in a restrictive system as an antecedent and industrial prosperity as a consequent What degree of presumption does this raise that the restrictive system caused the prosperity One so trifling as to be equivalent to none at all That some one antecedent is the cause of a given effect because all other antecedents have been found capable of being eliminated is a just inference only if the effect can have but one cause If it admits of several nothing is more natural than that each of these should separately admit of being eliminated Now in the case of political phenomena the supposition of unity of cause is not only wide of the truth but at an immeasurable distance from it The causes of every social phenomenon which we are particularly interested about security wealth freedom good government public virtue general intelligence or their opposites are infinitely numerous especially the external or remote causes which alone are for the most part accessible to direct observation No one cause suffices of itself to produce any of these phenomena while there are countless causes which have some influence over them and may cooperate either in their production or in their prevention From the mere fact therefore of our having been able to eliminate some circumstance we can by no means infer that this circumstance was not instrumental to the effect in some of the very instances from which we have eliminated it We can conclude that the effect is sometimes produced without it but not that when present it does not contribute its share Similar objections will be found to apply to the Method of Concomitant Variations If the causes which act upon the state of any society produced effects differing from one another in kind if wealth depended on one cause peace on another a third made people virtuous a fourth intelligent we might though unable to sever the causes from one another refer to each of them that property of the effect which waxed as it waxed and which waned as it waned But every attribute of the social body is influenced by innumerable causes and such is the mutual action of the coexisting elements of society that whatever affects any one of the more important of them will by that alone if it does not affect the others directly affect them indirectly The effects therefore of different agents not being different in quality while the quantity of each is the mixed result of all the agents the variations of the aggregate can not bear a uniform proportion to those of any one of its component parts There remains the Method of Residues which appears on the first view less foreign to this kind of inquiry than the three other methods because it only requires that we should accurately note the circumstances of some one country or state of society Making allowance thereupon for the effect of all causes whose tendencies are known the residue which those causes are inadequate to explain may plausibly be imputed to the remainder of the circumstances which are known to have existed in the case Something similar to this is the method which Coleridge describes himself as having followed in his political essays in the Morning Post On every great occurrence I endeavoured to discover in past history the event that most nearly resembled it I procured whenever it was possible the contemporary historians memorialists and pamphleteers Then fairly subtracting the points of difference from those of likeness as the balance favoured the former or the latter I conjectured that the result would be the same or different As for instance in the series of essays entitled A Comparison of France under Napoleon with Rome under the first Caesars’ and in those which followed on the probable final restoration of the Bourbons’ The same plan I pursued at the commencement of the Spanish Revolution and with the same success taking the war of the United Provinces with Philip II as the groundwork of the comparison In this inquiry he no doubt employed the Method of Residues for in subtracting the points of difference from those of likeness he doubtless weighed and did not content himself with numbering them he doubtless took those points of agreement only which he presumed from their own nature to be capable of influencing the effect and allowing for that influence concluded that the remainder of the result would be referable to the points of difference Whatever may be the efficacy of this method it is as we long ago remarked not a method of pure observation and experiment it concludes not from a comparison of instances but from the comparison of an instance with the result of a previous deduction Applied to social phenomena it presupposes that the causes from which part of the effect proceeded are already known and as we have shown that these can not have been known by specific experience they must have been learned by deduction from principles of human nature experience being called in only as a supplementary resource to determine the causes which produced an unexplained residue But if the principles of human nature may be had recourse to for the establishment of some political truths they may for all If it be admissible to say England must have prospered by reason of the prohibitory system because after allowing for all the other tendencies which have been operating there is a portion of prosperity still to be accounted for it must be admissible to go to the same source for the effect of the prohibitory system and examine what account the laws of human motives and actions will enable us to give of its tendencies Nor in fact will the experimental argument amount to any thing except in verification of a conclusion drawn from those general laws For we may subtract the effect of one two three or four causes but we shall never succeed in subtracting the effect of all causes except one while it would be a curious instance of the dangers of too much caution if to avoid depending on a priori reasoning concerning the effect of a single cause we should oblige ourselves to depend on as many separate a priori reasonings as there are causes operating concurrently with that particular cause in some given instance We have now sufficiently characterized the gross misconception of the mode of investigation proper to political phenomena which I have termed the Chemical Method So lengthened a discussion would not have been necessary if the claim to decide authoritatively on political doctrines were confined to persons who had competently studied any one of the higher departments of physical science But since the generality of those who reason on political subjects satisfactorily to themselves and to a more or less numerous body of admirers know nothing whatever of the methods of physical investigation beyond a few precepts which they continue to parrot after Bacon being entirely unaware that Bacon’s conception of scientific inquiry has done its work and that science has now advanced into a higher stage there are probably many to whom such remarks as the foregoing may still be useful In an age in which chemistry itself when attempting to deal with the more complex chemical sequences those of the animal or even the vegetable organism has found it necessary to become and has succeeded in becoming a Deductive Science it is not to be apprehended that any person of scientific habits who has kept pace with the general progress of the knowledge of nature can be in danger of applying the methods of elementary chemistry to explore the sequences of the most complex order of phenomena in existence The misconception discussed in the preceding chapter is as we said chiefly committed by persons not much accustomed to scientific investigation practitioners in politics who rather employ the commonplaces of philosophy to justify their practice than seek to guide their practice by philosophic principles or imperfectly educated persons who in ignorance of the careful selection and elaborate comparison of instances required for the formation of a sound theory attempt to found one upon a few coincidences which they have casually noticed The erroneous method of which we are now to treat is on the contrary peculiar to thinking and studious minds It never could have suggested itself but to persons of some familiarity with the nature of scientific research who being aware of the impossibility of establishing by casual observation or direct experimentation a true theory of sequences so complex as are those of the social phenomena have recourse to the simpler laws which are immediately operative in those phenomena and which are no other than the laws of the nature of the human beings therein concerned These thinkers perceive what the partisans of the chemical or experimental theory do not that the science of society must necessarily be deductive But from an insufficient consideration of the specific nature of the subjectmatter and often because their own scientific education having stopped short in too early a stage geometry stands in their minds as the type of all deductive science it is to geometry rather than to astronomy and natural philosophy that they unconsciously assimilate the deductive science of society Among the differences between geometry a science of coexistent facts altogether independent of the laws of the succession of phenomena and those physical Sciences of Causation which have been rendered deductive the following is one of the most conspicuous That geometry affords no room for what so constantly occurs in mechanics and its applications the case of conflicting forces of causes which counteract or modify one another In mechanics we continually find two or more moving forces producing not motion but rest or motion in a different direction from that which would have been produced by either of the generating forces It is true that the effect of the joint forces is the same when they act simultaneously as if they had acted one after another or by turns and it is in this that the difference between mechanical and chemical laws consists But still the effects whether produced by successive or by simultaneous action do wholly or in part cancel one another what the one force does the other partly or altogether undoes There is no similar state of things in geometry The result which follows from one geometrical principle has nothing that conflicts with the result which follows from another What is proved true from one geometrical theorem what would be true if no other geometrical principles existed can not be altered and made no longer true by reason of some other geometrical principle What is once proved true is true in all cases whatever supposition may be made in regard to any other matter Now a conception similar to this last would appear to have been formed of the social science in the minds of the earlier of those who have attempted to cultivate it by a deductive method Mechanics would be a science very similar to geometry if every motion resulted from one force alone and not from a conflict of forces In the geometrical theory of society it seems to be supposed that this is really the case with the social phenomena that each of them results always from only one force one single property of human nature At the point which we have now reached it can not be necessary to say any thing either in proof or in illustration of the assertion that such is not the true character of the social phenomena There is not among these most complex and for that reason most modifiable of all phenomena any one over which innumerable forces do not exercise influence which does not depend on a conjunction of very many causes We have not therefore to prove the notion in question to be an error but to prove that the error has been committed that so mistaken a conception of the mode in which the phenomena of society are produced has actually been ascertained One numerous division of the reasoners who have treated social facts according to geometrical methods not admitting any modification of one law by another must for the present be left out of consideration because in them this error is complicated with and is the effect of another fundamental misconception of which we have already taken some notice and which will be further treated of before we conclude I speak of those who deduce political conclusions not from laws of nature not from sequences of phenomena real or imaginary but from unbending practical maxims Such for example are all who found their theory of politics on what is called abstract right that is to say on universal precepts a pretension of which we have already noticed the chimerical nature Such in like manner are those who make the assumption of a social contract or any other kind of original obligation and apply it to particular cases by mere interpretation But in this the fundamental error is the attempt to treat an art like a science and to have a deductive art the irrationality of which will be shown in a future chapter It will be proper to take our exemplification of the geometrical theory from those thinkers who have avoided this additional error and who entertain so far a juster idea of the nature of political inquiry We may cite in the first instance, those who assume as the principle of their political philosophy that government is founded on fear that the dread of each other is the one motive by which human beings were originally brought into a state of society and are still held in it Some of the earlier scientific inquirers into politics in particular Hobbes assumed this proposition not by implication but avowedly as the foundation of their doctrine and attempted to build a complete philosophy of politics thereupon It is true that Hobbes did not find this one maxim sufficient to carry him through the whole of his subject but was obliged to eke it out by the double sophism of an original contract I call this a double sophism first as passing off a fiction for a fact and secondly assuming a practical principle or precept as the basis of a theory which is a petitio principii since as we noticed in treating of that Fallacy every rule of conduct even though it be so binding a one as the observance of a promise must rest its own foundations on the theory of the subject and the theory therefore can not rest upon it Passing over less important instances I shall come at once to the most remarkable example afforded by our own times of the geometrical method in politics emanating from persons who are well aware of the distinction between science and art who knew that rules of conduct must follow not precede the ascertainment of laws of nature and that the latter not the former is the legitimate field for the application of the deductive method I allude to the interestphilosophy of the Bentham school The profound and original thinkers who are commonly known under this description founded their general theory of government on one comprehensive premise namely that men’s actions are always determined by their interests There is an ambiguity in this last expression for as the same philosophers especially Bentham gave the name of an interest to any thing which a person likes the proposition may be understood to mean only this that men’s actions are always determined by their wishes In this sense however it would not bear out any of the consequences which these writers drew from it and the word therefore in their political reasonings must be understood to mean which is also the explanation they themselves on such occasions gave of it what is commonly termed private or worldly interest Taking the doctrine then in this sense an objection presents itself in limine which might be deemed a fatal one namely that so sweeping a proposition is far from being universally true Human beings are not governed in all their actions by their worldly interests This however is by no means so conclusive an objection as it at first appears because in politics we are for the most part concerned with the conduct not of individual persons but either of a series of persons as a succession of kings or a body or mass of persons as a nation an aristocracy or a representative assembly And whatever is true of a large majority of mankind may without much error be taken for true of any succession of persons considered as a whole or of any collection of persons in which the act of the majority becomes the act of the whole body Although therefore the maxim is sometimes expressed in a manner unnecessarily paradoxical the consequences drawn from it will hold equally good if the assertion be limited as follows Any succession of persons or the majority of any body of persons will be governed in the bulk of their conduct by their personal interests We are bound to allow to this school of thinkers the benefit of this more rational statement of their fundamental maxim which is also in strict conformity to the explanations which when considered to be called for have been given by themselves The theory goes on to infer quite correctly that if the actions of mankind are determined in the main by their selfish interests the only rulers who will govern according to the interest of the governed are those whose selfish interests are in accordance with it And to this is added a third proposition namely that no rulers have their selfish interest identical with that of the governed unless it be rendered so by accountability that is by dependence on the will of the governed In other words and as the result of the whole that the desire of retaining or the fear of losing their power and whatever is thereon consequent is the sole motive which can be relied on for producing on the part of rulers a course of conduct in accordance with the general interest We have thus a fundamental theorem of political science consisting of three syllogisms and depending chiefly on two general premises in each of which a certain effect is considered as determined only by one cause not by a concurrence of causes In the one it is assumed that the actions of average rulers are determined solely by selfinterest in the other that the sense of identity of interest with the governed is produced and producible by no other cause than responsibility Neither of these propositions is by any means true the last is extremely wide of the truth It is not true that the actions even of average rulers are wholly or any thing approaching to wholly determined by their personal interest or even by their own opinion of their personal interest I do not speak of the influence of a sense of duty or feelings of philanthropy motives never to be mainly relied on though except in countries or during periods of great moral debasement they influence almost all rulers in some degree and some rulers in a very great degree But I insist only on what is true of all rulers viz that the character and course of their actions is largely influenced independently of personal calculation by the habitual sentiments and feelings the general modes of thinking and acting which prevail throughout the community of which they are members as well as by the feelings habits and modes of thought which characterize the particular class in that community to which they themselves belong And no one will understand or be able to decipher their system of conduct who does not take all these things into account They are also much influenced by the maxims and traditions which have descended to them from other rulers their predecessors which maxims and traditions have been known to retain an ascendancy during long periods even in opposition to the private interests of the rulers for the time being I put aside the influence of other less general causes Although therefore the private interest of the rulers or of the ruling class is a very powerful force constantly in action and exercising the most important influence upon their conduct there is also in what they do a large portion which that private interest by no means affords a sufficient explanation of and even the particulars which constitute the goodness or badness of their government are in some and no small degree influenced by those among the circumstances acting upon them which can not with any propriety be included in the term selfinterest Turning now to the other proposition that responsibility to the governed is the only cause capable of producing in the rulers a sense of identity of interest with the community this is still less admissible as a universal truth than even the former I am not speaking of perfect identity of interest which is an impracticable chimera which most assuredly responsibility to the people does not give I speak of identity in essentials and the essentials are different at different places and times There are a large number of cases in which those things which it is most for the general interest that the rulers should do are also those which they are prompted to do by their strongest personal interest the consolidation of their power The suppression for instance of anarchy and resistance to law the complete establishment of the authority of the central government in a state of society like that of Europe in the Middle Ages is one of the strongest interests of the people and also of the rulers simply because they are the rulers and responsibility on their part could not strengthen though in many conceivable ways it might weaken the motives prompting them to pursue this object During the greater part of the reign of Queen Elizabeth and of many other monarchs who might be named the sense of identity of interest between the sovereign and the majority of the people was probably stronger than it usually is in responsible governments every thing that the people had most at heart the monarch had at heart too Had Peter the Great or the rugged savages whom he began to civilize the truest inclination toward the things which were for the real interest of those savages I am not here attempting to establish a theory of government and am not called upon to determine the proportional weight which ought to be given to the circumstances which this school of geometrical politicians left out of their system and those which they took into it I am only concerned to show that their method was unscientific not to measure the amount of error which may have affected their practical conclusions It is but justice to them however to remark that their mistake was not so much one of substance as of form and consisted in presenting in a systematic shape and as the scientific treatment of a great philosophical question what should have passed for that which it really was the mere polemics of the day Although the actions of rulers are by no means wholly determined by their selfish interests it is chiefly as a security against those selfish interests that constitutional checks are required and for that purpose such checks in England and the other nations of modern Europe can in no manner be dispensed with It is likewise true that in these same nations and in the present age responsibility to the governed is the only means practically available to create a feeling of identity of interest in the cases and on the points where that feeling does not sufficiently exist To all this and to the arguments which may be founded on it in favour of measures for the correction of our representative system I have nothing to object but I confess my regret that the small though highly important portion of the philosophy of government which was wanted for the immediate purpose of serving the cause of parliamentary reform should have been held forth by thinkers of such eminence as a complete theory It is not to be imagined possible nor is it true in point of fact, that these philosophers regarded the few premises of their theory as including all that is required for explaining social phenomena or for determining the choice of forms of government and measures of legislation and administration They were too highly instructed of too comprehensive intellect and some of them of too sober and practical a character for such an error They would have applied and did apply their principles with innumerable allowances But it is not allowances that are wanted There is little chance of making due amends in the superstructure of a theory for the want of sufficient breadth in its foundations It is unphilosophical to construct a science out of a few of the agencies by which the phenomena are determined and leave the rest to the routine of practice or the sagacity of conjecture We either ought not to pretend to scientific forms or we ought to study all the determining agencies equally and endeavour so far as it can be done to include all of them within the pale of the science else we shall infallibly bestow a disproportionate attention upon those which our theory takes into account while we misestimate the rest and probably underrate their importance That the deductions should be from the whole and not from a part only of the laws of nature that are concerned would be desirable even if those omitted were so insignificant in comparison with the others that they might for most purposes and on most occasions be left out of the account But this is far indeed from being true in the social science The phenomena of society do not depend in essentials on some one agency or law of human nature with only inconsiderable modifications from others The whole of the qualities of human nature influence those phenomena and there is not one which influences them in a small degree There is not one the removal or any great alteration of which would not materially affect the whole aspect of society and change more or less the sequences of social phenomena generally The theory which has been the subject of these remarks is in this country at least the principal contemporary example of what I have styled the geometrical method of philosophizing in the social science and our examination of it has for this reason been more detailed than would otherwise have been suitable to a work like the present Having now sufficiently illustrated the two erroneous methods we shall pass without further preliminary to the true method that which proceeds conformably to the practice of the more complex physical sciences deductively indeed but by deduction from many not from one or a very few original premises considering each effect as what it really is an aggregate result of many causes operating sometimes through the same sometimes through different mental agencies or laws of human nature After what has been said to illustrate the nature of the inquiry into social phenomena the general character of the method proper to that inquiry is sufficiently evident and needs only to be recapitulated not proved However complex the phenomena all their sequences and coexistences result from the laws of the separate elements The effect produced in social phenomena by any complex set of circumstances amounts precisely to the sum of the effects of the circumstances taken singly and the complexity does not arise from the number of the laws themselves which is not remarkably great but from the extraordinary number and variety of the data or elements of the agents which in obedience to that small number of laws cooperate toward the effect The Social Science therefore which by a convenient barbarism has been termed Sociology is a deductive science not indeed after the model of geometry but after that of the more complex physical sciences It infers the law of each effect from the laws of causation on which that effect depends not however from the law merely of one cause as in the geometrical method but by considering all the causes which conjunctly influence the effect and compounding their laws with one another Its method in short is the Concrete Deductive Method that of which astronomy furnishes the most perfect natural philosophy a somewhat less perfect example and the employment of which with the adaptations and precautions required by the subject is beginning to regenerate physiology Nor does it admit of doubt that similar adaptations and precautions are indispensable in sociology In applying to that most complex of all studies what is demonstrably the sole method capable of throwing the light of science even upon phenomena of a far inferior degree of complication we ought to be aware that the same superior complexity which renders the instrument of Deduction more necessary renders it also more precarious and we must be prepared to meet by appropriate contrivances this increase of difficulty The actions and feelings of human beings in the social state are no doubt entirely governed by psychological and ethological laws whatever influence any cause exercises upon the social phenomena it exercises through those laws Supposing therefore the laws of human actions and feelings to be sufficiently known there is no extraordinary difficulty in determining from those laws the nature of the social effects which any given cause tends to produce But when the question is that of compounding several tendencies together and computing the aggregate result of many coexistent causes and especially when by attempting to predict what will actually occur in a given case we incur the obligation of estimating and compounding the influences of all the causes which happen to exist in that case we attempt a task to proceed far in which surpasses the compass of the human faculties If all the resources of science are not sufficient to enable us to calculate a priori with complete precision the mutual action of three bodies gravitating toward one another it may be judged with what prospect of success we should endeavour to calculate the result of the conflicting tendencies which are acting in a thousand different directions and promoting a thousand different changes at a given instant in a given society although we might and ought to be able from the laws of human nature to distinguish correctly enough the tendencies themselves so far as they depend on causes accessible to our observation and to determine the direction which each of them if acting alone would impress upon society as well as in a general way at least to pronounce that some of these tendencies are more powerful than others But without dissembling the necessary imperfections of the a priori method when applied to such a subject neither ought we on the other hand to exaggerate them The same objections which apply to the Method of Deduction in this its most difficult employment apply to it as we formerly showed in its easiest and would even there have been insuperable if there had not existed as was then fully explained an appropriate remedy This remedy consists in the process which under the name of Verification we have characterized as the third essential constituent part of the Deductive Method that of collating the conclusions of the ratiocination either with the concrete phenomena themselves or when such are obtainable with their empirical laws The ground of confidence in any concrete deductive science is not the a priori reasoning itself but the accordance between its results and those of observation a posteriori Either of these processes apart from the other diminishes in value as the subject increases in complication and this is in so rapid a ratio as soon to become entirely worthless but the reliance to be placed in the concurrence of the two sorts of evidence not only does not diminish in any thing like the same proportion but is not necessarily much diminished at all Nothing more results than a disturbance in the order of precedency of the two processes sometimes amounting to its actual inversion insomuch that instead of deducing our conclusions by reasoning and verifying them by observation we in some cases begin by obtaining them provisionally from specific experience and afterward connect them with the principles of human nature by a priori reasonings which reasonings are thus a real Verification The only thinker who with a competent knowledge of scientific methods in general has attempted to characterize the Method of Sociology M Comte considers this inverse order as inseparably inherent in the nature of sociological speculation He looks upon the social science as essentially consisting of generalizations from history verified not originally suggested by deduction from the laws of human nature Though there is a truth contained in this opinion of which I shall presently endeavour to show the importance I can not but think that this truth is enunciated in too unlimited a manner and that there is considerable scope in sociological inquiry for the direct as well as for the inverse Deductive Method It will in fact be shown in the next chapter that there is a kind of sociological inquiries to which from their prodigious complication the method of direct deduction is altogether inapplicable while by a happy compensation it is precisely in these cases that we are able to obtain the best empirical laws to these inquiries therefore the Inverse Method is exclusively adapted But there are also as will presently appear other cases in which it is impossible to obtain from direct observation any thing worthy the name of an empirical law and it fortunately happens that these are the very cases in which the Direct Method is least affected by the objection which undoubtedly must always affect it in a certain degree We shall begin then by looking at the Social Science as a science of direct Deduction and considering what can be accomplished in it and under what limitations by that mode of investigation We shall then in a separate chapter examine and endeavour to characterize the inverse process It is evident in the first place that Sociology considered as a system of deductions a priori can not be a science of positive predictions but only of tendencies We may be able to conclude from the laws of human nature applied to the circumstances of a given state of society that a particular cause will operate in a certain manner unless counteracted but we can never be assured to what extent or amount it will so operate or affirm with certainty that it will not be counteracted because we can seldom know even approximately all the agencies which may coexist with it and still less calculate the collective result of so many combined elements The remark however must here be once more repeated that knowledge insufficient for prediction may be most valuable for guidance It is not necessary for the wise conduct of the affairs of society no more than of any one’s private concerns that we should be able to foresee infallibly the results of what we do We must seek our objects by means which may perhaps be defeated and take precautions against dangers which possibly may never be realized The aim of practical politics is to surround any given society with the greatest possible number of circumstances of which the tendencies are beneficial and to remove or counteract as far as practicable those of which the tendencies are injurious A knowledge of the tendencies only though without the power of accurately predicting their conjunct result gives us to a considerable extent this power It would however be an error to suppose that even with respect to tendencies we could arrive in this manner at any great number of propositions which will be true in all societies without exception Such a supposition would be inconsistent with the eminently modifiable nature of the social phenomena and the multitude and variety of the circumstances by which they are modified circumstances never the same or even nearly the same in two different societies or in two different periods of the same society This would not be so serious an obstacle if though the causes acting upon society in general are numerous those which influence any one feature of society were limited in number for we might then insulate any particular social phenomenon and investigate its laws without disturbance from the rest But the truth is the very opposite of this Whatever affects in an appreciable degree any one element of the social state affects through it all the other elements The mode of production of all social phenomena is one great case of Intermixture of Laws We can never either understand in theory or command in practice the condition of a society in any one respect without taking into consideration its condition in all other respects There is no social phenomenon which is not more or less influenced by every other part of the condition of the same society and therefore by every cause which is influencing any other of the contemporaneous social phenomena There is in short what physiologists term a consensus similar to that existing among the various organs and functions of the physical frame of man and the more perfect animals and constituting one of the many analogies which have rendered universal such expressions as the body politic and body natural It follows from this consensus that unless two societies could be alike in all the circumstances which surround and influence them which would imply their being alike in their previous history no portion whatever of the phenomena will unless by accident precisely correspond no one cause will produce exactly the same effects in both Every cause as its effect spreads through society comes somewhere in contact with different sets of agencies and thus has its effects on some of the social phenomena differently modified and these differences by their reaction produce a difference even in those of the effects which would otherwise have been the same We can never therefore affirm with certainty that a cause which has a particular tendency in one people or in one age will have exactly the same tendency in another without referring back to our premises and performing over again for the second age or nation that analysis of the whole of its influencing circumstances which we had already performed for the first The deductive science of society will not lay down a theorem asserting in a universal manner the effect of any cause but will rather teach us how to frame the proper theorem for the circumstances of any given case It will not give the laws of society in general but the means of determining the phenomena of any given society from the particular elements or data of that society All the general propositions which can be framed by the deductive science are therefore in the strictest sense of the word hypothetical They are grounded on some suppositious set of circumstances and declare how some given cause would operate in those circumstances supposing that no others were combined with them If the set of circumstances supposed have been copied from those of any existing society the conclusions will be true of that society provided and in as far as the effect of those circumstances shall not be modified by others which have not been taken into the account If we desire a nearer approach to concrete truth we can only aim at it by taking or endeavouring to take a greater number of individualizing circumstances into the computation Considering however in how accelerating a ratio the uncertainty of our conclusions increases as we attempt to take the effect of a greater number of concurrent causes into our calculations the hypothetical combinations of circumstances on which we construct the general theorems of the science can not be made very complex without so rapidly accumulating a liability to error as must soon deprive our conclusions of all value This mode of inquiry considered as a means of obtaining general propositions must therefore on pain of frivolity be limited to those classes of social facts which though influenced like the rest by all sociological agents are under the immediate influence principally at least of a few only Notwithstanding the universal consensus of the social phenomena whereby nothing which takes place in any part of the operations of society is without its share of influence on every other part and notwithstanding the paramount ascendancy which the general state of civilization and social progress in any given society must hence exercise over all the partial and subordinate phenomena it is not the less true that different species of social facts are in the main dependent immediately and in the first resort on different kinds of causes and therefore not only may with advantage but must be studied apart just as in the natural body we study separately the physiology and pathology of each of the principal organs and tissues though every one is acted upon by the state of all the others and though the peculiar constitution and general state of health of the organism cooperates with and often preponderates over the local causes in determining the state of any particular organ On these considerations is grounded the existence of distinct and separate though not independent branches or departments of sociological speculation There is for example one large class of social phenomena in which the immediately determining causes are principally those which act through the desire of wealth and in which the psychological law mainly concerned is the familiar one that a greater gain is preferred to a smaller I mean of course that portion of the phenomena of society which emanate from the industrial or productive operations of mankind and from those of their acts through which the distribution of the products of those industrial operations takes place in so far as not effected by force or modified by voluntary gift By reasoning from that one law of human nature and from the principal outward circumstances whether universal or confined to particular states of society which operate upon the human mind through that law we may be enabled to explain and predict this portion of the phenomena of society so far as they depend on that class of circumstances only overlooking the influence of any other of the circumstances of society and therefore neither tracing back the circumstances which we do take into account to their possible origin in some other facts in the social state nor making allowance for the manner in which any of those other circumstances may interfere with and counteract or modify the effect of the former A department of science may thus be constructed which has received the name of Political Economy The motive which suggests the separation of this portion of the social phenomena from the rest and the creation of a distinct branch of science relating to them is that they do mainly depend at least in the first resort on one class of circumstances only and that even when other circumstances interfere the ascertainment of the effect due to the one class of circumstances alone is a sufficiently intricate and difficult business to make it expedient to perform it once for all and then allow for the effect of the modifying circumstances especially as certain fixed combinations of the former are apt to recur often in conjunction with evervarying circumstances of the latter class Political Economy as I have said on another occasion concerns itself only with such of the phenomena of the social state as take place in consequence of the pursuit of wealth It makes entire abstraction of every other human passion or motive except those which may be regarded as perpetually antagonizing principles to the desire of wealth namely aversion to labour and desire of the present enjoyment of costly indulgences These it takes to a certain extent into its calculations because these do not merely like our other desires occasionally conflict with the pursuit of wealth but accompany it always as a drag or impediment and are therefore inseparably mixed up in the consideration of it Political Economy considers mankind as occupied solely in acquiring and consuming wealth and aims at showing what is the course of action into which mankind living in a state of society would be impelled if that motive except in the degree in which it is checked by the two perpetual countermotives above adverted to were absolute ruler of all their actions Under the influence of this desire it shows mankind accumulating wealth and employing that wealth in the production of other wealth sanctioning by mutual agreement the institution of property establishing laws to prevent individuals from encroaching upon the property of others by force or fraud adopting various contrivances for increasing the productiveness of their labour settling the division of the produce by agreement under the influence of competition competition itself being governed by certain laws which laws are therefore the ultimate regulators of the division of the produce and employing certain expedients as money credit etc to facilitate the distribution All these operations though many of them are really the result of a plurality of motives are considered by political economy as flowing solely from the desire of wealth The science then proceeds to investigate the laws which govern these several operations under the supposition that man is a being who is determined by the necessity of his nature to prefer a greater portion of wealth to a smaller in all cases without any other exception than that constituted by the two countermotives already specified Not that any political economist was ever so absurd as to suppose that mankind are really thus constituted but because this is the mode in which science must necessarily proceed When an effect depends on a concurrence of causes these causes must be studied one at a time and their laws separately investigated if we wish through the causes to obtain the power of either predicting or controlling the effect since the law of the effect is compounded of the laws of all the causes which determine it The law of the centripetal and that of the projectile force must have been known before the motions of the earth and planets could be explained or many of them predicted The same is the case with the conduct of man in society In order to judge how he will act under the variety of desires and aversions which are concurrently operating upon him we must know how he would act under the exclusive influence of each one in particular There is perhaps no action of a man’s life in which he is neither under the immediate nor under the remote influence of any impulse but the mere desire of wealth With respect to those parts of human conduct of which wealth is not even the principal object to these political economy does not pretend that its conclusions are applicable But there are also certain departments of human affairs in which the acquisition of wealth is the main and acknowledged end It is only of these that political economy takes notice The manner in which it necessarily proceeds is that of treating the main and acknowledged end as if it were the sole end which of all hypotheses equally simple is the nearest to the truth The political economist inquires what are the actions which would be produced by this desire if within the departments in question it were unimpeded by any other In this way a nearer approximation is obtained than would otherwise be practicable to the real order of human affairs in those departments This approximation has then to be corrected by making proper allowance for the effects of any impulses of a different description which can be shown to interfere with the result in any particular case Only in a few of the most striking cases such as the important one of the principle of population are these corrections interpolated into the expositions of political economy itself the strictness of purely scientific arrangement being thereby somewhat departed from for the sake of practical utility So far as it is known or may be presumed that the conduct of mankind in the pursuit of wealth is under the collateral influence of any other of the properties of our nature than the desire of obtaining the greatest quantity of wealth with the least labour and selfdenial the conclusions of political economy will so far fail of being applicable to the explanation or prediction of real events until they are modified by a correct allowance for the degree of influence exercised by the other cause Extensive and important practical guidance may be derived in any given state of society from general propositions such as those above indicated even though the modifying influence of the miscellaneous causes which the theory does not take into account as well as the effect of the general social changes in progress be provisionally overlooked And though it has been a very common error of political economists to draw conclusions from the elements of one state of society and apply them to other states in which many of the elements are not the same it is even then not difficult by tracing back the demonstrations and introducing the new premises in their proper places to make the same general course of argument which served for the one case serve for the others too For example it has been greatly the custom of English political economists to discuss the laws of the distribution of the produce of industry on a supposition which is scarcely realized anywhere out of England and Scotland namely that the produce is shared among three classes altogether distinct from one another labourers capitalists and landlords and that all these are free agents permitted in law and in fact to set upon their labour their capital and their land whatever price they are able to get for it The conclusions of the science being all adapted to a society thus constituted require to be revised whenever they are applied to any other They are inapplicable where the only capitalists are the landlords and the labourers are their property as in slave countries They are inapplicable where the almost universal landlord is the state as in India They are inapplicable where the agricultural labourer is generally the owner both of the land itself and of the capital as frequently in France or of the capital only as in Ireland But though it may often be very justly objected to the existing race of political economists that they attempt to construct a permanent fabric out of transitory materials that they take for granted the immutability of arrangements of society many of which are in their nature fluctuating or progressive and enunciate with as little qualification as if they were universal and absolute truths propositions which are perhaps applicable to no state of society except the particular one in which the writer happened to live this does not take away the value of the propositions considered with reference to the state of society from which they were drawn And even as applicable to other states of society it must not be supposed that the science is so incomplete and unsatisfactory as this might seem to prove Though many of its conclusions are only locally true its method of investigation is applicable universally and as whoever has solved a certain number of algebraic equations can without difficulty solve all others of the same kind so whoever knows the political economy of England or even of Yorkshire knows that of all nations actual or possible provided he have good sense enough not to expect the same conclusion to issue from varying premises Whoever has mastered with the degree of precision which is attainable the laws which under free competition determine the rent profits and wages received by landlords capitalists and labourers in a state of society in which the three classes are completely separate will have no difficulty in determining the very different laws which regulate the distribution of the produce among the classes interested in it in any of the states of cultivation and landed property set forth in the foregoing extract I would not here undertake to decide what other hypothetical or abstract sciences similar to Political Economy may admit of being carved out of the general body of the social science what other portions of the social phenomena are in a sufficiently close and complete dependence in the first resort on a peculiar class of causes to make it convenient to create a preliminary science of those causes postponing the consideration of the causes which act through them or in concurrence with them to a later period of the inquiry There is however among these separate departments one which can not be passed over in silence being of a more comprehensive and commanding character than any of the other branches into which the social science may admit of being divided Like them it is directly conversant with the causes of only one class of social facts but a class which exercises immediately or remotely a paramount influence over the test I allude to what may be termed Political Ethology or the theory of the causes which determine the type of character belonging to a people or to an age Of all the subordinate branches of the social science this is the most completely in its infancy The causes of national character are scarcely at all understood and the effect of institutions or social arrangements upon the character of the people is generally that portion of their effects which is least attended to and least comprehended Nor is this wonderful when we consider the infant state of the science of Ethology itself from whence the laws must be drawn of which the truths of political ethology can be but results and exemplifications Yet to whoever well considers the matter it must appear that the laws of national or collective character are by far the most important class of sociological laws In the first place the character which is formed by any state of social circumstances is in itself the most interesting phenomenon which that state of society can possibly present Secondly it is also a fact which enters largely into the production of all the other phenomena And above all the character that is the opinions feelings and habits of the people though greatly the results of the state of society which precedes them are also greatly the causes of the state of society which follows them and are the power by which all those of the circumstances of society which are artificial laws and customs for instance are altogether moulded customs evidently laws no less really either by the direct influence of public sentiment upon the ruling powers or by the effect which the state of national opinion and feeling has in determining the form of government and shaping the character of the governors As might be expected the most imperfect part of those branches of social inquiry which have been cultivated as separate sciences is the theory of the manner in which their conclusions are affected by ethological considerations The omission is no defect in them as abstract or hypothetical sciences but it vitiates them in their practical application as branches of a comprehensive social science In political economy for instance empirical laws of human nature are tacitly assumed by English thinkers which are calculated only for Great Britain and the United States Among other things an intensity of competition is constantly supposed which as a general mercantile fact exists in no country in the world except those two An English political economist like his countrymen in general has seldom learned that it is possible that men in conducting the business of selling their goods over a counter should care more about their ease or their vanity than about their pecuniary gain Yet those who know the habits of the continent of Europe are aware how apparently small a motive often outweighs the desire of money getting even in the operations which have money getting for their direct object The more highly the science of ethology is cultivated and the better the diversities of individual and national character are understood the smaller probably will the number of propositions become which it will be considered safe to build on as universal principles of human nature These considerations show that the process of dividing off the social science into compartments in order that each may be studied separately and its conclusions afterward corrected for practice by the modifications supplied by the others must be subject to at least one important limitation Those portions alone of the social phenomena can with advantage be made the subjects even provisionally of distinct branches of science into which the diversities of character between different nations or different times enter as influencing causes only in a secondary degree Those phenomena on the contrary with which the influences of the ethological state of the people are mixed up at every step so that the connection of effects and causes can not be even rudely marked out without taking those influences into consideration could not with any advantage nor without great disadvantage be treated independently of political ethology nor therefore of all the circumstances by which the qualities of a people are influenced For this reason as well as for others which will hereafter appear there can be no separate Science of Government that being the fact which of all others is most mixed up both as cause and effect with the qualities of the particular people or of the particular age All questions respecting the tendencies of forms of government must stand part of the general science of society not of any separate branch of it This general Science of Society as distinguished from the separate departments of the science each of which asserts its conclusions only conditionally subject to the paramount control of the laws of the general science now remains to be characterized And as will be shown presently nothing of a really scientific character is here possible except by the inverse deductive method But before we quit the subject of those sociological speculations which proceed by way of direct deduction we must examine in what relation they stand to that indispensable element in all deductive sciences Verification by Specific Experience comparison between the conclusions of reasoning and the results of observation We have seen that in most deductive sciences and among the rest in Ethology itself which is the immediate foundation of the Social Science a preliminary work of preparation is performed on the observed facts to fit them for being rapidly and accurately collated sometimes even for being collated at all with the conclusions of theory This preparatory treatment consists in finding general propositions which express concisely what is common to large classes of observed facts and these are called the empirical laws of the phenomena We have therefore to inquire whether any similar preparatory process can be performed on the facts of the social science whether there are any empirical laws in history or statistics In statistics it is evident that empirical laws may sometimes be traced and the tracing them forms an important part of that system of indirect observation on which we must often rely for the data of the Deductive Science The process of the science consists in inferring effects from their causes but we have often no means of observing the causes except through the medium of their effects In such cases the deductive science is unable to predict the effects for want of the necessary data it can determine what causes are capable of producing any given effect but not with what frequency and in what quantities those causes exist An instance in point is afforded by a newspaper now lying before me A statement was furnished by one of the official assignees in bankruptcy showing among the various bankruptcies which it had been his duty to investigate in how many cases the losses had been caused by misconduct of different kinds and in how many by unavoidable misfortunes The result was that the number of failures caused by misconduct greatly preponderated over those arising from all other causes whatever Nothing but specific experience could have given sufficient ground for a conclusion to this purport To collect therefore such empirical laws which are never more than approximate generalizations from direct observation is an important part of the process of sociological inquiry The experimental process is not here to be regarded as a distinct road to the truth but as a means happening accidentally to be the only or the best available for obtaining the necessary data for the deductive science When the immediate causes of social facts are not open to direct observation the empirical law of the effects gives us the empirical law which in that case is all that we can obtain of the causes likewise But those immediate causes depend on remote causes and the empirical law obtained by this indirect mode of observation can only be relied on as applicable to unobserved cases so long as there is reason to think that no change has taken place in any of the remote causes on which the immediate causes depend In making use therefore of even the best statistical generalizations for the purpose of inferring though it be only conjecturally that the same empirical laws will hold in any new case it is necessary that we be well acquainted with the remoter causes in order that we may avoid applying the empirical law to cases which differ in any of the circumstances on which the truth of the law ultimately depends And thus even where conclusions derived from specific observation are available for practical inferences in new cases it is necessary that the deductive science should stand sentinel over the whole process that it should be constantly referred to and its sanction obtained to every inference The same thing holds true of all generalizations which can be grounded on history Not only there are such generalizations but it will presently be shown that the general science of society which inquires into the laws of succession and coexistence of the great facts constituting the state of society and civilization at any time can proceed in no other manner than by making such generalizations afterward to be confirmed by connecting them with the psychological and ethological laws on which they must really depend But reserving this question for its proper place in those more special inquiries which form the subject of the separate branches of the social science this twofold logical process and reciprocal verification is not possible specific experience affords nothing amounting to empirical laws This is particularly the case where the object is to determine the effect of any one social cause among a great number acting simultaneously the effect for example of corn laws or of a prohibitive commercial system generally Though it may be perfectly certain from theory what kind of effects corn laws must produce and in what general direction their influence must tell upon industrial prosperity their effect is yet of necessity so much disguised by the similar or contrary effects of other influencing agents that specific experience can at most only show that on the average of some great number of instances the cases where there were corn laws exhibited the effect in a greater degree than those where there were not Now the number of instances necessary to exhaust the whole round of combinations of the various influential circumstances and thus afford a fair average never can be obtained Not only we can never learn with sufficient authenticity the facts of so many instances but the world itself does not afford them in sufficient numbers within the limits of the given state of society and civilization which such inquiries always presuppose Having thus no previous empirical generalizations with which to collate the conclusions of theory the only mode of direct verification which remains is to compare those conclusions with the result of an individual experiment or instance But here the difficulty is equally great For in order to verify a theory by an experiment the circumstances of the experiment must be exactly the same with those contemplated in the theory But in social phenomena the circumstances of no two cases are exactly alike A trial of corn laws in another country or in a former generation would go a very little way toward verifying a conclusion drawn respecting their effect in this generation and in this country It thus happens in most cases that the only individual instance really fitted to verify the predictions of theory is the very instance for which the predictions were made and the verification comes too late to be of any avail for practical guidance Although however direct verification is impossible there is an indirect verification which is scarcely of less value and which is always practicable The conclusion drawn as to the individual case can only be directly verified in that case but it is verified indirectly by the verification of other conclusions drawn in other individual cases from the same laws The experience which comes too late to verify the particular proposition to which it refers is not too late to help toward verifying the general sufficiency of the theory The test of the degree in which the science affords safe ground for predicting and consequently for practically dealing with what has not yet happened is the degree in which it would have enabled us to predict what has actually occurred Before our theory of the influence of a particular cause in a given state of circumstances can be entirely trusted we must be able to explain and account for the existing state of all that portion of the social phenomena which that cause has a tendency to influence If for instance we would apply our speculations in political economy to the prediction or guidance of the phenomena of any country we must be able to explain all the mercantile or industrial facts of a general character appertaining to the present state of that country to point out causes sufficient to account for all of them and prove or show good ground for supposing that these causes have really existed If we can not do this it is a proof either that the facts which ought to be taken into account are not yet completely known to us or that although we know the facts we are not masters of a sufficiently perfect theory to enable us to assign their consequences In either case we are not in the present state of our knowledge fully competent to draw conclusions speculative or practical for that country In like manner if we would attempt to judge of the effect which any political institution would have supposing that it could be introduced into any given country we must be able to show that the existing state of the practical government of that country and of whatever else depends thereon together with the particular character and tendencies of the people and their state in respect to the various elements of social wellbeing are such as the institutions they have lived under in conjunction with the other circumstances of their nature or of their position were calculated to produce To prove in short that our science and our knowledge of the particular case render us competent to predict the future we must show that they would have enabled us to predict the present and the past If there be any thing which we could not have predicted this constitutes a residual phenomenon requiring further study for the purpose of explanation and we must either search among the circumstances of the particular case until we find one which on the principles of our existing theory accounts for the unexplained phenomenon or we must turn back and seek the explanation by an extension and improvement of the theory itself There are two kinds of sociological inquiry In the first kind the question proposed is what effect will follow from a given cause a certain general condition of social circumstances being presupposed As for example what would be the effect of imposing or of repealing corn laws of abolishing monarchy or introducing universal suffrage in the present condition of society and civilization in any European country or under any other given supposition with regard to the circumstances of society in general without reference to the changes which might take place or which may already be in progress in those circumstances But there is also a second inquiry namely what are the laws which determine those general circumstances themselves In this last the question is not what will be the effect of a given cause in a certain state of society but what are the causes which produce and the phenomena which characterize states of society generally In the solution of this question consists the general Science of Society by which the conclusions of the other and more special kind of inquiry must be limited and controlled In order to conceive correctly the scope of this general science and distinguish it from the subordinate departments of sociological speculation it is necessary to fix the ideas attached to the phrase A State of Society What is called a state of society is the simultaneous state of all the greater social facts or phenomena Such are the degree of knowledge and of intellectual and moral culture existing in the community and in every class of it the state of industry of wealth and its distribution the habitual occupations of the community their division into classes and the relations of those classes to one another the common beliefs which they entertain on all the subjects most important to mankind and the degree of assurance with which those beliefs are held their tastes and the character and degree of their aesthetic development their form of government and the more important of their laws and customs The condition of all these things and of many more which will readily suggest themselves constitute the state of society or the state of civilization at any given time When states of society and the causes which produce them are spoken of as a subject of science it is implied that there exists a natural correlation among these different elements that not every variety of combination of these general social facts is possible but only certain combinations that in short there exist Uniformities of Coexistence between the states of the various social phenomena And such is the truth as is indeed a necessary consequence of the influence exercised by every one of those phenomena over every other It is a fact implied in the consensus of the various parts of the social body States of society are like different constitutions or different ages in the physical frame they are conditions not of one or a few organs or functions but of the whole organism Accordingly the information which we possess respecting past ages and respecting the various states of society now existing in different regions of the earth does when duly analysed exhibit uniformities It is found that when one of the features of society is in a particular state a state of many other features more or less precisely determinate always or usually coexists with it But the uniformities of coexistence obtaining among phenomena which are effects of causes must as we have so often observed be corollaries from the laws of causation by which these phenomena are really determined The mutual correlation between the different elements of each state of society is therefore a derivative law resulting from the laws which regulate the succession between one state of society and another for the proximate cause of every state of society is the state of society immediately preceding it The fundamental problem therefore of the social science is to find the laws according to which any state of society produces the state which succeeds it and takes its place This opens the great and vexed question of the progressiveness of man and society an idea involved in every just conception of social phenomena as the subject of a science It is one of the characters not absolutely peculiar to the sciences of human nature and society but belonging to them in a peculiar degree to be conversant with a subjectmatter whose properties are changeable I do not mean changeable from day to day but from age to age so that not only the qualities of individuals vary but those of the majority are not the same in one age as in another The principal cause of this peculiarity is the extensive and constant reaction of the effects upon their causes The circumstances in which mankind are placed operating according to their own laws and to the laws of human nature form the characters of the human beings but the human beings in their turn mould and shape the circumstances for themselves and for those who come after them From this reciprocal action there must necessarily result either a cycle or a progress In astronomy also every fact is at once effect and cause the successive positions of the various heavenly bodies produce changes both in the direction and in the intensity of the forces by which those positions are determined But in the case of the solar system these mutual actions bring around again after a certain number of changes the former state of circumstances which of course leads to the perpetual recurrence of the same series in an unvarying order Those bodies in short revolve in orbits but there are or conformably to the laws of astronomy there might be others which instead of an orbit describe a trajectory a course not returning into itself One or other of these must be the type to which human affairs must conform One of the thinkers who earliest conceived the succession of historical events as subject to fixed laws and endeavoured to discover these laws by an analytical survey of history Vico the celebrated author of the Scienza Nuova adopted the former of these opinions He conceived the phenomena of human society as revolving in an orbit as going through periodically the same series of changes Though there were not wanting circumstances tending to give some plausibility to this view it would not bear a close scrutiny and those who have succeeded Vico in this kind of speculations have universally adopted the idea of a trajectory or progress in lieu of an orbit or cycle The words Progress and Progressiveness are not here to be understood as synonymous with improvement and tendency to improvement It is conceivable that the laws of human nature might determine and even necessitate a certain series of changes in man and society which might not in every case or which might not on the whole be improvements It is my belief indeed that the general tendency is and will continue to be saving occasional and temporary exceptions one of improvement a tendency toward a better and happier state This however is not a question of the method of the social science but a theorem of the science itself For our purpose it is sufficient that there is a progressive change both in the character of the human race and in their outward circumstances so far as moulded by themselves that in each successive age the principal phenomena of society are different from what they were in the age preceding and still more different from any previous age the periods which most distinctly mark these successive changes being intervals of one generation during which a new set of human beings have been educated have grown up from childhood and taken possession of society The progressiveness of the human race is the foundation on which a method of philosophizing in the social science has been of late years erected far superior to either of the two modes which had previously been prevalent the chemical or experimental and the geometrical modes This method which is now generally adopted by the most advanced thinkers on the Continent consists in attempting by a study and analysis of the general facts of history to discover what these philosophers term the law of progress which law once ascertained must according to them enable us to predict future events just as after a few terms of an infinite series in algebra we are able to detect the principle of regularity in their formation and to predict the rest of the series to any number of terms we please The principal aim of historical speculation in France of late years has been to ascertain this law But while I gladly acknowledge the great services which have been rendered to historical knowledge by this school I can not but deem them to be mostly chargeable with a fundamental misconception of the true method of social philosophy The misconception consists in supposing that the order of succession which we may be able to trace among the different states of society and civilization which history presents to us even if that order were more rigidly uniform than it has yet been proved to be could ever amount to a law of nature It can only be an empirical law The succession of states of the human mind and of human society can not have an independent law of its own it must depend on the psychological and ethological laws which govern the action of circumstances on men and of men on circumstances It is conceivable that those laws might be such and the general circumstances of the human race such as to determine the successive transformations of man and society to one given and unvarying order But even if the case were so it can not be the ultimate aim of science to discover an empirical law Until that law could be connected with the psychological and ethological laws on which it must depend and by the consilience of deduction a priori with historical evidence could be converted from an empirical law into a scientific one it could not be relied on for the prediction of future events beyond at most strictly adjacent cases M Comte alone among the new historical school has seen the necessity of thus connecting all our generalizations from history with the laws of human nature But while it is an imperative rule never to introduce any generalization from history into the social science unless sufficient grounds can be pointed out for it in human nature I do not think any one will contend that it would have been possible setting out from the principles of human nature and from the general circumstances of the position of our species to determine a priori the order in which human development must take place and to predict consequently the general facts of history up to the present time After the first few terms of the series the influence exercised over each generation by the generations which preceded it becomes as is well observed by the writer last referred to more and more preponderant over all other influences until at length what we now are and do is in a very small degree the result of the universal circumstances of the human race or even of our own circumstances acting through the original qualities of our species but mainly of the qualities produced in us by the whole previous history of humanity So long a series of actions and reactions between Circumstances and Man each successive term being composed of an ever greater number and variety of parts could not possibly be computed by human faculties from the elementary laws which produce it The mere length of the series would be a sufficient obstacle since a slight error in any one of the terms would augment in rapid progression at every subsequent step If therefore the series of the effects themselves did not when examined as a whole manifest any regularity we should in vain attempt to construct a general science of society We must in that case have contented ourselves with that subordinate order of sociological speculation formerly noticed namely with endeavouring to ascertain what would be the effect of the introduction of any new cause in a state of society supposed to be fixed a knowledge sufficient for the more common exigencies of daily political practice but liable to fail in all cases in which the progressive movement of society is one of the influencing elements and therefore more precarious in proportion as the case is more important But since both the natural varieties of mankind and the original diversities of local circumstances are much less considerable than the points of agreement there will naturally be a certain degree of uniformity in the progressive development of the species and of its works And this uniformity tends to become greater not less as society advances since the evolution of each people which is at first determined exclusively by the nature and circumstances of that people is gradually brought under the influence which becomes stronger as civilization advances of the other nations of the earth and of the circumstances by which they have been influenced History accordingly does when judiciously examined afford Empirical Laws of Society And the problem of general sociology is to ascertain these and connect them with the laws of human nature by deductions showing that such were the derivative laws naturally to be expected as the consequences of those ultimate ones It is indeed hardly ever possible even after history has suggested the derivative law to demonstrate a priori that such was the only order of succession or of coexistence in which the effects could consistently with the laws of human nature have been produced We can at most make out that there were strong a priori reasons for expecting it and that no other order of succession or coexistence would have been so likely to result from the nature of man and the general circumstances of his position Often we can not do even this we can not even show that what did take place was probable a priori but only that it was possible This however which in the Inverse Deductive Method that we are now characterizing is a real process of verification is as indispensable as verification by specific experience has been shown to be where the conclusion is originally obtained by the direct way of deduction The empirical laws must be the result of but a few instances since few nations have ever attained at all and still fewer by their own independent development a high stage of social progress If therefore even one or two of these few instances be insufficiently known or imperfectly analysed into their elements and therefore not adequately compared with other instances nothing is more probable than that a wrong empirical law will emerge instead of the right one Accordingly the most erroneous generalizations are continually made from the course of history not only in this country where history can not yet be said to be at all cultivated as a science but in other countries where it is so cultivated and by persons well versed in it The only check or corrective is constant verification by psychological and ethological laws We may add to this that no one but a person competently skilled in those laws is capable of preparing the materials for historical generalization by analyzing the facts of history or even by observing the social phenomena of his own time No other will be aware of the comparative importance of different facts nor consequently know what facts to look for or to observe still less will he be capable of estimating the evidence of facts which as is the case with most can not be ascertained by direct observation or learned from testimony but must be inferred from marks The Empirical Laws of Society are of two kinds some are uniformities of coexistence some of succession According as the science is occupied in ascertaining and verifying the former sort of uniformities or the latter M Comte gives it the title of Social Statics or of Social Dynamics conformably to the distinction in mechanics between the conditions of equilibrium and those of movement or in biology between the laws of organization and those of life The first branch of the science ascertains the conditions of stability in the social union the second the laws of progress Social Dynamics is the theory of Society considered in a state of progressive movement while Social Statics is the theory of the consensus already spoken of as existing among the different parts of the social organism in other words the theory of the mutual actions and reactions of contemporaneous social phenomena making provisionally as far as possible abstraction for scientific purposes of the fundamental movement which is at all times gradually modifying the whole of them In this first point of view the provisions of sociology will enable us to infer one from another subject to ulterior verification by direct observation the various characteristic marks of each distinct mode of social existence in a manner essentially analogous to what is now habitually practiced in the anatomy of the physical body This preliminary aspect therefore of political science of necessity supposes that contrary to the existing habits of philosophers each of the numerous elements of the social state ceasing to be looked at independently and absolutely shall be always and exclusively considered relatively to all the other elements with the whole of which it is united by mutual interdependence It would be superfluous to insist here upon the great and constant utility of this branch of sociological speculation It is in the first place the indispensable basis of the theory of social progress It may moreover be employed immediately and of itself to supply the place provisionally at least of direct observation which in many cases is not always practicable for some of the elements of society the real condition of which may however be sufficiently judged of by means of the relations which connect them with others previously known The history of the sciences may give us some notion of the habitual importance of this auxiliary resource by reminding us for example how the vulgar errors of mere erudition concerning the pretended acquirements of the ancient Egyptians in the higher astronomy were irrevocably dissipated even before sentence had been passed on them by a sounder erudition from the single consideration of the inevitable connection between the general state of astronomy and that of abstract geometry then evidently in its infancy It would be easy to cite a multitude of analogous cases the character of which could admit of no dispute In order to avoid exaggeration however it should be remarked that these necessary relations among the different aspects of society can not from their very nature be so simple and precise that the results observed could only have arisen from some one mode of mutual coordination Such a notion already too narrow in the science of life would be completely at variance with the still more complex nature of sociological speculations But the exact estimation of these limits of variation both in the healthy and in the morbid state constitutes at least as much as in the anatomy of the natural body an indispensable complement to every theory of Sociological Statics without which the indirect exploration above spoken of would often lead into error This is not the place for methodically demonstrating the existence of a necessary relation among all the possible aspects of the same social organism a point on which in principle at least there is now little difference of opinion among sound thinkers From whichever of the social elements we choose to set out we may easily recognize that it has always a connection more or less immediate with all the other elements even with those which at first sight appear the most independent of it The dynamical consideration of the progressive development of civilized humanity affords no doubt a still more efficacious means of effecting this interesting verification of the consensus of the social phenomena by displaying the manner in which every change in any one part operates immediately or very speedily upon all the rest But this indication may be preceded or at all events followed by a confirmation of a purely statical kind for in politics as in mechanics the communication of motion from one object to another proves a connection between them Without descending to the minute interdependence of the different branches of any one science or art is it not evident that among the different sciences as well as among most of the arts there exists such a connection that if the state of any one wellmarked division of them is sufficiently known to us we can with real scientific assurance infer from their necessary correlation the contemporaneous state of every one of the others By a further extension of this consideration we may conceive the necessary relation which exists between the condition of the sciences in general and that of the arts in general except that the mutual dependence is less intense in proportion as it is more indirect The same is the case when instead of considering the aggregate of the social phenomena in some one people we examine it simultaneously in different contemporaneous nations between which the perpetual reciprocity of influence especially in modern times can not be contested though the consensus must in this case be ordinarily of a less decided character and must decrease gradually with the affinity of the cases and the multiplicity of the points of contact so as at last in some cases to disappear almost entirely as for example between Western Europe and Eastern Asia of which the various general states of society appear to have been hitherto almost independent of one another These remarks are followed by illustrations of one of the most important and until lately most neglected of the general principles which in this division of the social science may be considered as established namely the necessary correlation between the form of government existing in any society and the contemporaneous state of civilization a natural law which stamps the endless discussions and innumerable theories respecting forms of government in the abstract as fruitless and worthless for any other purpose than as a preparatory treatment of materials to be afterward used for the construction of a better philosophy As already remarked one of the main results of the science of social statics would be to ascertain the requisites of stable political union There are some circumstances which being found in all societies without exception and in the greatest degree where the social union is most complete may be considered when psychological and ethological laws confirm the indication as conditions of the existence of the complex phenomena called a State For example no numerous society has ever been held together without laws or usages equivalent to them without tribunals and an organized force of some sort to execute their decisions There have always been public authorities whom with more or less strictness and in cases more or less accurately defined the rest of the community obeyed or according to general opinion were bound to obey By following out this course of inquiry we shall find a number of requisites which have been present in every society that has maintained a collective existence and on the cessation of which it has either merged in some other society or reconstructed itself on some new basis in which the conditions were conformed to Although these results obtained by comparing different forms and states of society amount in themselves only to empirical laws some of them when once suggested are found to follow with so much probability from general laws of human nature that the consilience of the two processes raises the evidence to proof and the generalizations to the rank of scientific truths This seems to be affirmable for instance of the conclusions arrived at in the following passage extracted with some alterations from a criticism on the negative philosophy of the eighteenth century and which I quote though as in some former instances from myself because I have no better way of illustrating the conception I have formed of the kind of theorems of which sociological statics would consist The very first element of the social union obedience to a government of some sort has not been found so easy a thing to establish in the world Among a timid and spiritless race like the inhabitants of the vast plains of tropical countries passive obedience may be of natural growth though even there we doubt whether it has ever been found among any people with whom fatalism or in other words, submission to the pressure of circumstances as a divine decree did not prevail as a religious doctrine But the difficulty of inducing a brave and warlike race to submit their individual arbitrium to any common umpire has always been felt to be so great that nothing short of supernatural power has been deemed adequate to overcome it and such tribes have always assigned to the first institution of civil society a divine origin So differently did those judge who knew savage men by actual experience from those who had no acquaintance with them except in the civilized state In modern Europe itself after the fall of the Roman empire to subdue the feudal anarchy and bring the whole people of any European nation into subjection to government though Christianity in the most concentrated form of its influence was cooperating in the work required thrice as many centuries as have elapsed since that time Now if these philosophers had known human nature under any other type than that of their own age and of the particular classes of society among whom they lived it would have occurred to them that wherever this habitual submission to law and government has been firmly and durably established and yet the vigor and manliness of character which resisted its establishment have been in any degree preserved certain requisites have existed certain conditions have been fulfilled of which the following may be regarded as the principal First there has existed for all who were accounted citizens for all who were not slaves kept down by brute force a system of education beginning with infancy and continued through life of which whatever else it might include one main and incessant ingredient was restraining discipline To train the human being in the habit and thence the power of subordinating his personal impulses and aims to what were considered the ends of society of adhering against all temptation to the course of conduct which those ends prescribed of controlling in himself all feelings which were liable to militate against those ends and encouraging all such as tended toward them this was the purpose to which every outward motive that the authority directing the system could command and every inward power or principle which its knowledge of human nature enabled it to evoke were endeavoured to be rendered instrumental The entire civil and military policy of the ancient commonwealths was such a system of training in modern nations its place has been attempted to be supplied principally by religious teaching And whenever and in proportion as the strictness of the restraining discipline was relaxed the natural tendency of mankind to anarchy reasserted itself the state became disorganized from within mutual conflict for selfish ends neutralized the energies which were required to keep up the contest against natural causes of evil and the nation after a longer or briefer interval of progressive decline became either the slave of a despotism or the prey of a foreign invader The second condition of permanent political society has been found to be the existence in some form or other of the feeling of allegiance or loyalty This feeling may vary in its objects and is not confined to any particular form of government but whether in a democracy or in a monarchy its essence is always the same viz that there be in the constitution of the state something which is settled something permanent and not to be called in question something which by general agreement has a right to be where it is and to be secure against disturbance whatever else may change This feeling may attach itself as among the Jews and in most of the commonwealths of antiquity to a common God or gods the protectors and guardians of their state Or it may attach itself to certain persons who are deemed to be whether by divine appointment by long prescription or by the general recognition of their superior capacity and worthiness the rightful guides and guardians of the rest Or it may connect itself with laws with ancient liberties or ordinances Or finally and this is the only shape in which the feeling is likely to exist hereafter it may attach itself to the principles of individual freedom and political and social equality as realized in institutions which as yet exist nowhere or exist only in a rudimentary state But in all political societies which have had a durable existence there has been some fixed point something which people agreed in holding sacred which wherever freedom of discussion was a recognized principle it was of course lawful to contest in theory but which no one could either fear or hope to see shaken in practice which in short except perhaps during some temporary crisis was in the common estimation placed beyond discussion And the necessity of this may easily be made evident A state never is nor until mankind are vastly improved can hope to be for any long time exempt from internal dissension for there neither is nor has ever been any state of society in which collisions did not occur between the immediate interests and passions of powerful sections of the people What then enables nations to weather these storms and pass through turbulent times without any permanent weakening of the securities for peaceable existence Precisely this that however important the interests about which men fell out the conflict did not affect the fundamental principle of the system of social union which happened to exist nor threaten large portions of the community with the subversion of that on which they had built their calculations and with which their hopes and aims had become identified But when the questioning of these fundamental principles is not the occasional disease or salutary medicine but the habitual condition of the body politic and when all the violent animosities are called forth which spring naturally from such a situation the state is virtually in a position of civil war and can never long remain free from it in act and fact The third essential condition of stability in political society is a strong and active principle of cohesion among the members of the same community or state We need scarcely say that we do not mean nationality in the vulgar sense of the term a senseless antipathy to foreigners indifference to the general welfare of the human race or an unjust preference of the supposed interests of our own country a cherishing of bad peculiarities because they are national or a refusal to adopt what has been found good by other countries We mean a principle of sympathy not of hostility of union not of separation We mean a feeling of common interest among those who live under the same government and are contained within the same natural or historical boundaries We mean that one part of the community do not consider themselves as foreigners with regard to another part that they set a value on their connection feel that they are one people that their lot is cast together that evil to any of their fellowcountrymen is evil to themselves and do not desire selfishly to free themselves from their share of any common inconvenience by severing the connection How strong this feeling was in those ancient commonwealths which attained any durable greatness every one knows How happily Rome in spite of all her tyranny succeeded in establishing the feeling of a common country among the provinces of her vast and divided empire will appear when any one who has given due attention to the subject shall take the trouble to point it out In modern times the countries which have had that feeling in the strongest degree have been the most powerful countries England France and in proportion to their territory and resources Holland and Switzerland while England in her connection with Ireland is one of the most signal examples of the consequences of its absence Every Italian knows why Italy is under a foreign yoke every German knows what maintains despotism in the Austrian empire the evils of Spain flow as much from the absence of nationality among the Spaniards themselves as from the presence of it in their relations with foreigners while the completest illustration of all is afforded by the republics of South America where the parts of one and the same state adhere so slightly together that no sooner does any province think itself aggrieved by the general government than it proclaims itself a separate nation While the derivative laws of social statics are ascertained by analyzing different states of society and comparing them with one another without regard to the order of their succession the consideration of the successive order is on the contrary predominant in the study of social dynamics of which the aim is to observe and explain the sequences of social conditions This branch of the social science would be as complete as it can be made if every one of the leading general circumstances of each generation were traced to its causes in the generation immediately preceding But the consensus is so complete especially in modern history that in the filiation of one generation and another it is the whole which produces the whole rather than any part a part Little progress therefore can be made in establishing the filiation directly from laws of human nature without having first ascertained the immediate or derivative laws according to which social states generate one another as society advances the axiomata media of General Sociology The empirical laws which are most readily obtained by generalization from history do not amount to this They are not the middle principles themselves but only evidence toward the establishment of such principles They consist of certain general tendencies which may be perceived in society a progressive increase of some social elements and diminution of others or a gradual change in the general character of certain elements It is easily seen for instance that as society advances mental tend more and more to prevail over bodily qualities and masses over individuals that the occupation of all that portion of mankind who are not under external restraint is at first chiefly military but society becomes progressively more and more engrossed with productive pursuits and the military spirit gradually gives way to the industrial to which many similar truths might be added And with generalizations of this description ordinary inquirers even of the historical school now predominant on the Continent are satisfied But these and all such results are still at too great a distance from the elementary laws of human nature on which they depend too many links intervene and the concurrence of causes at each link is far too complicated to enable these propositions to be presented as direct corollaries from those elementary principles They have therefore in the minds of most inquirers remained in the state of empirical laws applicable only within the bounds of actual observation without any means of determining their real limits and of judging whether the changes which have hitherto been in progress are destined to continue indefinitely or to terminate or even to be reversed In order to obtain better empirical laws we must not rest satisfied with noting the progressive changes which manifest themselves in the separate elements of society and in which nothing is indicated but the relation of fragments of the effect to corresponding fragments of the cause It is necessary to combine the statical view of social phenomena with the dynamical considering not only the progressive changes of the different elements but the contemporaneous condition of each and thus obtain empirically the law of correspondence not only between the simultaneous states but between the simultaneous changes of those elements This law of correspondence it is which duly verified a priori would become the real scientific derivative law of the development of humanity and human affairs In the difficult process of observation and comparison which is here required it would evidently be a great assistance if it should happen to be the fact that some one element in the complex existence of social man is preeminent over all others as the prime agent of the social movement For we could then take the progress of that one element as the central chain to each successive link of which the corresponding links of all the other progressions being appended the succession of the facts would by this alone be presented in a kind of spontaneous order far more nearly approaching to the real order of their filiation than could be obtained by any other merely empirical process Now the evidence of history and that of human nature combine by a striking instance of consilience to show that there really is one social element which is thus predominant and almost paramount among the agents of the social progression This is the state of the speculative faculties of mankind including the nature of the beliefs which by any means they have arrived at concerning themselves and the world by which they are surrounded It would be a great error and one very little likely to be committed to assert that speculation intellectual activity the pursuit of truth is among the more powerful propensities of human nature or holds a predominating place in the lives of any save decidedly exceptional individuals But notwithstanding the relative weakness of this principle among other sociological agents its influence is the main determining cause of the social progress all the other dispositions of our nature which contribute to that progress being dependent on it for the means of accomplishing their share of the work Thus to take the most obvious case first the impelling force to most of the improvements effected in the arts of life is the desire of increased material comfort but as we can only act upon external objects in proportion to our knowledge of them the state of knowledge at any time is the limit of the industrial improvements possible at that time and the progress of industry must follow and depend on the progress of knowledge The same thing may be shown to be true though it is not quite so obvious of the progress of the fine arts Further as the strongest propensities of uncultivated or halfcultivated human nature being the purely selfish ones and those of a sympathetic character which partake most of the nature of selfishness evidently tend in themselves to disunite mankind not to unite them to make them rivals not confederates social existence is only possible by a disciplining of those more powerful propensities which consists in subordinating them to a common system of opinions The degree of this subordination is the measure of the completeness of the social union and the nature of the common opinions determines its kind But in order that mankind should conform their actions to any set of opinions these opinions must exist must be believed by them And thus the state of the speculative faculties the character of the propositions assented to by the intellect essentially determines the moral and political state of the community as we have already seen that it determines the physical These conclusions deduced from the laws of human nature are in entire accordance with the general facts of history Every considerable change historically known to us in the condition of any portion of mankind when not brought about by external force has been preceded by a change of proportional extent in the state of their knowledge or in their prevalent beliefs As between any given state of speculation and the correlative state of every thing else it was almost always the former which first showed itself though the effects no doubt reacted potently upon the cause Every considerable advance in material civilization has been preceded by an advance in knowledge and when any great social change has come to pass either in the way of gradual development or of sudden conflict it has had for its precursor a great change in the opinions and modes of thinking of society Polytheism Judaism Christianity Protestantism the critical philosophy of modern Europe and its positive science each of these has been a primary agent in making society what it was at each successive period while society was but secondarily instrumental in making them each of them so far as causes can be assigned for its existence being mainly an emanation not from the practical life of the period but from the previous state of belief and thought The weakness of the speculative propensity in mankind generally has not therefore prevented the progress of speculation from governing that of society at large it has only and too often prevented progress altogether where the intellectual progression has come to an early stand for want of sufficiently favourable circumstances From this accumulated evidence we are justified in concluding that the order of human progression in all respects will mainly depend on the order of progression in the intellectual convictions of mankind that is on the law of the successive transformations of human opinions The question remains whether this law can be determined at first from history as an empirical law then converted into a scientific theorem by deducing it a priori from the principles of human nature As the progress of knowledge and the changes in the opinions of mankind are very slow and manifest themselves in a welldefined manner only at long intervals it can not be expected that the general order of sequence should be discoverable from the examination of less than a very considerable part of the duration of the social progress It is necessary to take into consideration the whole of past time from the first recorded condition of the human race to the memorable phenomena of the last and present generations The investigation which I have thus endeavoured to characterize has been systematically attempted up to the present time by M Comte alone His work is hitherto the only known example of the study of social phenomena according to this conception of the Historical Method Without discussing here the worth of his conclusions and especially of his predictions and recommendations with respect to the Future of society which appear to me greatly inferior in value to his appreciation of the Past I shall confine myself to mentioning one important generalization which M Comte regards as the fundamental law of the progress of human knowledge Speculation he conceives to have on every subject of human inquiry three successive stages in the first of which it tends to explain the phenomena by supernatural agencies in the second by metaphysical abstractions and in the third or final state confines itself to ascertaining their laws of succession and similitude This generalization appears to me to have that high degree of scientific evidence which is derived from the concurrence of the indications of history with the probabilities derived from the constitution of the human mind Nor could it be easily conceived from the mere enunciation of such a proposition what a flood of light it lets in upon the whole course of history when its consequences are traced by connecting with each of the three states of human intellect which it distinguishes and with each successive modification of those three states the correlative condition of other social phenomena But whatever decision competent judges may pronounce on the results arrived at by any individual inquirer the method now characterized is that by which the derivative laws of social order and of social progress must be sought By its aid we may hereafter succeed not only in looking far forward into the future history of the human race but in determining what artificial means may be used and to what extent to accelerate the natural progress in so far as it is beneficial to compensate for whatever may be its inherent inconveniences or disadvantages and to guard against the dangers or accidents to which our species is exposed from the necessary incidents of its progression Such practical instructions founded on the highest branch of speculative sociology will form the noblest and most beneficial portion of the Political Art That of this science and art even the foundations are but beginning to be laid is sufficiently evident But the superior minds are fairly turning themselves toward that object It has become the aim of really scientific thinkers to connect by theories the facts of universal history it is acknowledged to be one of the requisites of a general system of social doctrine that it should explain so far as the data exist the main facts of history and a Philosophy of History is generally admitted to be at once the verification and the initial form of the Philosophy of the Progress of Society If the endeavours now making in all the more cultivated nations and beginning to be made even in England usually the last to enter into the general movement of the European mind for the construction of a Philosophy of History shall be directed and controlled by those views of the nature of sociological evidence which I have very briefly and imperfectly attempted to characterize they can not fail to give birth to a sociological system widely removed from the vague and conjectural character of all former attempts and worthy to take its place at last among the sciences When this time shall come no important branch of human affairs will be any longer abandoned to empiricism and unscientific surmise the circle of human knowledge will be complete and it can only thereafter receive further enlargement by perpetual expansion from within The doctrine which the preceding chapters were intended to enforce and elucidate that the collective series of social phenomena in other words the course of history is subject to general laws which philosophy may possibly detect has been familiar for generations to the scientific thinkers of the Continent and has for the last quarter of a century passed out of their peculiar domain into that of newspapers and ordinary political discussion In our own country however at the time of the first publication of this Treatise it was almost a novelty and the prevailing habits of thought on historical subjects were the very reverse of a preparation for it Since then a great change has taken place and has been eminently promoted by the important work of Mr Buckle who with characteristic energy flung down this great principle together with many striking exemplifications of it into the arena of popular discussion to be fought over by a sort of combatants in the presence of a sort of spectators who would never even have been aware that there existed such a principle if they had been left to learn its existence from the speculations of pure science And hence has arisen a considerable amount of controversy tending not only to make the principle rapidly familiar to the majority of cultivated minds but also to clear it from the confusions and misunderstandings by which it was but natural that it should for a time be clouded and which impair the worth of the doctrine to those who accept it and are the stumblingblock of many who do not Among the impediments to the general acknowledgment by thoughtful minds of the subjection of historical facts to scientific laws the most fundamental continues to be that which is grounded on the doctrine of Free Will or, in other words, on the denial that the law of invariable Causation holds true of human volitions for if it does not the course of history being the result of human volitions can not be a subject of scientific laws since the volitions on which it depends can neither be foreseen nor reduced to any canon of regularity even after they have occurred I have discussed this question as far as seemed suitable to the occasion in a former chapter and I only think it necessary to repeat that the doctrine of the Causation of human actions improperly called the doctrine of Necessity affirms no mysterious nexus or overruling fatality it asserts only that men’s actions are the joint result of the general laws and circumstances of human nature and of their own particular characters those characters again being the consequence of the natural and artificial circumstances that constituted their education among which circumstances must be reckoned their own conscious efforts Any one who is willing to take if the expression may be permitted the trouble of thinking himself into the doctrine as thus stated will find it I believe not only a faithful interpretation of the universal experience of human conduct but a correct representation of the mode in which he himself in every particular case spontaneously interprets his own experience of that conduct But if this principle is true of individual man it must be true of collective man If it is the law of human life the law must be realized in history The experience of human affairs when looked at en masse must be in accordance with it if true or repugnant to it if false The support which this a posteriori verification affords to the law is the part of the case which has been most clearly and triumphantly brought out by Mr Buckle The facts of statistics since they have been made a subject of careful recordation and study have yielded conclusions some of which have been very startling to persons not accustomed to regard moral actions as subject to uniform laws The very events which in their own nature appear most capricious and uncertain and which in any individual case no attainable degree of knowledge would enable us to foresee occur when considerable numbers are taken into the account with a degree of regularity approaching to mathematical What act is there which all would consider as more completely dependent on individual character and on the exercise of individual free will than that of slaying a fellowcreature Yet in any large country the number of murders in proportion to the population varies it has been found very little from one year to another and in its variations never deviates widely from a certain average What is still more remarkable there is a similar approach to constancy in the proportion of these murders annually committed with every particular kind of instrument There is a like approximation to identity as between one year and another in the comparative number of legitimate and of illegitimate births The same thing is found true of suicides accidents and all other social phenomena of which the registration is sufficiently perfect one of the most curiously illustrative examples being the fact ascertained by the registers of the London and Paris postoffices that the number of letters posted which the writers have forgotten to direct is nearly the same in proportion to the whole number of letters posted in one year as in another Year after year says Mr Buckle the same proportion of letterwriters forget this simple act so that for each successive period we can actually foretell the number of persons whose memory will fail them in regard to this trifling and as it might appear accidental occurrence This singular degree of regularity en masse combined with the extreme of irregularity in the cases composing the mass is a felicitous verification a posteriori of the law of causation in its application to human conduct Assuming the truth of that law every human action every murder for instance is the concurrent result of two sets of causes On the one part the general circumstances of the country and its inhabitants the moral educational economical and other influences operating on the whole people and constituting what we term the state of civilization On the other part the great variety of influences special to the individual his temperament and other peculiarities of organization his parentage habitual associates temptations and so forth If we now take the whole of the instances which occur within a sufficiently large field to exhaust all the combinations of these special influences or, in other words, to eliminate chance and if all these instances have occurred within such narrow limits of time that no material change can have taken place in the general influences constituting the state of civilization of the country we may be certain that if human actions are governed by invariable laws the aggregate result will be something like a constant quantity The number of murders committed within that space and time being the effect partly of general causes which have not varied and partly of partial causes the whole round of whose variations has been included will be practically speaking invariable Literally and mathematically invariable it is not and could not be expected to be because the period of a year is too short to include all the possible combinations of partial causes while it is, at the same time sufficiently long to make it probable that in some years at least of every series there will have been introduced new influences of a more or less general character such as a more vigorous or a more relaxed police some temporary excitement from political or religious causes or some incident generally notorious of a nature to act morbidly on the imagination That in spite of these unavoidable imperfections in the data there should be so very trifling a margin of variation in the annual results is a brilliant continuation of the general theory The same considerations which thus strikingly corroborate the evidence of the doctrine that historical facts are the invariable effects of causes tend equally to clear that doctrine from various misapprehensions the existence of which has been put in evidence by the recent discussions Some persons for instance seemingly imagine the doctrine to imply not merely that the total number of murders committed in a given space and time is entirely the effect of the general circumstances of society but that every particular murder is so too that the individual murderer is so to speak a mere instrument in the hands of general causes that he himself has no option or if he has and chose to exercise it some one else would be necessitated to take his place that if any one of the actual murderers had abstained from the crime some person who would otherwise have remained innocent would have committed an extra murder to make up the average Such a corollary would certainly convict any theory which necessarily led to it of absurdity It is obvious however that each particular murder depends not on the general state of society only but on that combined with causes special to the case which are generally much more powerful and if these special causes which have greater influence than the general ones in causing every particular murder have no influence on the number of murders in a given period it is because the field of observation is so extensive as to include all possible combinations of the special causes all varieties of individual character and individual temptation compatible with the general state of society The collective experiment as it may be termed exactly separates the effect of the general from that of the special causes and shows the net result of the former but it declares nothing at all respecting the amount of influence of the special causes be it greater or smaller since the scale of the experiment extends to the number of cases within which the effects of the special causes balance one another and disappear in that of the general causes I will not pretend that all the defenders of the theory have always kept their language free from this same confusion and have shown no tendency to exalt the influence of general causes at the expense of special I am of opinion on the contrary that they have done so in a very great degree and by so doing have encumbered their theory with difficulties and laid it open to objections which do not necessarily affect it Some for example among whom is Mr Buckle himself have inferred or allowed it to be supposed that they inferred from the regularity in the recurrence of events which depend on moral qualities that the moral qualities of mankind are little capable of being improved or are of little importance in the general progress of society compared with intellectual or economic causes But to draw this inference is to forget that the statistical tables from which the invariable averages are deduced were compiled from facts occurring within narrow geographical limits and in a small number of successive years that is from a field the whole of which was under the operation of the same general causes and during too short a time to allow of much change therein All moral causes but those common to the country generally have been eliminated by the great number of instances taken and those which are common to the whole country have not varied considerably in the short space of time comprised in the observations If we admit the supposition that they have varied if we compare one age with another or one country with another or even one part of a country with another differing in position and character as to the moral elements the crimes committed within a year give no longer the same but a widely different numerical aggregate And this can not but be the case for inasmuch as every single crime committed by an individual mainly depends on his moral qualities the crimes committed by the entire population of the country must depend in an equal degree on their collective moral qualities To render this element inoperative upon the large scale it would be necessary to suppose that the general moral average of mankind does not vary from country to country or from age to age which is not true and even if it were true could not possibly be proved by any existing statistics I do not on this account the less agree in the opinion of Mr Buckle that the intellectual element in mankind including in that expression the nature of their beliefs the amount of their knowledge and the development of their intelligence is the predominant circumstance in determining their progress But I am of this opinion not because I regard their moral or economical condition either as less powerful or less variable agencies but because these are in a great degree the consequences of the intellectual condition and are in all cases limited by it as was observed in the preceding chapter The intellectual changes are the most conspicuous agents in history not from their superior force considered in themselves but because practically they work with the united power belonging to all three There is another distinction often neglected in the discussion of this subject which it is extremely important to observe The theory of the subjection of social progress to invariable laws is often held in conjunction with the doctrine that social progress can not be materially influenced by the exertions of individual persons or by the acts of governments But though these opinions are often held by the same persons they are two very different opinions and the confusion between them is the eternally recurring error of confounding Causation with Fatalism Because whatever happens will be the effect of causes human volitions among the rest it does not follow that volitions even those of peculiar individuals are not of great efficacy as causes If any one in a storm at sea because about the same number of persons in every year perish by shipwreck should conclude that it was useless for him to attempt to save his own life we should call him a Fatalist and should remind him that the efforts of shipwrecked persons to save their lives are so far from being immaterial that the average amount of those efforts is one of the causes on which the ascertained annual number of deaths by shipwreck depend However universal the laws of social development may be they can not be more universal or more rigorous than those of the physical agencies of nature yet human will can convert these into instruments of its designs and the extent to which it does so makes the chief difference between savages and the most highly civilized people Human and social facts from their more complicated nature are not less but more modifiable than mechanical and chemical facts human agency therefore has still greater power over them And accordingly those who maintain that the evolution of society depends exclusively or almost exclusively on general causes always include among these the collective knowledge and intellectual development of the race But if of the race why not also of some powerful monarch or thinker or of the ruling portion of some political society acting through its government Though the varieties of character among ordinary individuals neutralize one another on any large scale exceptional individuals in important positions do not in any given age neutralize one another there was not another Themistocles or Luther or Julius Caesar of equal powers and contrary dispositions who exactly balanced the given Themistocles Luther and Caesar and prevented them from having any permanent effect Moreover for aught that appears the volitions of exceptional persons or the opinions and purposes of the individuals who at some particular time compose a government may be indispensable links in the chain of causation by which even the general causes produce their effects and I believe this to be the only tenable form of the theory Lord Macaulay in a celebrated passage of one of his early essays let me add that it was one which he did not himself choose to reprint gives expression to the doctrine of the absolute inoperativeness of great men more unqualified I should think than has been given to it by any writer of equal abilities He compares them to persons who merely stand on a loftier height and thence receive the sun’s rays a little earlier than the rest of the human race The sun illuminates the hills while it is still below the horizon and truth is discovered by the highest minds a little before it becomes manifest to the multitude This is the extent of their superiority They are the first to catch and reflect a light which without their assistance must in a short time be visible to those who lie far beneath them If this metaphor is to be carried out it follows that if there had been no Newton the world would not only have had the Newtonian system but would have had it equally soon as the sun would have risen just as early to spectators in the plain if there had been no mountain at hand to catch still earlier rays And so it would be if truths like the sun rose by their own proper motion without human effort but not otherwise I believe that if Newton had not lived the world must have waited for the Newtonian philosophy until there had been another Newton or his equivalent No ordinary man and no succession of ordinary men could have achieved it I will not go the length of saying that what Newton did in a single life might not have been done in successive steps by some of those who followed him each singly inferior to him in genius But even the least of those steps required a man of great intellectual superiority Eminent men do not merely see the coming light from the hilltop they mount on the hilltop and evoke it and if no one had ever ascended thither the light in many cases might never have risen upon the plain at all Philosophy and religion are abundantly amenable to general causes yet few will doubt that had there been no Socrates no Plato and no Aristotle there would have been no philosophy for the next two thousand years nor in all probability then and that if there had been no Christ and no St Paul there would have been no Christianity The point in which above all the influence of remarkable individuals is decisive is in determining the celerity of the movement In most states of society it is the existence of great men which decides even whether there shall be any progress It is conceivable that Greece or that Christian Europe might have been progressive in certain periods of their history through general causes only but if there had been no Mohammed would Arabia have produced Avicenna or Averroes or Caliphs of Bagdad or of Cordova In determining however in what manner and order the progress of mankind shall take place if it take place at all much less depends on the character of individuals There is a sort of necessity established in this respect by the general laws of human nature by the constitution of the human mind Certain truths can not be discovered nor inventions made unless certain others have been made first certain social improvements from the nature of the case can only follow and not precede others The order of human progress therefore may to a certain extent have definite laws assigned to it while as to its celerity or even as to its taking place at all no generalization extending to the human species generally can possibly be made but only some very precarious approximate generalizations confined to the small portion of mankind in whom there has been any thing like consecutive progress within the historical period and deduced from their special position or collected from their particular history Even looking to the manner of progress the order of succession of social states there is need of great flexibility in our generalizations The limits of variation in the possible development of social as of animal life are a subject of which little is yet understood and are one of the great problems in social science It is at all events a fact that different portions of mankind under the influence of different circumstances have developed themselves in a more or less different manner and into different forms and among these determining circumstances the individual character of their great speculative thinkers or practical organizers may well have been one Who can tell how profoundly the whole subsequent history of China may have been influenced by the individuality of Confucius and of Sparta and hence of Greece and the world by that of Lycurgus Concerning the nature and extent of what a great man under favourable circumstances can do for mankind as well as of what a government can do for a nation many different opinions are possible and every shade of opinion on these points is consistent with the fullest recognition that there are invariable laws of historical phenomena Of course the degree of influence which has to be assigned to these more special agencies makes a great difference in the precision which can be given to the general laws and in the confidence with which predictions can be grounded on them Whatever depends on the peculiarities of individuals combined with the accident of the positions they hold is necessarily incapable of being foreseen Undoubtedly these casual combinations might be eliminated like any others by taking a sufficiently large cycle the peculiarities of a great historical character make their influence felt in history sometimes for several thousand years but it is highly probable that they will make no difference at all at the end of fifty millions Since however we can not obtain an average of the vast length of time necessary to exhaust all the possible combinations of great men and circumstances as much of the law of evolution of human affairs as depends upon this average is and remains inaccessible to us and within the next thousand years which are of considerably more importance to us than the whole remainder of the fifty millions the favourable and unfavourable combinations which will occur will be to us purely accidental We can not foresee the advent of great men Those who introduce new speculative thoughts or great practical conceptions into the world can not have their epoch fixed beforehand What science can do is this It can trace through past history the general causes which had brought mankind into that preliminary state which when the right sort of great man appeared rendered them accessible to his influence If this state continues experience renders it tolerably certain that in a longer or shorter period the great man will be produced provided that the general circumstances of the country and people are which very often they are not compatible with his existence of which point also science can in some measure judge It is in this manner that the results of progress except as to the celerity of their production can be to a certain extent reduced to regularity and law And the belief that they can be so is equally consistent with assigning very great or very little efficacy to the influence of exceptional men or of the acts of governments And the same may be said of all other accidents and disturbing causes It would nevertheless be a great error to assign only a trifling importance to the agency of eminent individuals or of governments It must not be concluded that the influence of either is small because they can not bestow what the general circumstances of society and the course of its previous history have not prepared it to receive Neither thinkers nor governments effect all that they intend but in compensation they often produce important results which they did not in the least foresee Great men and great actions are seldom wasted they send forth a thousand unseen influences more effective than those which are seen and though nine out of every ten things done with a good purpose by those who are in advance of their age produce no material effect the tenth thing produces effects twenty times as great as any one would have dreamed of predicting from it Even the men who for want of sufficiently favourable circumstances left no impress at all upon their own age have often been of the greatest value to posterity Who could appear to have lived more entirely in vain than some of the early heretics They were burned or massacred their writings extirpated their memory anathematized and their very names and existence left for seven or eight centuries in the obscurity of musty manuscripts their history to be gathered perhaps only from the sentences by which they were condemned Yet the memory of these men who resisted certain pretensions or certain dogmas of the Church in the very age in which the unanimous assent of Christendom was afterward claimed as having been given to them and asserted as the ground of their authority broke the chain of tradition established a series of precedents for resistance inspired later Reformers with the courage and armed them with the weapons which they needed when mankind were better prepared to follow their impulse To this example from men let us add another from governments The comparatively enlightened rule of which Spain had the benefit during a considerable part of the eighteenth century did not correct the fundamental defects of the Spanish people and in consequence though it did great temporary good so much of that good perished with it that it may plausibly be affirmed to have had no permanent effect The case has been cited as a proof how little governments can do in opposition to the causes which have determined the general character of the nation It does show how much there is which they can not do but not that they can do nothing Compare what Spain was at the beginning of that halfcentury of liberal government with what she had become at its close That period fairly let in the light of European thought upon the more educated classes and it never afterward ceased to go on spreading Previous to that time the change was in an inverse direction culture light intellectual and even material activity were becoming extinguished Was it nothing to arrest this downward and convert it into an upward course How much that Charles the Third and Aranda could not do has been the ultimate consequence of what they did To that halfcentury Spain owes that she has got rid of the Inquisition that she has got rid of the monks that she now has parliaments and save in exceptional intervals a free press and the feelings of freedom and citizenship and is acquiring railroads and all the other constituents of material and economical progress In the Spain which preceded that era there was not a single element at work which could have led to these results in any length of time if the country had continued to be governed as it was by the last princes of the Austrian dynasty or if the Bourbon rulers had been from the first what both in Spain and in Naples they afterward became And if a government can do much even when it seems to have done little in causing positive improvement still greater are the issues dependent on it in the way of warding off evils both internal and external which else would stop improvement altogether A good or a bad counsellor in a single city at a particular crisis has affected the whole subsequent fate of the world It is as certain as any contingent judgment respecting historical events can be that if there had been no Themistocles there would have been no victory of Salamis and had there not where would have been all our civilization How different again would have been the issue if Epaminondas or Timoleon or even Iphicrates instead of Chares and Lysicles had commanded at Chaeroneia As is well said in the second of two Essays on the Study of History in my judgment the soundest and most philosophical productions which the recent controversies on this subject have called forth historical science authorizes not absolute but only conditional predictions General causes count for much but individuals also produce great changes in history and color its whole complexion long after their death No one can doubt that the Roman republic would have subsided into a military despotism if Julius Caesar had never lived thus much was rendered practically certain by general causes but is it at all clear that in that case Gaul would ever have formed a province of the empire Might not Varus have lost his three legions on the banks of the Rhone and might not that river have become the frontier instead of the Rhine This might well have happened if Caesar and Crassus had changed provinces and it is surely impossible to say that in such an event the venue as lawyers say of European civilization might not have been changed The Norman Conquest in the same way was as much the act of a single man as the writing of a newspaper article and knowing as we do the history of that man and his family we can retrospectively predict with all but infallible certainty that no other person no other in that age I presume is meant could have accomplished the enterprise If it had not been accomplished is there any ground to suppose that either our history or our national character would have been what they are As is most truly remarked by the same writer the whole stream of Grecian history as cleared up by Mr Grote is one series of examples how often events on which the whole destiny of subsequent civilization turned were dependent on the personal character for good or evil of some one individual It must be said however that Greece furnishes the most extreme example of this nature to be found in history and is a very exaggerated specimen of the general tendency It has happened only that once and will probably never happen again that the fortunes of mankind depended upon keeping a certain order of things in existence in a single town or a country scarcely larger than Yorkshire capable of being ruined or saved by a hundred causes of very slight magnitude in comparison with the general tendencies of human affairs Neither ordinary accidents nor the characters of individuals can ever again be so vitally important as they then were The longer our species lasts and the more civilized it becomes the more as Comte remarks does the influence of past generations over the present and of mankind en masse over every individual in it predominate over other forces and though the course of affairs never ceases to be susceptible of alteration both by accidents and by personal qualities the increasing preponderance of the collective agency of the species over all minor causes is constantly bringing the general evolution of the race into something which deviates less from a certain and preappointed track Historical science therefore is always becoming more possible not solely because it is better studied but because in every generation it becomes better adapted for study In the preceding chapters we have endeavoured to characterize the present state of those among the branches of knowledge called Moral which are sciences in the only proper sense of the term that is inquiries into the course of nature It is customary however to include under the term moral knowledge and even though improperly under that of moral science an inquiry the results of which do not express themselves in the indicative but in the imperative mood or in periphrases equivalent to it what is called the knowledge of duties practical ethics or morality Now the imperative mood is the characteristic of art as distinguished from science Whatever speaks in rules or precepts not in assertions respecting matters of fact is art and ethics or morality is properly a portion of the art corresponding to the sciences of human nature and society The Method therefore of Ethics can be no other than that of Art or Practice in general and the portion yet uncompleted of the task which we proposed to ourselves in the concluding Book is to characterize the general Method of Art as distinguished from Science In all branches of practical business there are cases in which individuals are bound to conform their practice to a preestablished rule while there are others in which it is part of their task to find or construct the rule by which they are to govern their conduct The first for example is the case of a judge under a definite written code The judge is not called upon to determine what course would be intrinsically the most advisable in the particular case in hand but only within what rule of law it falls what the legislature has ordained to be done in the kind of case and must therefore be presumed to have intended in the individual case The method must here be wholly and exclusively one of ratiocination or syllogism and the process is obviously what in our analysis of the syllogism we showed that all ratiocination is namely the interpretation of a formula In order that our illustration of the opposite case may be taken from the same class of subjects as the former we will suppose in contrast with the situation of the judge the position of the legislator As the judge has laws for his guidance so the legislator has rules and maxims of policy but it would be a manifest error to suppose that the legislator is bound by these maxims in the same manner as the judge is bound by the laws and that all he has to do is to argue down from them to the particular case as the judge does from the laws The legislator is bound to take into consideration the reasons or grounds of the maxim the judge has nothing to do with those of the law except so far as a consideration of them may throw light upon the intention of the lawmaker where his words have left it doubtful To the judge the rule once positively ascertained is final but the legislator or other practitioner who goes by rules rather than by their reasons like the oldfashioned German tacticians who were vanquished by Napoleon or the physician who preferred that his patients should die by rule rather than recover contrary to it is rightly judged to be a mere pedant and the slave of his formulas Now the reasons of a maxim of policy or of any other rule of art can be no other than the theorems of the corresponding science The relation in which rules of art stand to doctrines of science may be thus characterized The art proposes to itself an end to be attained defines the end and hands it over to the science The science receives it considers it as a phenomenon or effect to be studied and having investigated its causes and conditions sends it back to art with a theorem of the combination of circumstances by which it could be produced Art then examines these combinations of circumstances and according as any of them are or are not in human power pronounces the end attainable or not The only one of the premises therefore which Art supplies is the original major premise which asserts that the attainment of the given end is desirable Science then lends to Art the proposition obtained by a series of inductions or of deductions that the performance of certain actions will attain the end From these premises Art concludes that the performance of these actions is desirable and finding it also practicable converts the theorem into a rule or precept It deserves particular notice that the theorem or speculative truth is not ripe for being turned into a precept until the whole and not a part merely of the operation which belongs to science has been performed Suppose that we have completed the scientific process only up to a certain point have discovered that a particular cause will produce the desired effect but have not ascertained all the negative conditions which are necessary that is all the circumstances which if present would prevent its production If in this imperfect state of the scientific theory we attempt to frame a rule of art we perform that operation prematurely Whenever any counteracting cause overlooked by the theorem takes place the rule will be at fault we shall employ the means and the end will not follow No arguing from or about the rule itself will then help us through the difficulty there is nothing for it but to turn back and finish the scientific process which should have preceded the formation of the rule We must reopen the investigation to inquire into the remainder of the conditions on which the effect depends and only after we have ascertained the whole of these are we prepared to transform the completed law of the effect into a precept in which those circumstances or combinations of circumstances which the science exhibits as conditions are prescribed as means It is true that for the sake of convenience rules must be formed from something less than this ideally perfect theory in the first place because the theory can seldom be made ideally perfect and next because if all the counteracting contingencies whether of frequent or of rare occurrence were included the rules would be too cumbrous to be apprehended and remembered by ordinary capacities on the common occasions of life The rules of art do not attempt to comprise more conditions than require to be attended to in ordinary cases and are therefore always imperfect In the manual arts where the requisite conditions are not numerous and where those which the rules do not specify are generally either plain to common observation or speedily learned from practice rules may often be safely acted on by persons who know nothing more than the rule But in the complicated affairs of life and still more in those of states and societies rules can not be relied on without constantly referring back to the scientific laws on which they are founded To know what are the practical contingencies which require a modification of the rule or which are altogether exceptions to it is to know what combinations of circumstances would interfere with or entirely counteract the consequences of those laws and this can only be learned by a reference to the theoretic grounds of the rule By a wise practitioner therefore rules of conduct will only be considered as provisional Being made for the most numerous cases or for those of most ordinary occurrence they point out the manner in which it will be least perilous to act where time or means do not exist for analyzing the actual circumstances of the case or where we can not trust our judgment in estimating them But they do not at all supersede the propriety of going through when circumstances permit the scientific process requisite for framing a rule from the data of the particular case before us At the same time the common rule may very properly serve as an admonition that a certain mode of action has been found by ourselves and others to be well adapted to the cases of most common occurrence so that if it be unsuitable to the case in hand the reason of its being so will be likely to arise from some unusual circumstance The error is therefore apparent of those who would deduce the line of conduct proper to particular cases from supposed universal practical maxims overlooking the necessity of constantly referring back to the principles of the speculative science in order to be sure of attaining even the specific end which the rules have in view How much greater still then must the error be of setting up such unbending principles not merely as universal rules for attaining a given end but as rules of conduct generally without regard to the possibility not only that some modifying cause may prevent the attainment of the given end by the means which the rule prescribes but that success itself may conflict with some other end which may possibly chance to be more desirable This is the habitual error of many of the political speculators whom I have characterized as the geometrical school especially in France where ratiocination from rules of practice forms the staple commodity of journalism and political oratory a misapprehension of the functions of Deduction which has brought much discredit in the estimation of other countries upon the spirit of generalization so honourably characteristic of the French mind The commonplaces of politics in France are large and sweeping practical maxims from which as ultimate premises men reason downward to particular applications and this they call being logical and consistent For instance they are perpetually arguing that such and such a measure ought to be adopted because it is a consequence of the principle on which the form of government is founded of the principle of legitimacy or the principle of the sovereignty of the people To which it may be answered that if these be really practical principles they must rest on speculative grounds the sovereignty of the people for example must be a right foundation for government because a government thus constituted tends to produce certain beneficial effects Inasmuch however as no government produces all possible beneficial effects but all are attended with more or fewer inconveniences and since these can not usually be combated by means drawn from the very causes which produce them it would be often a much stronger recommendation of some practical arrangement that it does not follow from what is called the general principle of the government than that it does Under a government of legitimacy the presumption is far rather in favour of institutions of popular origin and in a democracy in favour of arrangements tending to check the impetus of popular will The line of augmentation so commonly mistaken in France for political philosophy tends to the practical conclusion that we should exert our utmost efforts to aggravate instead of alleviating whatever are the characteristic imperfections of the system of institutions which we prefer or under which we happen to live The grounds then of every rule of art are to be found in the theorems of science An art or a body of art consists of the rules together with as much of the speculative propositions as comprises the justification of those rules The complete art of any matter includes a selection of such a portion from the science as is necessary to show on what conditions the effects which the art aims at producing depend And Art in general consists of the truths of Science arranged in the most convenient order for practice instead of the order which is the most convenient for thought Science groups and arranges its truths so as to enable us to take in at one view as much as possible of the general order of the universe Art though it must assume the same general laws follows them only into such of their detailed consequences as have led to the formation of rules of conduct and brings together from parts of the field of science most remote from one another the truths relating to the production of the different and heterogeneous conditions necessary to each effect which the exigencies of practical life require to be produced Science therefore following one cause to its various effects while art traces one effect to its multiplied and diversified causes and conditions there is need of a set of intermediate scientific truths derived from the higher generalities of science and destined to serve as the generalia or first principles of the various arts The scientific operation of framing these intermediate principles M Comte characterizes as one of those results of philosophy which are reserved for futurity The only complete example which he points out as actually realized and which can be held up as a type to be imitated in more important matters is the general theory of the art of Descriptive Geometry as conceived by M Monge It is not however difficult to understand what the nature of these intermediate principles must generally be After framing the most comprehensive possible conception of the end to be aimed at that is of the effect to be produced and determining in the same comprehensive manner the set of conditions on which that effect depends there remains to be taken a general survey of the resources which can be commanded for realizing this set of conditions and when the result of this survey has been embodied in the fewest and most extensive propositions possible those propositions will express the general relation between the available means and the end and will constitute the general scientific theory of the art from which its practical methods will follow as corollaries But though the reasonings which connect the end or purpose of every art with its means belong to the domain of Science the definition of the end itself belongs exclusively to Art and forms its peculiar province Every art has one first principle or general major premise not borrowed from science that which enunciates the object aimed at and affirms it to be a desirable object The builder’s art assumes that it is desirable to have buildings architecture as one of the fine arts that it is desirable to have them beautiful or imposing The hygienic and medical arts assume the one that the preservation of health the other that the cure of disease are fitting and desirable ends These are not propositions of science Propositions of science assert a matter of fact an existence a coexistence a succession or a resemblance The propositions now spoken of do not assert that any thing is but enjoin or recommend that something should be They are a class by themselves A proposition of which the predicate is expressed by the words ought or should be is generically different from one which is expressed by is or will be It is true that in the largest sense of the words even these propositions assert something as a matter of fact The fact affirmed in them is that the conduct recommended excites in the speaker’s mind the feeling of approbation This however does not go to the bottom of the matter for the speaker’s approbation is no sufficient reason why other people should approve nor ought it to be a conclusive reason even with himself For the purposes of practice every one must be required to justify his approbation and for this there is need of general premises determining what are the proper objects of approbation and what the proper order of precedence among those objects These general premises together with the principal conclusions which may be deduced from them form or rather might form a body of doctrine which is properly the Art of Life in its three departments Morality Prudence or Policy and Aesthetics the Right the Expedient and the Beautiful or Noble in human conduct and works To this art which in the main is unfortunately still to be created all other arts are subordinate since its principles are those which must determine whether the special aim of any particular art is worthy and desirable and what is its place in the scale of desirable things Every art is thus a joint result of laws of nature disclosed by science and of the general principles of what has been called Teleology or the Doctrine of Ends which borrowing the language of the German metaphysicians may also be termed not improperly the principles of Practical Reason A scientific observer or reasoner merely as such is not an adviser for practice His part is only to show that certain consequences follow from certain causes and that to obtain certain ends certain means are the most effectual Whether the ends themselves are such as ought to be pursued and if so in what cases and to how great a length it is no part of his business as a cultivator of science to decide and science alone will never qualify him for the decision In purely physical science there is not much temptation to assume this ulterior office but those who treat of human nature and society invariably claim it they always undertake to say not merely what is but what ought to be To entitle them to do this a complete doctrine of Teleology is indispensable A scientific theory however perfect of the subjectmatter considered merely as part of the order of nature can in no degree serve as a substitute In this respect the various subordinate arts afford a misleading analogy In them there is seldom any visible necessity for justifying the end since in general its desirableness is denied by nobody and it is only when the question of precedence is to be decided between that end and some other that the general principles of Teleology have to be called in but a writer on Morals and Politics requires those principles at every step The most elaborate and welldigested exposition of the laws of succession and coexistence among mental or social phenomena and of their relation to one another as causes and effects will be of no avail toward the art of Life or of Society if the ends to be aimed at by that art are left to the vague suggestions of the intellectus sibi permissus or are taken for granted without analysis or questioning There is then a philosophia prima peculiar to Art as there is one which belongs to Science There are not only first principles of Knowledge but first principles of Conduct There must be some standard by which to determine the goodness or badness absolute and comparative of ends or objects of desire And whatever that standard is there can be but one for if there were several ultimate principles of conduct the same conduct might be approved by one of those principles and condemned by another and there would be needed some more general principle as umpire between them Accordingly writers on Moral Philosophy have mostly felt the necessity not only of referring all rules of conduct and all judgments of praise and blame to principles but of referring them to some one principle some rule or standard with which all other rules of conduct were required to be consistent and from which by ultimate consequence they could all be deduced Those who have dispensed with the assumption of such a universal standard have only been enabled to do so by supposing that a moral sense or instinct inherent in our constitution informs us both what principles of conduct we are bound to observe and also in what order these should be subordinated to one another The theory of the foundations of morality is a subject which it would be out of place in a work like this to discuss at large and which could not to any useful purpose be treated incidentally I shall content myself therefore with saying that the doctrine of intuitive moral principles even if true would provide only for that portion of the field of conduct which is properly called moral For the remainder of the practice of life some general principle or standard must still be sought and if that principle be rightly chosen it will be found I apprehend to serve quite as well for the ultimate principle of Morality as for that of Prudence Policy or Taste Without attempting in this place to justify my opinion or even to define the kind of justification which it admits of I merely declare my conviction that the general principle to which all rules of practice ought to conform and the test by which they should be tried is that of conduciveness to the happiness of mankind or rather of all sentient beings in other words that the promotion of happiness is the ultimate principle of Teleology I do not mean to assert that the promotion of happiness should be itself the end of all actions or even of all rules of action It is the justification and ought to be the controller of all ends but it is not itself the sole end There are many virtuous actions and even virtuous modes of action though the cases are I think less frequent than is often supposed by which happiness in the particular instance is sacrificed more pain being produced than pleasure But conduct of which this can be truly asserted admits of justification only because it can be shown that on the whole more happiness will exist in the world if feelings are cultivated which will make people in certain cases regardless of happiness I fully admit that this is true that the cultivation of an ideal nobleness of will and conduct should be to individual human beings an end to which the specific pursuit either of their own happiness or of that of others except so far as included in that idea should in any case of conflict give way But I hold that the very question what constitutes this elevation of character is itself to be decided by a reference to happiness as the standard The character itself should be to the individual a paramount end simply because the existence of this ideal nobleness of character or of a near approach to it in any abundance would go farther than all things else toward making human life happy both in the comparatively humble sense of pleasure and freedom from pain and in the higher meaning of rendering life not what it now is almost universally puerile and insignificant but such as human beings with highly developed faculties can care to have With these remarks we must close this summary view of the application of the general logic of scientific inquiry to the moral and social departments of science Notwithstanding the extreme generality of the principles of method which I have laid down a generality which I trust is not in this instance synonymous with vagueness I have indulged the hope that to some of those on whom the task will devolve of bringing those most important of all sciences into a more satisfactory state these observations may be useful both in removing erroneous and in clearing up the true conceptions of the means by which on subjects of so high a degree of complication truth can be attained Should this hope be realized what is probably destined to be the great intellectual achievement of the next two or three generations of European thinkers will have been in some degree forwarded THE END