exist necessarily, and that there may come a time when this beautiful star no longer exists, at least in its present form, nor its whole system. From this it appears that necessary truths, such as we find in pure mathematics and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances nor, consequently, on the testimony of the senses, even though without the senses it would never occur to us to think of them. This distinction must be thoroughly observed, and Euclid understood that so well that he demonstrates by reason things that experience and sense-images make very evident. Logic also abounds in such truths, and so do metaphysics and ethics, together with their respective products, natural theology and natural jurisprudence; and so the proof of them can only come from inner principles, which are described as innate. It would indeed be wrong to think that we can easily read these eternal laws of reason in the soul, as the Praetor's edict can be read on his notice-board, without effort or inquiry; but it is enough that they can be discovered within us by dint of attention: the senses give the occasion, and the results of experiments also serve to corroborate reason, somewhat as checks in arithmetic help us to avoid errors of calculation in long chains of reasoning. It is in this same respect that manÕs knowledge differs from that of beasts: beasts are sheer empirics and are guided entirely by instances. While men are capable of demonstrative knowledge [science], beasts, so far as one can judge, never manage to form necessary propositions, since the faculty by which they make thought sequences is something lower than the reason that occurs in men. Beasts9 thought sequences are just like those of simple empirics who maintain that what has happened once will happen again in a case which is similar in the respects that they are impressed by, although that does not enable them to judge whether the same reasons are at work. That is what makes it so easy for men to ensnare beasts, and so easy for simple empirics to make mistakes. Even people made cunning by age and experience are not proof against this when they trust too much to their past experience; as has happened to various people engaged in civil or military affairs, through their not taking sufficiently to heart that the world changes and that men become cleverer and find hundreds of new tricks Ñ whereas the deer and hares of our time are not becoming craftier than those of long ago. The thought sequences of beasts are only a shadow of reasoning, that is, they are nothing but a connection in the