have propounded the laws of motion have not complied with this law, since they have believed that a body can instantaneously receive a motion contrary to its preceding one. All of which supports the judgment that noticeable perceptions arise by degrees from 57 ones which are too minute to be noticed. To think otherwise is to be ignorant of the immeasurable fineness of things, which always and everywhere involves an actual infinity.
I have also pointed out that in consequence of imperceptible variations no two individual things could be perfectly alike, and that they must always differ more than numerically [e.g. 'On nature itselfÕ]. This puts an end to the blank tablets of the soul, a soul without thought, a substance without action, empty space, atoms, and even to portions of matter which are not actually divided, and also to absolute rest, completely uniform parts of time or place or matter, perfect spheres of the #second element which take their origin from perfect cubes, and hundreds of other fictions which have arisen from the incompleteness of philosophers' notions. They are something which the nature of things does not allow of. They escape challenge because of our ignorance and our neglect of the insensible; but nothing could make them acceptable, short of their being confined to abstractions of the mind, with a formal declaration that the mind is not denying what it sets aside as irrelevant to some present concern. On the other hand if we meant literally that things of which we are unaware exist neither in the soul nor in the body, then we would fail in philosophy as in politics, because we would be neglecting to mikron?imperceptible changes. Whereas abstraction is not an error as long as one knows that what one is pretending not to notice, is there. This is what mathematicians are doing when they ask us to consider perfect lines and uniform motions and other regular effects, although matter (i.e. the jumble of effects of the surrounding infinity) always provides some exception. This is done so as to separate one circumstance from another and, as far as we can, to trace effects back to their causes and to foresee some of their results; the more care we take not to overlook any circumstance that we can control, the more closely practice corresponds to theory. But only the supreme Reason, who overlooks nothing, can distinctly grasp the entire infinite and see all the causes and all the results. All we can do with infinities is to know them confusedly and at least to know distinctly that they are there. Otherwise we shall not only judge quite wrongly as to the beauty and grandeur of the universe