Metaphysics

​It is possible for anything to be or to become like something else without being modeled after it, so that whether Socrates exists or does not exist, a man like Socrates might arise; and it is clear that the same would hold even if Socrates were eternal. And there will be several patterns of the same thing, and therefore several Forms; for example, of ‘man’, ‘animal’ and ‘two-footed’, and at the same time ‘man-himself’. Further, the Forms will be patterns not only of sensible things but of themselves also—for example, the genus, as genus of forms; so that the same thing will be both pattern and image. Further, it would seem impossible for the substance and that of which it is the substance to exist apart; how then, if the Ideas are the substances of things, could they exist apart? But in the Phaedo it is said in this way, that the Forms are causes both of being and of becoming. And yet, though the Forms exist, the things that participate in them do not come into being unless there is something to impart motion; and many other things come into being, such as a house and a ring, of which we say there are no Forms. So that it is clear that other things also can both be and become through such causes as those of the things just mentioned. — Further, if the Forms are numbers, how will they be causes? Is it because existing things are other numbers, e.g. this number is man, this Socrates, and this Callias? Why then are those causes of these? For even if the former are eternal and the latter are not, it will make no difference. But if it is because things here are ratios of numbers (e.g. harmony), it is clear that there is some one thing of which they are ratios. If then this is something, namely matter, it is manifest that the numbers themselves will also be certain ratios of one thing to another. I mean, for instance, if Callias is a ratio in numbers of fire, earth, water, and air, his Idea also will be a number of certain other underlying things; and ‘man-himself’, whether it is a certain number or not, will still be a ratio in numbers of certain things and not a number, nor will it be a number because of this. Further, one number is formed from many numbers, but how can one Form be formed from Forms? And if it is not from them but from the units in the number (for instance, in the ten thousand), how are the units circumstanced? For if they are of the same kind, many absurdities will follow, and if they are not of the same kind, neither will those in the same number be like one another, nor will all the others be like all. For in what will they differ, being without properties? For these views are neither reasonable nor consistent with thought. Further, it is necessary to construct another kind of number, about which arithmetic is concerned, and all the things called ‘intermediates’ by some; and how or from what principles do these exist? Or why will they be intermediate between the things here and those? Further, each of the units in the dyad must come from some prior dyad; and yet this is impossible. Further, why is a number, taken collectively, one? And besides what has been said, if the units are different, they ought to speak in the same way as those who say the elements are four or two; for each of these speaks not of a common element, e.g. body, but of fire and earth, whether there is a common element, body, or not. But as it is, they speak of ‘the one’ as if it were homogeneous, like fire or water; but if this is so, numbers will not be substances. And it is clear that if there is a ‘one-itself’ and this is a principle, ‘the one’ is said in many ways; for otherwise it is impossible. — And wishing to reduce substances to their principles, we posit lengths as coming from ‘the short and long’, from a certain ‘small and great’, and plane from ‘the wide and narrow’, and body from ‘the deep and shallow’. Yet how will the plane contain a line, or the solid a line and a plane? For the wide and narrow, and the deep and shallow, are another genus. Therefore, just as number is not present in them, because the ‘many and few’ is different from these, it is clear that none of the other higher things will be present in the lower.