Book 13
3
for how can we regard the Idea of Man or Animal, or any other Form, as a number? There is one Idea of each kind of thing: e.g. one of Humanity and another one of Animality; but the numbers which are similar and do not differ in kind are infinitely many, so that this is no more the Idea of Man than any other 3 is. But if the Ideas are not numbers, they cannot exist at all;
4
for from what principles can the Ideas be derived? Number is derived from Unity and the indeterminate dyad, and the principles and elements are said to be the principles and elements of number, and the Ideas cannot be placed either as prior or as posterior to numbers.Since the only principles which Plato recognizes are Unity and the Dyad, which are numerical (Aristotle insists on regarding them as a kind of 1 and 2), and therefore clearly principles of number; and the Ideas can only be derived from these principles if they (the Ideas) are (a) numbers (which has been proved impossible) or (b) prior or posterior to numbers (i.e., causes or effects of numbers, which they cannot be if they are composed of a different kind of units); then the Ideas are not derived from any principle at all, and therefore do not exist.
