Kitap 13
29
Hence they have to say that when we count like this, l, 2, we do not add to the already existing number; for if we do, (a) number will not be generated from the indeterminate dyad, and (b) a number cannot be an Idea; because one Idea will pre-exist in another, and all the Forms will be parts of one Form.i.e., the biggest number.
30
Thus in relation to their hypothesis they are right, but absolutely they are wrong, for their view is very destructive, inasmuch as they will say that this point presents a difficulty: whether, when we count and say 1, 2, 3, we count by addition or by enumerating distinct portions.This is Apelt’s interpretation of κατὰ μερίδας. For this sense of the word he quotes Plut. Mor. 644c. The meaning then is: If you count by addition, you regard number as exhibited only in concrete instances; if you treat each number as a distinct portion (i.e. generated separately), you admit another kind of number besides the mathematical. Aristotle says that number can be regarded in both ways. But we do both; and therefore it is ridiculous to refer this point to so great a difference in essence.
1
First of all it would be well to define the differentia of a number; and of a unit, if it has a differentia. Now units must differ either in quantity or in quality; and clearly neither of these alternatives can be true. But units may differ, as number does, in quantity. But if units also differed in quantity, number would differ from number, although equal in number of units.
