Book 13
27
We assume that in general 1 and 1, whether the things are equal or unequal, make 2; e.g. good and bad, or man and horse; but the supporters of this theory say that not even two units make 2.
27
If the number of the Ideal 3 is not greater than that of the Ideal 2, it is strange; and if it is greater, then clearly there is a number in it equal to the 2, so that this number is not different from the Ideal 2.
28
But this is impossible, if there is a first and second number.i.e., if numbers are specifically different. Cf. Aristot. Met. 13.6.1. Nor will the Ideas be numbers. For on this particular point they are right who claim that the units must be different if there are to be Ideas, as has been already stated.sect. 2-4 above. For the form is unique; but if the units are undifferentiated, the 2’s and 3’s will be undifferentiated.
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.
