Kitap 14
18
In the case of particular substances, however, it is explicable how the particular thing can be many, if we do not regard a thing both as a particular substance and as a certain characteristic.This, according to Aristotle, is how the Platonists regard the Ideas. See Introduction. The real difficulty which arises from these considerations is how substances are actually many and not one.
18
Again, even if a particular thing and a quantity are not the same, it is not explained how and why existing things are many, but only how quantities are many;
19
for all number denotes quantity, and the unit, if it does not mean a measure, means that which is quantitatively indivisible. If, then, quantity and substance are different, it is not explained whence or how substance is many; but if they are the same, he who holds this has to face many logical contradictions.
19
One might fasten also upon the question with respect to numbers, whence we should derive the belief that they exist.
20
For onePlato and his orthodox followers. who posits Ideas, numbers supply a kind of cause for existing things; that is if each of the numbers is a kind of Idea, and the Idea is, in some way or other, the cause of existence for other things; for let us grant them this assumption.
21
But as for himSpeusippus. who does not hold this belief, because he can see the difficulties inherent in the Ideal theory (and so has not this reason for positing numbers), and yet posits mathematical number, what grounds have we for believing his statement that there is a number of this kind, and what good is this number to other things? He who maintains its existence does not claim that it is the cause of anything, but regards it as an independent entity; nor can we observe it to be the cause of anything; for the theorems of the arithmeticians will all apply equally well to sensible things, as we have said.Aristot. Met. 13.3.1.
