Kitap 13
17
For if attributes, such as moving or white, do not exist apart from their substances, white will be prior in formula to white man, but not in substantiality; for it cannot exist in separation, but always exists conjointly with the concrete whole—by which I mean white man.
18
Thus it is obvious that neither is the result of abstraction prior, nor the result of adding a determinant posterior—for the expression white man is the result of adding a determinant to white.
18
Thus we have sufficiently shown (a) that the objects of mathematics are not more substantial than corporeal objects; (b) that they are not prior in point of existence to sensible things, but only in formula; and (c) that they cannot in any way exist in separation.
19
And since we have seensect. 1-3 above. that they cannot exist in sensible things, it is clear that either they do not exist at all, or they exist only in a certain way, and therefore not absolutely; for exist has several senses.
1
The general propositions in mathematics are not concerned with objects which exist separately apart from magnitudes and numbers; they are concerned with magnitudes and numbers, but not with them as possessing magnitude or being divisible. It is clearly possible that in the same way propositions and logical proofs may apply to sensible magnitudes; not qua sensible, but qua having certain characteristics.
