Kitap 13
5
And further, the greater part of our discussion must bear directly upon this second question—viz. when we are considering whether the substances and first principles of existing things are numbers and Ideas; for after we have dealt with the Ideas there remains this third question.
6
Now if the objects of mathematics exist, they must be either in sensible things, as some hold; or separate from them (there are some also who hold this view); or if they are neither the one nor the other, either they do not exist at all, or they exist in some other way. Thus the point which we shall have to discuss is concerned not with their existence, but with the mode of their existence.
1
That the objects of mathematics cannot be in sensible things, and that moreover the theory that they are is a fabrication, has been observed already in our discussion of difficultiesCf. Aristot. Met. 3.2.23-30. —the reasons being (a) that two solids cannot occupy the same space, and (b) that on this same theory all other potentialities and characteristics would exist in sensible things, and none of them would exist separately. This, then, has been already stated;
2
but in addition to this it is clearly impossible on this theory for any body to be divided. For it must be divided in a plane, and the plane in a line, and the line at a point; and therefore if the point is indivisible, so is the line, and so on.
3
For what difference does it make whether entities of this kind are sensible objects, or while not being the objects themselves, are yet present in them? the consequence will be the same, for either they must be divided when the sensible objects are divided, or else not even the sensible objects can be divided.
3
Nor again can entities of this kind exist separately.
