Kitap 14
5
But those who treat number as separable assume that it exists and is separable because the axioms will not apply to sensible objects; whereas the statements of mathematics are true and appeal to the soul.The statements of mathematics appeal so strongly to our intelligence that they must be true; therefore if they are not true of sensible things, there must be some class of objects of which they are true. The same applies to mathematical extended magnitudes.
6
It is clear, then, both that the contrary theoryThe Pythagorean theory, which maintains that numbers not only are present in sensible things but actually compose them, is in itself an argument against the Speusippean view, which in separating numbers from sensible things has to face the question why sensible things exhibit numerical attributes. can make out a case for the contrary view, and that those who hold this theory must find a solution for the difficulty which was recently raisedsect. 3.—why it is that while numbers are in no way present in sensible things, their attributes are present in sensible things.
6
There are someProbably Pythagoreans. Cf. Aristot. Met. 7.2.2, Aristot. Met. 3.5.3. who think that, because the point is the limit and extreme of the line, and the line of the plane, and the plane of the solid, there must be entities of this kind.
7
We must, then, examine this argument also, and see whether it is not exceptionally weak. For (1.) extremes are not substances; rather all such things are merely limits. Even walking, and motion in general, has some limit; so on the view which we are criticizing this will be an individual thing, and a kind of substance. But this is absurd. And moreover (2.) even if they are substances, they will all be substances of particular sensible things, since it was to these that the argument applied. Why, then, should they be separable?
