Book 13
9
The Pythagorean view in one way contains fewer difficulties than the view described above, but in another way it contains further difficulties peculiar to itself. By not regarding number as separable, it disposes of many of the impossibilities; but that bodies should be composed of numbers, and that these numbers should be mathematical, is impossible.See Introduction.
10
For (a) it is not true to speak of indivisible magnitudesThis is proved in Aristot. De Gen. et. Corr. 315b 24-317a 17.; (b) assuming that this view is perfectly true, still units at any rate have no magnitude; and how can a magnitude be composed of indivisible parts? Moreover arithmetical number consists of abstract units. But the Pythagoreans identify number with existing things; at least they apply mathematical propositions to bodies as though they consisted of those numbers.See Introduction.
11
Thus if number, if it is a self-subsistent reality, must be regarded in one of the ways described above, and if it cannot be regarded in any of these ways, clearly number has no such nature as is invented for it by those who treat it as separable.
12
Again, does each unit come from the Great and the Small, when they are equalizedCf. Aristot. Met. 13.7.5 n. Aristotle is obviously referring to the two units in the Ideal 2.; or does one come from the Small and another from the Great? If the latter, each thing is not composed of all the elements, nor are the units undifferentiated; for one contains the Great, and the other the Small, which is by nature contrary to the Great.
