Kitap 14
1
Those, then, who posit the Ideas and identify them with numbers, by their assumption (in accordance with their method of abstracting each general term from its several concrete examples) that every general term is a unity, make some attempt to explain why number exists.I have followed Ross’s text and interpretation of this sentence. For the meaning cf. Aristot. Met. 14.2.20. Since, however, their arguments are neither necessarily true nor indeed possible, there is no justification on this ground for maintaining the existence of number.
2
The Pythagoreans, on the other hand, observing that many attributes of numbers apply to sensible bodies, assumed that real things are numbers; not that numbers exist separately, but that real things are composed of numbers.See Introduction. But why? Because the attributes of numbers are to be found in a musical scale, in the heavens, and in many other connections.Cf. Aristot. Met. 14.6.5.
3
As for those who hold that mathematical number alone exists,Cf. Aristot. Met. 14.2.21. they cannot allege anything of this kindi.e., that things are composed of numbers. consistently with their hypotheses; what they did say was that the sciences could not have sensible things as their objects. But we maintain that they can; as we have said before. And clearly the objects of mathematics do not exist in separation; for if they did their attributes would not be present in corporeal things.
4
Thus in this respect the Pythagoreans are immune from criticism; but in so far as they construct natural bodies, which have lightness and weight, out of numbers which have no weight or lightness, they appear to be treating of another universe and other bodies, not of sensible ones.See Introduction.
