Kitap 14
12
For if it is composed of the Great and Small, it will be the same as the former, i.e. Ideal, number. But of what other Great and Small can it be composed? for Plato makes spatial magnitudes out of a Great and Small.This interpretation (Ross’s second alternative, reading τίνος for τινος) seems to be the most satisfactory. For the objection cf. Aristot. Met. 3.4.34. And if he speaks of some other component, he will be maintaining too many elements; while if some one thing is the first principle of each kind of number, unity will be something common to these several kinds.
13
We must inquire how it is that unity is these many things, when at the same time number, according to him, cannot be derived otherwise than from unity and an indeterminate dyad.The argument may be summarized thus. If mathematical number cannot be derived from the Great-and-Small or a species of the Great-and-Small, either it has a different material principle (which is not economical) or its formal principle is in some sense distinct from that of the Ideal numbers. But this implies that unity is a kind of plurality, and number or plurality can only be referred to the dyad or material principle.
13
All these views are irrational; they conflict both with one another and with sound logic, and it seems that in them we have a case of Simonides’ long storyThe exact reference is uncertain, but Aristotle probably means Simonides of Ceos. Cf. Simonides Fr. 189 (Bergk).; for men have recourse to the long story, such as slaves tell, when they have nothing satisfactory to say.
14
The very elements too, the Great and Small, seem to protest at being dragged in; for they cannot possibly generate numbers except rising powers of 2.Assuming that the Great-and-Small, or indeterminate dyad, is duplicative (Aristot. Met. 13.7.18).
14
It is absurd also, or rather it is one of the impossibilities of this theory, to introduce generation of things which are eternal.
