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[1091a] [1] 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.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.1

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 story2"; for men have recourse to the "long story," such as slaves tell, when they have nothing satisfactory to say.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 2.3

It is absurd also, or rather it is one of the impossibilities of this theory, to introduce generation of things which are eternal.There is no reason to doubt whether the Pythagoreans do or do not introduce it; for they clearly state that when the One had been constituted—whether out of planes or superficies or seed or out of something that they cannot explain—immediately the nearest part of the Infinite began to be drawn in and limited by the Limit.4 However, since they are here explaining the construction of the universe and meaning to speak in terms of physics, although we may somewhat criticize their physical theories, [20] it is only fair to exempt them from the present inquiry; for it is the first principles in unchangeable things that we are investigating, and therefore we have to consider the generation of this kind of numbers.

They5 say that there is no generation of odd numbers,6 which clearly implies that there is generation of even ones; and some hold that the even is constructed first out of unequals—the Great and Small—when they are equalized.7 Therefore the inequality must apply to them before they are equalized. If they had always been equalized they would not have been unequal before; for there is nothing prior to that which has always been.Hence evidently it is not for the sake of a logical theory that they introduce the generation of numbers

A difficulty, and a discredit to those who make light of the difficulty, arises out of the question how the elements and first principles are related to the the Good and the Beautiful. The difficulty is this: whether any of the elements is such as we mean when we8 speak of the Good or the Supreme Good, or whether on the contrary these are later in generation than the elements.It would seem that there is an agreement between the mythologists and some present-day thinkers,9 who deny that there is such an element, and say that it was only after some evolution in the natural order of things that both the Good and the Beautiful appeared. They do this to avoid a real difficulty which confronts those who hold, as some do, that unity is a first principle.

1 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.

2 The exact reference is uncertain, but Aristotle probably means Simonides of Ceos. Cf. Simonides Fr. 189 (Bergk).

3 Assuming that the Great-and-Small, or indeterminate dyad, is duplicative (Aristot. Met. 13.7.18).

4 Cf. Aristot. Physics 3.4, Aristot. Physics 4.6, and Burnet, E.G.P. sect. 53.

5 The Platonists.

6 This statement was probably symbolical. "They described the odd numbers as ungenerated because they likened them to the One, the principle of pure form" (Ross ad loc.).

7 Cf. Aristot. Met. 13.7.5.

8 Aristotle speaks as a Platonist. See Introduction.

9 The Pythagoreans and Speusippus; cf. Aristot. Met. 12.7.10.

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