Metaphysics

(But nature does not seem to be episodic from what appears, like a bad tragedy.) But for those who posit Ideas, this difficulty is escaped—for they make magnitudes out of matter and number: lengths from the dyad, planes perhaps from the triad, solids from the tetrad, or from other numbers—for it makes no difference—but will these be Ideas, or what is their mode of existence, and what do they contribute to existing things? For they contribute nothing, just as mathematical objects do not. Moreover, no theorem even holds of them, unless one wants to change mathematical objects and make some private opinions. And it is not difficult to spin out and connect arguments, taking any hypotheses whatsoever. These people, then, by clinging to the Ideas in this way, miss the truth about mathematical objects; but those who first made two kinds of numbers, both the number of forms and mathematical number, have neither explained nor could explain how and from what mathematical number will exist. For they make it intermediate between the formal and the sensible. For if it is from the great and small, it will be the same as the number of Ideas (and he makes magnitudes from another kind of small and great); while if he mentions some other thing, he will be saying that the elements are more numerous; and if the principle of each is some one thing, the ‘one’ will be something common to these, and we must inquire how ‘the one’ is both these many things, and at the same time how it is possible for number to be generated otherwise than from ’one’ and the ‘indefinite dyad’, which is impossible according to him. All these things indeed are irrational, and conflict both with themselves and with reasonable views, and there seems to be in them the ‘long speech’ of Simonides; for a long speech is like that of slaves when they say nothing sound. And the elements themselves, the great and the small, seem to cry out as if they were being dragged; for they cannot by any means generate number except that which is doubled starting from one. — And it is absurd also to make a generation of things that are eternal, or rather it is one of the impossibilities. Therefore, as to whether the Pythagoreans do or do not make a generation, there is no need to doubt; for they clearly say that when the one had been constructed—whether out of planes or surface-color or seed or from things they are at a loss to state—immediately the nearest part of the infinite was drawn in and limited by the limit. But since they construct a world and wish to speak physically, it is right to examine them somewhat concerning nature, but to dismiss them from the present inquiry; for we are seeking the principles in things that are unchangeable, so that we must examine the generation of numbers of this kind.