Aristotle, Metaphysics

[1089a] [1] the chief being that they visualized the problem in an archaic form. They supposed that all existing things would be one, absolute Being, unless they encountered and refuted Parmenides' dictum:

It will ne'er be proved that things which are not, are,¹

i.e., that they must show that that which is not, is; for only so—of that which is, and of something else—could existing things be composed, if they are more than one.²

However, (i) in the first place, if "being" has several meanings (for sometimes it means substance, sometimes quality, sometimes quantity, and so on with the other categories), what sort of unity will all the things that are constitute, if not-being is not to be? Will it be the substances that are one, or the affections (and similarly with the other categories), or all the categories together? in which case the "this" and the "such" and the "so great," and all the other categories which denote some sense of Being, will be one.But it is absurd, or rather impossible, that the introduction of one thing should account for the fact that "what is" sometimes means "so-and-so," sometimes "such-and-such," sometimes "of such-and-such a size," sometimes "in such-and-such a place."

(2) Of what sort of not-being and Being do real things consist? Not-being, too, has several senses, inasmuch as Being has; and "not-man" means "not so-and-so," whereas "not straight" means "not such-and-such," and "not five feet long" means "not of such-and-such a size." What sort of Being and not-being, then, make existing things a plurality? [20] This thinker means by the not-being which together with Being makes existing things a plurality, falsity and everything of this nature³; and for this reason also it was said⁴ that we must assume something which is false, just as geometricians assume that a line is a foot long when it is not.But this cannot be so; for (a) the geometricians do not assume anything that is false (since the proposition is not part of the logical inference⁵), and (b) existing things are not generated from or resolved into not-being in this sense. But not only has "not-being" in its various cases as many meanings as there are categories, but moreover the false and the potential are called "not-being"; and it is from the latter that generation takes place—man comes to be from that which is not man but is potentially man, and white from that which is not white but is potentially white; no matter whether one thing is generated or many.

Clearly the point at issue is how "being" in the sense of the substances is many; for the things that are generated are numbers and lines and bodies. It is absurd to inquire how Being as substance is many, and not how qualities or quantities are many.Surely the indeterminate dyad or the Great and Small is no reason why there should be two whites or many colors or flavors or shapes;