16 A. E. TAYLOR : all, is itself a manifold of lesser parts (TrXetw evo? ecrn rd re rov evbs fj.opiov /cal ra rov 1/09 6ov pere^ovra, 158 B). And it follows at once that there can be no limit to this subdi- vision ; the " parts " of the whole manifold are numerically infinite. For (158 c) each subordinate part of the manifold being itself the combination of unity and multiplicity, if we take any the least part we please and make abstraction from its aspect of unity (cricorrovvrt, avrr)v Kad' avrrjv rr)v erepav fyvcriv rov etoovs, sc., the side of diversity), we shall find that it contains in itself an indefinite plurality (arreipov co-rat rrridei). Yet on the other hand each part is one part con- tributing its particular share to the life of the whole, and is thus wrought into definite systematic relations (irepas TJ&T) e^et) to the other parts and to the whole. So that the multi- plicity which considered in abstraction from the unity it derives from its relations to the whole, is without limit, re- ceivesfrom its position as one element in the single whole that character of definiteness and limitation which would otherwise be foreign to it. It is in fact at once infinite in one sense and in another finite. So the Manifold turns out to be that very systematic whole of subordinate systems with which we have already in hypothesis 2 identified the One. Each side, as Hegel might have said, is discovered to be itself and its complement in one : from whichever side of the anti- thesis you start you find in the end that it contains the whole. It is now, of course, a mere matter of the detailed following up of our main result to show that each and all of the affirmative and negative judgments which we have vindicated for the One can also be made about the Many. They are like and yet unlike themselves and one another. For in so far as each and all have the same quality, e.g., infinite divisibility, they are alike, and again in so far as they have antagonistic qualities they are unlike. And we may say in one word now, and without troubling ourselves to go over the ground once more in detail (159 B), that every result which we have proved for the One can by the same process be shown to be true of its complement. We may then, I think, sum up the argument of this hypothesis in one sentence, thus : As we rescued the real One from non- existence and unknowability by proving that it contains diversity, so by the aid of the same principle we have now saved the actual multiplicity of the world from the same fate by showing that it forms a unity. Our next task, which we shall attack in hypothesis 5, is to establish the same con- clusion negatively by showing that the severance of unity from diversity, which condemned the former to non-existence
