[Footnote 22: However, in the verse of Xenophanes, the predecessor of Parmenides--[Greek: Ou(=los o(ra=|, ou(=los de\ noei=, ou(=los de/ t' a)kou/ei]--the Universe is described as a thinking, seeing, hearing God--[Greek: E(\n kai\ Pa=n]. Sextus Empir. adv. Mathemat. ix. 144; Xenophan. Fragm. p. 36, ed. Karsten.] [Side-note: The doctrine compared to that of Plato--changes in Plato.] Plato departs from Sokrates on the same point. He agrees with Eukleides in recognising a Transcendental Bonum. But it appears that his doctrines on this head underwent some change. He held for some time what is called the doctrine of Ideas: transcendental Forms, Entia, Essences: he considered the Transcendental to be essentially multiple, or to be an aggregate--whereas Eukleides had regarded it as essentially One. This is the doctrine which we find in some of the Platonic dialogues. In the Republic, the Idea of Good appears as one of these, though it is declared to be the foremost in rank and the most ascendant in efficacy.[23] But in the later part of his life, and in his lectures (as we learn from Aristotle), Plato came to adopt a different view. He resolved the Ideas into numbers. He regarded them as made up by the combination of two distinct factors:--1. The One--the Essentially One. 2. The Essentially Plural: The Indeterminate Dyad: the Great and Little.--Of these two elements he considered the Ideas to be compounded. And he identified the Idea of Good with the essentially One--[Greek: to\ a)gatho\n] with [Greek: to\ e(/n]: the principle of Good with the principle of Unity: also the principle of Evil with the Indeterminate. But though Unity and Good were thus identical, he considered Unity as logically antecedent, or the subject--Good as logically consequent, or the predicate.[24] [Footnote 23: Plato, Republic, vi. p. 508 E, vii. p. 517 A.] [Footnote 24: The account given by Aristotle of Plato's doctrine of Ideas, as held by Plato in his later years, appears in various passages of the Metaphysica, and in the curious account repeated by Aristoxenus (who had often heard it from Aristotle--[Greek: A)ristote/lês a)ei\ diêgei=to]) of the [Greek: a)kro/asis] or lecture delivered by Plato, De Bono. See Aristoxen. Harmon. ii. p. 30, Meibom. Compare the eighth chapter in this work,--Platonic Compositions Generally. Metaphys. N. 1091, b. 13.[Greek: tô=n de\ ta\s a)kinê/tous ou)si/as ei)=nai lego/ntôn] (sc. Platonici) [Greek: oi( me/n phasin au)to\ to\ e(\n to\ a)gatho\n au)to\ ei)=nai; ou)si/an me/ntoi to\ e(\n au)tou= ô)/|onto ei)=nai ma/lista], which words are very clearly explained by Bonitz in the note to his Commentary, p. 586: also Metaphys. 987, b. 20, and Scholia, p. 551, b. 20, p. 567, b. 34, where the work of Aristotle, [Greek: Peri\ Ta\gathou=], is referred to: probably the memoranda taken down by Aristotle from Plato's lecture on that subject, accompanied by notes of his own.