8 A. E. TAYLOE: was current in the Academy in Aristotle's time, supposed to be an Idea, come into existence at all ? If you say, No, and fall back, as Plato himself usually does, on the thought that the Idea is a formal, or as the Neo-Platonists said, a para- deigmatic cause, but the agency of Soul the efficient cause of all changes, the question at once arises, how your two ultimate principles, Ideas and Soul, are to be co-ordinated. (A problem, be it observed, which is simply ignored when it is coolly taken for granted without inquiry that the " Demi- urge " of the TimcBus is "purely allegorical".) I may perhaps be allowed in passing to observe as an act of justice to an often unintelligently decried school of thinkers that it is precisely the absence of a clear answer to this all- important question in Plato's own thought which led to the so-called " trinity" of Plotinus and the still more elaborate triadic constructions of Proclus. Whatever else we may think of these doctrines they manifestly represent a legiti- mate attempt to bring Plato's two principles, "the Good," or supreme Idea, and the Soul, into some intelligible relation with one another, and the Neo-Platonists may therefore, as to the central doctrine of their system, fairly claim to be true continuers of the Master's work. To return for a moment to the Platonic theory as out- lined in the Phcedo. It should be apparent that the dialogue suggests the ancient problem of the One and the Many in what at first might seem two distinct forms. We may ask (1) how the one Idea can be equally present to an indefinite multiplicity of things without losing its unity, and (2) whether the problem of the One and the Many will not break out again within the Idea's own nature. It is the great achieve- ment of the first part of the Parmenides that it shows these two questions to be really one, and indicates that the true way to deal with (1) is by finding the answer to (2). That answer itself might be discovered, as I think I myself among others have previously shown, in the "hypotheses" of our dialogue, but is still more directly contained in the Philebus and TimcBus. We may now attack the portion of the Parmenides with which my paper announced its intention of dealing. And in doing so we shall be greatly assisted by turning at the various stages of the argument to those mathematical illus- trations which are never far from Plato's thought and never long absent from his language. What obscurity there is in the reasoning of Parmenides is in the main, I think, due to our reluctance to "clothe his principles in facts" by con-
