10 A. E. TAYLOE I problem just raised, how to conceive of the Idea without making it a constituent part of the thing to which it is present, that the whole of 'the following argumentation turns. The polemic of Parmenides in the dialogue aims in fact at one simple result, viz., the proof that the Idea must not be conceived as a constituent part of the sensible thing of the same common name. This has been in my judgment so conclusively shown by M. Milhaud in his already quoted work (bk. ii., ch. v.), that I should have thought it super- fluous to publish the present paper, were it not that his admirable remarks on the text of our particular dialogue seemed capable of being reinforced by a more detailed ex- amination of the actual words of the text than was suitable for a work dealing with the Platonic philosophy in its whole extent. On the speech with which Socrates follows up his reca- pitulation of the argument of Zeno it is not necessary to dwell at length. Two points in it we may just take note of in passing. One is that the passage 129 d-e aims at in- dicating that the problem of Idea and thing is only a corollary of the more fundamental problem of the double character of the Idea itself, as at once One and Many, or, to use another Platonic name for it, the problem of the intercommunion of the Ideas. Hence the inclusion of rest and motion among the " separate and self-existing forms " of this passage ought of itself to warn us against any interpretation of Plato which sets up a difference between the Ideas canvassed in the first part of the Parmenides and the categories of the Sophistes. The other is that with this speech of Socrates the geometrical problem in Plato's mind takes on a slightly different form. The question, What is the relation between the circle as defined by its equation and the various circles obtained by giving a series of numerical values to the coefficients ? to avail ourselves once more of the convenient modern way of putting a perennial problem, passes into the root-question, What is the meaning of speaking of the circle or other curve as a locus, or as constituted by an equation ? (This seems to me one of the simplest illustrations I can devise of Plato's meaning when he says we have to ask how the Idea itself can be both one and many, and I recommend the study of it to any one who is tempted to think that showing an Idea to be at once one and many amounts to proving it "a non- sensical conception ".) The argumentation of Parmenides himself begins at page 131 a with a dilemma. It is assumed that, if the Idea is inherent in the thing, it must be present to it either as a
