The doctrine of ideas appears in the Parmenides as the positive consequence and progressive development of the Eleatic principle. Indeed in this dialogue, in that Plato makes Parmenides the chief speaker, he seems willing to allow that his doctrine is in substance that of the Eleatic sage. True, the fundamental thought of the dialogue—that the one is not conceivable in its complete singleness without the many, nor the many without the one, that each necessarily presupposes and reciprocally conditions the other—stands in the most direct contradiction to Eleaticism. Yet Parmenides himself, by dividing his poem into two parts, and treating in the first of the one and in the second of the many, postulates an inner mediation between these two externally so disjointed parts of his philosophy, and in this respect the Platonic theory of ideas might give itself out as the farther elimination, and the true sense of the Parmenidean philosophizing. This dialectical mediation between the one and the not-one or the many Plato now attempts in four antinomies, which have ostensibly only a negative result in so far as they show that contradictions arise both whether the one be adopted or rejected. The positive sense of these antinomies, though it can be gained only through inferences which Plato himself does not expressly utter, but leaves to be drawn by the reader—is as follows. The first antinomy shows that the one is inconceivable as such since it is only apprehended in its abstract opposition to the many; the second, that in this case also the reality of the many is inconceivable; the third, that the one or the idea cannot be conceived as not-being, since there can be neither conception nor predicate of the absolute not-being, and since, if not-being is excluded from all fellowship with being, all becoming and departing, all similarity and difference, every representation and explanation concerning it must also be denied; and lastly, the fourth affirms that the not-one or the many cannot be conceived without the one or the idea. What now is Plato’s aim in this discussion of the dialectic relations between the conceptions of the one and the many? Would he use the conception of the one only as an example to explain his dialectic method with conceptions, or is the discussion of this conception itself the very object before him? Manifestly the latter, or the dialogue ends without result and without any inner connection of its two parts. But how came Plato to make such a special investigation of this conception of the one? If we bear in mind that the Eleatics had already perceived the antithesis of the actual and the phenomenal world in the antithesis of the one and the many, and that Plato himself had also regarded his ideas as the unity of the manifold, as the one and the same in the many—since he repeatedly uses “idea” and “the one” in the same sense, and places (_Rep._ VII. 537) dialectics in the same rank with the