METAPHYSICS regard them as valid? Either way, what is the relevance of the second part to the assault on the Ideas in the Wrst part?1 Before outlining the main problems for the Theory of Ideas that are put forward in the Wrst part, it is worth repeating at this point the six principles that we identiWed in Chapter as constituting the core of the classical Theory (1) The Principle of Commonality Wherever several things are F, this is because they participate in or imitate a single Idea of F (Rep 476a) (2) The Principle of Separation The Idea of F is distinct from all the things that are F (Phd 74c) (3) The Principle of Self-Predication The Idea of F is itself F (4) The Principle of Purity The Idea of F is nothing but F (Phd 74c) (5) The Principle of Uniqueness Nothing but the Idea of F is really, truly, altogether F (Phd 74d; Rep 479a–d) (6) The Principle of Sublimity Ideas are everlasting, they have no parts and undergo no change, and they are not perceptible to the senses (Phd 78d) The problems set out in the Wrst part of the dialogue are as follows According to the theory, particular Fs are F because they participate in the Idea of F But what does ‘participation’ mean? Does a particular F share only a part of the Idea, or does it contain the whole of the Idea? There are diYculties either way If a particular large thing L has the whole Idea of Large, then the Idea seems to be scattered and lack the unity of an Idea; but if L shares only a part of the Large, then it is large by something which is itself small, because being only a part it must be smaller than the Large (131a V.) It is essential to the theory that wherever several things are F they derive this from some other entity which is the Idea of F Thus, the several large things derive their largeness from the Idea of Large But if we put together the original set of large things plus the Idea, we have a new set of large things, which must derive their largeness from some other entity ‘So another form of largeness will appear, alongside the Idea of Large and the things that participated in it, and then another again over all of these’—so that we are set oV on an inWnite regress (132b) This line of thought much In what follows I am indebted to Constance C Meinwald’s Plato’s Parmenides (New York: Oxford University Press, 1991), though I diVer from her on important points of interpretation 208