PYTHAGORAS TO PLATO (2) The Principle of Separation The Idea of F is distinct from all the things that are F (Phd 74c; Smp 211b) (3) The Principle of Self-Predication The Idea of F is itself F (Hp Ma 292e; Prt 230c–e; Prm 132a–b) (4) The Principle of Purity The Idea of F is nothing but F (Phd 74c; Smp 211e) (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; Smp 211b) The Principle of Commonality is not, by itself, uniquely Platonic Many people who are unhappy with talk of ‘participation’ are content to speak of attributes as being ‘in common’ among many things which have them They may say, for instance, ‘If A, B, and C are all red, then this is because they have the property of being red in common, and we learn the meaning of ‘red’ by seeing what is common among the red things.’ What is peculiar to Plato is that he seriously follows up what is implied if one uses the metaphor of ‘having in common’.26 For instance, there must be only a single Idea of F, otherwise we could not explain why the F things have something in common (Rep 597b–c) The Principle of Separation is linked with the notion of a hierarchy between Ideas and the individuals that exemplify them To participate and to be participated in are two quite diVerent relationships, and the two terms of these relationships must be on a diVerent level The Principle of Self-Predication is important for Plato, because without it he could not show how the Ideas explain the occurrence of properties in individuals Only what is hot will make something hot; and it is no good drying yourself with a wet towel So, in general, only what is itself F can explain how something else is F So if the Idea of Cold is to explain why snow is cold, it must itself be cold (Phd 103b–e) The Idea of F is not only F, it is a perfect specimen of an F It cannot be diluted or adulterated by any element other than Fness: hence the Principle of Purity If it were to possess any property other than being F, it would have to so by participating in some other Idea, which would 26 I owe this point to G E M Anscombe, Three Philosophers (Oxford: Blackwell, 1961), 28 52