METAPHYSICS impressed Aristotle, who, substituting ‘man’ instead of ‘large’ for F in the original premiss, named it the Third Man argument, after the Man who would appear as a Super-idea, after (a) the men in the world and (b) the Ideal Man There is a special diYculty with relational predicates Suppose I am a slave According to the theory, that must be because I resemble the Ideal Slave But who is the Ideal Slave’s owner? Surely, the Ideal Owner But I am not a slave of the Ideal Owner but of whoever is my terrestrial slave-owner So the relationships between entities in the world cannot be explained by relationships between the Ideas (133e) These diYculties are genuine problems for the Theory of Ideas, and surely Plato means us to realize this At the very least they demand substantial modiWcation of the theory, and in other dialogues Plato undertakes such modiWcation In the Parmenides, however, he does not explicitly present the necessary modiWcations We might expect, though, that the second part of the dialogue oVers some guidance over the lines the modiWcation needs to take A major problem with the second part is that it is not clear exactly what is the pair of hypotheses from which Parmenides starts his argument (137b) He describes the hypotheses as hypotheses about the One itself, but the Greek in which they are stated can be rendered in several ways The two following pairs are the most promising translations: (1) If the One is (2) If it is one v v If the One is not If it is not one (2) is the reading that best Wts the Greek of the received text of this passage of the dialogue, where no deWnite article occurs before the word ‘one’ (hen) Indeed, even the most enthusiastic partisans of the Wrst reading agree that it can only be sustained if one amends the text at this point On the other hand, (1) seems to be a better Wt not only to the immediately preceding wording, but to the whole series of subsequent arguments, which quite frequently unambiguously refer to the One, with a deWnite article Moreover, anyone who accepts reading (2) has to answer the question what the ‘it’ stands for On my view, there is no need to amend the text The second reading, which is the most natural translation, can easily be reconciled with the subsequent argument There are two ways to this 209