In this paper i offer a detailed analysis of the dilemma of participation (parmenides, 130e-131e), in which plato considers the consequences of participation in the whole, and in a part of, a form. This analysis explains, in contrast to existing interpretations of the argument, plato's claim that participation in parts of a form is incompatible with the uniqueness of the form, and his modal claim that becoming equal by possessing part of the equal is absurd. In the second part of (...) the paper, i give the premisses and logical steps of the third man argument in the parmenides, and show the premisses to be committed to absurdity, even without the assumption that there is a unique form per character f. (shrink)

At Phaedo 74b–c an important argument is given for the non–identity of perceptible equals and equality. The argument is usually understood as an application of Leibniz’s Law in which the predicate appears unequal is affirmed of perceptible equals but not equality. But this reading requires explaining why the plural locution the equals themselves is initially used for equality, and why the additional predicate appears as inequality is denied of it. In this paper, an account of the equality premise is given (...) which allows for an initial grasp of equality as a plurality (suitably expressed by a plural locution), and introduces a generic predicate for appearance, appears its opposite (rightly denied of equality). The former ensures that the question of non–identity is not begged, while the latter secures a role for every element in the premise. So understood, the argument is both more robust and carefully formulated than is usually thought. (shrink)