A Reconstruction of the Non–Identity Argument at Phaedo 74b–c

Abstract 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.