Abstract
This paper examines the second regress argument of the Parmenides (132c12–133a7), and focusses on the question: why is the argument effective? There is widespread disagreement about how this question should be answered. Broadly speaking, recent commentators have given three explanations: (i) the regress contradicts the uniqueness of Forms. That is, each Form is unique, and an infinite regress contradicts this uniqueness. (ii) The regress demonstrates that Forms cannot account for why particulars have the characters they do, since the regress prevents the account from ever being complete. (iii) The regress contradicts the unity of the Form, and since each member of the infinite series participates in an infinite number of Forms, each Form has an infinite number of parts. I examine these positions in some detail. While each has its virtues, it is impossible to adjudicate between them without a theoretical framework dedicated to infinite regress arguments. I find a reasonable theoretical framework for infinite regress arguments in a little-known work of T. Roy, “What’s So Bad about Infinite Regress?”. After articulating Roy’s framework, and extending it to make it useful for an analysis of the second regress argument of the Parmenides, I propose three different readings of the regress: Reading A, which supposes that resemblance between particular and Form trigger an infinite number of resemblance relations; Reading B, which supposes that that the regress is ultimately vicious because it fails to account for the F-ness of a given particular, even when that particular participates in an infinite number of Forms; and Reading C, which supposes that there is an inconsistency between the unity of the Form and many particulars participating in the Form. While none of these readings is absolutely definitive, and Reading B has some significant textual challenges, I argue that Reading B must be the way we are meant to understand Plato’s argument. I then argue that Reading B is the best account of why the second regress is effective.
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