The Likeness Regress: Plato's Parmenides 132cl2-133a7

Abstract

Since Forms and particulars are separate, Plato is left with the task of describing the way in which they are related. One possible way of construing this relation is to suppose that particulars resemble Forms. Socrates proposes this and is refuted by Parmenides in the so-called Likeness Regress (Parmenzdes 132c12-133a7). This work comprises both an exposition and an analysis of the Likeness Regress. In the exposition, I work out the argument-form of the Likeness Regress in second-order logic (and later, show that first-order logic is sufficient). This symbolisation provides a baseline for the balance of the exposition, which has two focuses: first, I define what it means for particulars to resemble Forms, with the help of D. M. Armstrong's account of resemblance in A Theory of Unwersals; second, I demonstrate that the infinite regress argument of the Likeness Regress is indeed vicious, with the help of T. Roy's theory of regress arguments. In the analysis, I proceed with the premiss that an asymmetrical account of the resemblance relation would allow Socrates to escape Parmenides' refutation. I examine various accounts of asymmetrical resemblance (including those accounts put forward by R. E. Allen, P. T. Geach and G. Vlastos), but reject these in favour of my own account. My account of asymmetrical resemblance is based on understanding the resemblance relation as a function that is not self-inverse. Finally, I argue that the Likeness Regress need not be considered definitive, since we find in the ontology of the Timaeus a conception of resemblance that fits my account of asymmetrical resemblance.