The Dilemma of Participation A Commentary on Plato's Parmenides 131A9-E3

Abstract

In separating the Form from its particulars, Plato is left with the task of describing the way in which they are related to one another. One possible way of construing this relation is to suppose that particulars receive a share ofthe Form. The discussion between Parmenides and Socrates, in the Parmenides 131 a9-e3, interprets this sharing in a material sense: either the whole of the Form is received by each particular, or part of the Form is received by each particular. This disjunction turns out to be a destructive dilemma -the socalled Dilemma of Participation. The three main sections ofthis work study in detail the Dilemma of Participation, as it is presented in the Parmenides. The first section considers the disjunct that the whole of the Form is received by each particular (13 la9-b2). By using a system of classical extensional mereology, it is demonstrated that Parmenides' reductio ad absurdum of this disjunct is deductively valid. The second section deals with Socrates' objection to this argument (which he makes in the guise of the Day Analogy), and Parmenides' response to the objection (which he makes in the guise ofthe Sail Analogy) (131 b3-c4). The validity of Parmenides' response depends on the sense of"day" Socrates intends in the Day Analogy. It is argued (against S. Panagiotou) that there is a sense of "day" that makes Parmenides' response invalid. The third section considers the disjunct that part of the Form is received by each particular (131 c5-e3). Two current interpretations of this disjunct (that ofT. Scaltsas and R. E. Allen) are recounted and critiqued, and a new interpretation is proposed (an interpretation based partially on that of Proclus, and under which Parmenides' argument against this disjunct is valid).