Suggestions on How to Combine the Platonic Forms to Overcome the Interpretative Difficulties of the Parmenides Dialogue(*)

Abstract

This paper provides an original approach to research on the logical processes that determine how certain forms participate in others. By introducing the concept of relational participation, the problems of self-referentiality of the Platonic forms can be dealt with more effectively. Applying this to the forms of likeness and unlikeness in Parmenides 132d-133a reveals a possible way to resolve different versions of the Third Man Argument. The method of generating numbers from oddness and evenness may also be of interest; relational participation in these forms clarifies the interpretation of Parmenides 143e-144a.