Abstract: The Third Man Argument is a regress argument that purports to show that if there is even one form of F, then there are infinitely many forms of F. That a regress can be identified is in itself an objection to the theory of forms because forms ought to be unique; and a regress would destroy the possibility of knowledge. Apart from the one in the Peri Idon, there are at least three other versions of the Third Man Argument; two in Plato's Parmenides, and one recorded by Eudemus. In this chapter, Fine explores the logic of and interconnections between the four regress arguments; she argues that the four arguments share the same premises (i.e. self-predication, the one over many assumption, and a non-identity assumption), and draw the same inference from these premises, i.e. that if there is one form of F, then there are infinitely many forms of F. Furthermore, each argument conceives the forms as properties (in particular Aristotle's and Eudemus’ versions); hence Fine argues that, logically, they are the same argument.

Keywords: Eudemus, non-identity assumption, Plato's Parmenides, regress, self-predication, the one over many assumption, Third Man Argument,