The second version in the text of Part I of the Parmenides of the Third Man regress against the theory of Forms has often been read in its critical thrust as essentially identical with the original version. That interpretation fails to do sufficient justice to the regress’s focus specifically on the Form of Likeness. Such a Form has to be posited once the application of the predicate like inherent in the original–copy model of participation in Forms is itself explained on that model. Are Platonists then trapped? Part II of the dialogue supplies indications to the contrary. Like figures in many of its arguments, where it is often construed as being qualified in the same way. What readers effectively come to recognise is that like is a second-order predicate: ‘is like’ means ‘share the same first-order predicate’, not ‘participates in the Form Likeness’. Part II of the Parmenides therefore supplies materials for resisting the regress; and the presentation of likeness as a theme which we are invited to pursue through both parts alerts us to the fact that they are available, and are pertinent to the business of evaluating Parmenides’ critique of Socrates.

The chapter asks if the first part of the Parmenides (including the “Third Man”) shows that Plato abandoned Platonic forms, and argues instead that Plato’s “Third Man” passage is not an indirect proof of anything: it simply shows the youthful Socrates not able to defend his views on forms. The exercise Parmenides then prescribes and demonstrates is the way forward Plato provided. It leads us to distinguish two kinds of predication, corresponding to two kinds of facts about forms. Better-organized thinking about forms lets us reject the notion that to perform their work in Plato’s theory, they must be perfect exemplars along the lines of “the Platonic ideal of the banana split.” This dispels the underlying problem which led to confusion over the “Third Man.” We can face down analogues of that argument for any form, from the Fox and Triangularity to Likeness and the Beautiful. This interpretation emerges from detailed construal of the text, taking account of both its literary and overtly philosophical aspects; the chapter brings together background for Plato’s agenda in his previous works, in the works of Anaxagoras and the historical Parmenides, and in Greek usage.