The Parmenides is an unprecedented, baffling, and even bizarre dialogue.  Two towering philosophical figures of yesteryear come to town, meet the young and up-and-coming Socrates, listen to him expound his theory of forms; Parmenides criticizes it, causing Socrates to despair; he then encourages him not to lose heart, but hone his philosophical skills, for which Parmenides offers an extended opportunity. 

            What should perhaps strike the reader is the fact that, for the first time ever in the Platonic corpus, Plato’s pet theory, the Theory of Forms, is put examined and cross-examined to test its coherence.  Plato has laid the foundations of the theory, notably in the Meno; suggested it, notably in the Symposium and Cratylus; introduced it, in the Phaedo; elaborated it, in the Republic; applied it, in the Phaedrus.  But he has never, ever, let anyone seriously challenge his foundational theory, much less refute it. 

            In the present dialogue, however, we have arguably the greatest of Presocratic philosophers both challenge and, apparently, demolish the Theory of Forms?  Why?  And why now, given that, presumably, Plato is the director of the one great educational institution of the time, the Academy, surrounded by brilliant colleagues and students.  

            Scholars note that there may be cracks in the theoretical edifice Plato has built.  That offers an important philosophical motivation: to find the flaws and repair the edifice.  But it leaves unanswered the historical question: why now?  Why after (or shortly before, depending on the timeline of current events) Plato’s second trip to Syracuse, so promising in its prospect, so disastrous in its outcome, does Plato present a devastating attack on the central pillar of his philosophy?  Why risk a breakdown in the idealistic theory that holds Plato’s worldview together? 

            It seems to me that there is only one plausible scenario that can account for Plato’s composition of the Parmenides.  It is the fact that Plato’s Theory of Forms had come under a withering attack.  Plato had rivals throughout his career.  Most notably, Isocrates the teacher of oratory, had founded his own school in Athens probably before Plato had founded his Academy, and the two schoolmasters had continued to compete for the minds and hearts of prospective students.  Yet Isocrates was no philosopher (much as he liked to call himself one, in the suitably broad sense of an intellectual).  There were several other Socratics still active who might challenge Plato.  But we have no record of their doing so in the public forum. 

            The one figure that seems to me to incite the Parmenides is the young man who is typically dismissed as too young and too inexperienced: Aristotle of Stagira.  He came to Plato’s Academy at the tender age of seventeen, an orphan from the north, but one with good family connections.  He likely arrived in the Academy when Plato was in Syracuse on his second visit, trying in vain to support his disciple and the erstwhile royal advisor Dion.  Coincidentally, the answerer of the second half of the dialogue is named Aristotle.  Commentators are quick to point out that the narrator identifies this Aristotle as one who later became one of the Thirty Tyrants.  (Get it?) 

            If that were all, the dramatis persona would be an interesting footnote.  But the pièce de résistance of the attack on Plato’s Forms is the Third Man Argument, whose champion is the historical Aristotle.  Perhaps Aristotle borrowed that argument from some other philosopher.  But we know it from an early dialogue of Aristotle (the work itself is lost, but its existence is well attested), On Ideas (where idea is one of Plato’s favorite words for Form).  In that work, Aristotle marshals five arguments for Platonic Forms, along with problems they raise for the theory.  One of the arguments in question is the One Over Many principle, according to which for every set of things that are called F (such as the many large things) there is a single form of F-ness (Largeness) that accounts for the property they share.  This principle, in turn, becomes a premise in the Third Man Argument.

            The argument goes like this:

The Third Man Argument

1.         There is one cause of the many Fs, in virtue of which they are F.  (OM)

2.         The cause of the many Fs is not identical with them.  (NI)

3.         The cause of the many Fs is F-ness.  (F-ness)

4.         F-ness is F.  (SP)

5.         The many Fs and F-ness are all F.  (1, 4)

6. There is one cause the many Fs and F-ness, in virtue of which they are F.  (1, 5)

7.         The cause of the many Fs and F-ness is not identical with them.  (2, 6)

8.         The cause of the many Fs and F-ness is F-ness₁.

9.         F-ness₁ is F.

. . . .

The point is, that, once you explain the existence of the property by the “one” over many, you can’t stop generating Forms with different subscripts. 

            The argument is quite brilliant: look at the propositions the philosopher (Plato) needs to justify the existence of Forms.  They are three: the One Over Many (OM), Non-Identity (NI), and Self-Predication (SP)—all of which Plato seems to endorse in talking (informally) about the Forms (for he had never given a formal account of his grand theory).  If you combine them in an argument, you generate an infinite number of similar Forms, none of which explains anything without the next member of the series.  You get a “vicious” regress.  The theory is revealed as self-refuting.