Christan asked:

Can Plato's theory of Forms be rescued from the 'third man' argument? Gregory Vlastos in his article
'The Third Man Argument in the Parmenides' argues that the argument depends on two hidden
assumptions, 'self-predication' and 'non-identity'. But these assumptions lead to a contradiction. Is
this right?

============

I talked about the notorious third man argument back in January in my online notebook page 43 at the
Glass House Philosopher site.

Here's what I said:

One issue debated amongst Plato scholars is whether Plato's Forms were 'self-predicating', e.g.
whether the Form of 'Red' isred, whether the Form of the 'Horse' isa horse, etc. This comes up in a
dialogue from his later period, the Parmenides,where Plato describes a fictional meeting between the
young Socrates and the great Presocratic philosopher Parmenides. Plato's aim in writing the dialogue
seems to have been to criticise his own theory, which he puts into the mouth of Socrates. In a few
sharp paragraphs, Parmenides wipes the floor with it, leaving Socrates - and Plato - looking pretty
foolish.

The argument - known as the 'Third Man'- goes like this. According to Plato's theory, if you take the
totality of things that fall under the concept X, what makes them all instances of X is their participation
in the Form of X. Over many instances, there must be a One. For example, men are 'men' are
because of their participation in the Form of Man. But the Form of Man, according to the theory, is
also a 'man'. It is indeed the perfect exemplar of Man-hood, just as the Form of Justice is the perfect
exemplar of Justice. So now we have a new totality, all men plusthe Form of Man. What makes them
all 'men' must be a second, higher Form. And now one has started on an infinite regress.

If you remove the doctrine of 'self-predication' you tear the guts out of Plato's theory. If you reject the
'One over many' assumption' you take away its motivation. An impasse.

The 'non-identity assumption' Vlastos is talking about appears to be an integral part of the principle of
'One over many'. If you take all men together with the Form of Man, then there must be a second,
higher-order Form of Man, over and above that collection, which is non-identical with the first-order
Form of Man which is included in that collection.

I think this is right. Given that the Form of Man is held to sharein something possessed by every
individual man, so that the Form of Man isin some metaphysical sense a 'man', then we require
reason, in formal terms, which accounts for what it is that these extraordinary disparate individuals,
an abstract Form and concrete individuals, have in common that makes them all 'men'. It seems that
any answer given to this isn't going to work, because the very same question reduplicates itself at the
next level.

Thinking about this concretely, I wonder if that is really so. By all means, let's go along with the idea
that an account needs to be given of how self-predication could possibly make sense, how the Form
of Man could have anything in common with individual men. Once that's done, once you have
constructed the conceptual bridge between the abstract and the concrete, then by all means call the
result a 'second-order Form of Man'. Having done that work, however, you don't have to go on doing
it again and again.

I see two alternatives. Either to say that there is not the same pressure to regard the second-order
Form of Man as self-predicating as there was with the first-order Form of Man. Or to say that there is
not the same pressure to posit a third-order Form of Man to explain what all men, taken together with
the first-order and second-order Forms of Man 'have in common'. Either way, the result: no infinite
regress, and Plato's theory of Forms is saved.

It is significant, though, that in none of Plato's writings is there any indication of how he proposed to
respond to the third man argument.

Geoffrey Klempner