From the Beginning to Plato

340 PLATO: METAPHYSICS AND EPISTEMOLOGY
Whereas Plato maintains that only one Form exists for any attribute, he appears
committed to infinitely many Forms for each attribute.
For suppose that sensibles
(1) a, b and c are large.
Then by (OM)
(2) there exists a Form of Largeness: Largeness 1.
By (SP) it follows that
(3) Largeness1 is large.
So now we have a new set of large things:
(4) a, b, c and Largeness, are large.
By (OM), applied to this new set of large objects,
(5) there exists a Form of Largeness: Largeness 2.
And given (NI), Largeness 2 differs from Largeness 1: since Largeness 1 is large by
virtue of participating in Largeness 2, it cannot be Largeness 2. When endlessly
repeated, these steps produce an infinite number of Forms of Largeness.
Since Plato nowhere explains his attitude toward this argument, we will never
know what he thought of it. The question must be addressed on the basis of
indirect evidence.
Attention has focused on self-predication since that is in fact a mistake. As we
saw, self-predication is essential to Plato’s earlier Theory of Forms, so the
TMA’s presumption of self-predication does not render it irrelevant to Plato’s
position. 36
The belief that the argument’s point is to prove the unacceptability of selfpredication
runs into the problem that self-predication is present in what is now
generally agreed to be a dialogue later than the Parmenides, namely the
Timaeus. 37 There, despite Parmenides 133a’s rejection of resemblance, sensibles
participate in paradigmatic Forms by resembling and imitating them.
Resemblance brings along self-predication.
That the target is not self-predication is also indicated by a peculiar argument
separating the two versions of the Third Man Argument. Socrates proposes that
Forms might be thoughts, to which Parmenides objects that then everything is a
thought, and hence either everything thinks or else, while being a thought, does
not think.