From the Beginning to Plato

The argument assumes that a thought thinks. Further, we saw that one
confusion behind self-predication is the failure to distinguish between
predications such as
and
(i) Man is eternal
(ii) Man is mortal.
If Socrates participates in the Form of Man, then only (ii)’s predicate can be
legitimately transferred to Socrates. But when from the proposal that Forms are
thoughts Parmenides concludes that
(iii) Man is a thought,
FROM THE BEGINNING TO PLATO 341
the predication is of the type that occurs in (i). So one who was clear about the
difference between (i) and (ii) would not take Socrates’ participation in Man
together with (iii) to imply that Socrates is a thought.
But such is Plato’s inference. Now, Plato certainly rejects the idea that Forms
are thoughts, so he is probably making what he considers a sound objection
against it. If the point of the TMA were to expose and reject self-predication,
why would Plato, in the midst of this demonstration, deliberately present a
fallacious argument against a view he wants to refute, where the fallacy is of
precisely the sort involved in the error of self-predication?
But if Plato did not abandon self-predication, how could he respond to the
Third Man Argument? By restricting the One over Many Assumption, the only
assumption expressly given in the text. 38 Platonists in the Academy regularly
limited the inference from a set of Fs to a Form of F to cases where the members
of the set do not stand in relations of priority and posteriority; and, according to
Aristotle, Plato himself accepted this restriction. 39 Aristotle reports this view in
the Eudemian Ethics (1218a1–8):
There is not something common over and above and separate from things
in which the prior and posterior exist. For what is common and separate is
prior (proteron) since the first (prōton) is taken away when what is
common is taken away. For example, if double is first of the multiples,
multiple, which is predicated [of particular multiples, namely double,
triple, etc.] in common, cannot be separate. For then there will be [a multiple]
prior to double.
But double is the first multiple and cannot have a multiple prior to it. So there is
no Form of Multiple over and above specific multiples. The rationale for this