16 April 2005

Multiplicity Implied by Multiple Predication

As we have seen, Rickless take the Third Man Argument (TMA) of the Parmenides to be arguing that each Form is inherently multiple. For him to claim this, he has to say that an argument such as the following is implicit in the passage:

(i) There is an infinite regress of Forms.
(ii) Each Form earlier in the sequence participates in all the Forms later in the sequence.
(iii) Thus an infinite number of predicates can be asserted of each Form in the sequence.
(iv) But that of which many predicates can be asserted is itself manifold.
(v) And that of which an infinity of predicates can be asserted is itself infinitely divided.
(vi) Thus, each Form in the sequence is infinitely divided.
The Standard Interpretation (as I've called it) can rest content with (i). Rickless has to say that all of (ii)-(v) is additionally present and implicit. This is already, I have argued, a large inconvenience with his interpretation.

My concern in this post is with the key premise of this proposed implicit argument, premise (iv): That of which many predicates can be asserted is itself manifold. Where does this come from? Why should Plato have accepted it? Why should Plato have represented his interlocutors as all accepting this? Why should Plato have thought that readers of the dialogue might have seen that this principle was operative?

Rickless locates it in the Philebus, but there are many difficulties in this, which I'll raise in a subsequent post.


Sam Rickless said...

I don't think this captures my reasoning *exactly*. For one thing, (v) and (vi) are otiose, because it follows directly from (i)-(iv) that each form in the regress is manifold. For another, you can get the same conclusion by replacing (iv) with the conjunction of (v) and the claim (call it (v*)) that anything that is (infinitely) divided is (infinitely) many. --By the way, (v*) is needed to get the conclusion of the argument that ends at Parm. 143a2-3, to the effect that, if the one is, then it is infinitely many (apeiron to plethos). It's also needed to get the conclusion of the Whole-Part Dilemma, as I argued in a previous comment. So it's pretty safe to assume that Parmenides takes it for granted at the time he's throwing the TMA at Socrates.-- The upshot is that each of (iv) and (v)+(v*) is sufficient, in conjunction with (i)-(iii), to get the desired conclusion, which is that each form in the hierarchy is infinitely many.

But, never mind that. I do, as you say, believe that Plato endorses (iv) (albeit only explicitly) in the *Parmenides*. And I do find evidence for this in the *Philebus*. Is this legitimate? For my answer, see my comment on your next post.