08 April 2005

Worth Pausing to Admire

"The argument itself is deceptively simple to state," Annas says, of the Third Man objection:

When we consider a number of large things, we notice that they all share a common feature, that of being large, and we take this to be the form; the form is the one item in virtue of which all the large things are large. But then we go on to consider a second group of large things: the original large things and the form itself. And now it seems that they share a common feature, requiring a form in turn to be the one item in virtue of which they are all large. But once introduced, this line of thought leads to the conclusion that if we have even one form, we have infinitely many (30).
But it's deceptively simple to state it that simply. Really, this is a masterful paragraph, not at all easy to write, and worth pausing to admire.


Sam Rickless said...

The last line of Annas's rendition is: "If we have even one form, we have infinitely many." But the actual text reads as follows: "Each of your forms will no longer be one, but infinitely many." The claim that each form (of largeness) is infinitely many does not follow directly from the claim that there are infinitely many forms of largeness. This is a puzzle. I've argued that it has a solution, which goes roughly as follows. Annas's version of the argument establishes that there are infinitely many forms of largeness, each of which partakes of infinitely many forms of largeness. But anything that partakes of (infinitely) many different things is itself (infinitely) many (either because infinitely many different things are true of it or because it has infinitely many parts). Hence, each form of largeness is infinitely many. And it is no longer one because no form can have contrary properties (and hence no form can be both one and many). What this brings out is that there is more to the argument than One-Over-Many, Self-Predication, and Non-Identity. There is also the claim (call it "Radical Purity") that no form can have contrary properties. In my view, one of the messages of the Parmenides is that we should respond to the Third Man, not by rejecting OM, SP, or NI, but by rejecting RP.

Michael Pakaluk said...

Plato's argument was the One Over Many. Parmenides is objecting that it might better be called the Infinite Over Many, which would be on its face objectionable, as making explanatory entities more numerous than entities to be explained. I don't see any need to take Parmenides to be putting forward "the claim that each form (of largeness) is infinitely many" but rather that "what you took to be single form (hekaston soi) turned out to be infinite"

Sam Rickless said...

Reply to Michael: Much as you (and many others) would like to read the last sentence of the TMA as saying something like "what you took to be a single form turned out to be infinite", that's not in fact what the sentence says. You're *imposing* this reading on the text, perhaps because you've already decided that the TMA does no more than generate infinitely many forms of largeness. Look again. I'm not alone here: I'm really just following Gill and Ryan. (By the way, even your gloss isn't quite what you want the sentence to say, which is closer to this: "though you took there to be exactly one form of largeness, it turns out that there are infinitely many (forms of largeness)". It's even clearer that this isn't what the sentence says.) For a reading of the entire dialogue that makes sense of the text as written (rather than of the text as one wishes that it had been written), see my Phil Review (1998) piece: "How Parmenides Saved the Theory of Forms".

Anonymous said...

Sam, I confess that I don't know your Phil Rev  piece, but will read it. How deliciously ironic, if your interpretation were correct--the TMA example would rather backfire then, wouldn't it?


Posted by Michael Pakaluk

Sam Rickless said...

Michael, Indeed it would backfire. In fact, the TMA would end up illustrating the very opposite conclusion, namely that logical reconstruction, when done carefully, provides the key that will unlock many an interpretive conundrum...For example, I think we can use this method to adjudicate the debate between Vlastos and Penner concerning Socrates' position on the unity of virtue in the *Protagoras*, the debate over the proper interpretation of the Two Worlds argument at the end of Republic V, and more. We can also learn a great deal about how Plato's theory of forms developed out of Socrates' theory of definition, as Russ Dancy argues in his fabulous book, *Plato's Introduction of Forms* (CUP, 2004).