16 April 2005

What Does the Text Not Say?

I had been going along, presuming that the Third Man Argument (TMA) was a vicious regress argument—that it was meant to show, in the words of Julia Annas, that, “if we have even one form, we have infinitely many.”

So naturally I was astonished when a reader of Dissoi Blogoi, Sam Rickless (UCSD), wrote in to say that the text says something very different:

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.
You may consult his original comment in its entirety, here .

The text reads: “And each of your Forms, then, will no longer be one, but rather an unlimited multitude. ( kai\ ou)ke/ti dh\ e(\n e(/kasto/n soi tw=n ei)dw=n e)/stai, a)lla\ a)/peira to\ plh=qoj.) Was Rickless right, and had everyone simply been misunderstanding the text, reading into it what they presumed was there, but wasn’t?

Yet when I looked more carefully at the context of the TMA, I concluded, to my satisfaction, that the argument should be understood as Annas had it, because ‘each of your Forms’ means, in effect, ‘what is implied by the One Over Many argument, in each of its applications’. See my post, What Does the Text Say?

And then it appeared to me that Rickless was making a claim about what the text said, by making a claim about what the text did not say. It was Rickless, it seemed, who was reading into the text something that was not there. This was so in his original post:

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.

But the words ‘of largeness’ do not occur in the text! It is Rickless' gloss.

And the same thing turned up in his 1998 Phil Review paper:

Parmenides then concludes that each Form of Largeness “will no longer be one, but unlimited in multitude”. (520)

But there is an additional problem for the standard answer. For at the conclusion of the argument, Parmenides says not only that each Form of Largeness “will no longer be one”, but also that each Form of Largeness will be “unlimited in multitude”, that is, infinitely many. But how are we to understand the statement that each Form of Largeness is infinitely many? (521)

Let’s begin with (M), the claim that each Form of Largeness is many. (522)

It may be true that Rickless' interpretation is consistent with the text of the TMA, but it's not true that his interpretation gets special support from the language of the text ("But the actual text reads as follows", he wrote), or pays attention to that language, in a way that the usual interpretation does not.


Sam Rickless said...

Dear Michael,

Very clever. You are right, of course, that the last line of the TMA does not say, in so many words, that each form "of largeness" is infinitely many. The addition of "of largeness" is my gloss. But I think it is more than justified by the overall context. Moreover, my gloss makes far better sense of the last sentence than does the standard gloss. That's why you find me adding it where I do.

The standard gloss is that, as you put it, "if we have even one form, we have infinitely many". What the text actually says, without my gloss, is that "each of your forms is no longer one, but infinitely many". Maybe I'm dreaming, but the text just does not support the standard gloss, period. As I argued in a previous comment, to say that F-ness is many is not to say that there are many F-nesses. (Similarly, to say that Socrates is many is not to say that there are many Socrateses.) The fact that the text as written does not support the standard gloss drives my attempt to read the text in a different way. As I argue in my paper and in various comments on previous posts on this blog, there is a great deal of evidence supporting the particular gloss that I added to the last line of the TMA.

First, on my gloss, the argument (with some of the reasoning filled in) comes out valid. That's a nice result. Second, my gloss brings out what Plato must have seen as a parallel between the claim that each form is many and the claim that Socrates is many. (Remember that Socrates accepts that each form is one. In his Speech, he tells Parmenides and Zeno on numerous occasions that he would be *astonished* to discover that FORMS have contrary properties, such as being one and being many. That is, he would be astonished to discover that each form is not only one, but also many.) Third, my gloss brings out the connection between the Whole-Part Dilemma and the TMA. As I read them, both arguments are designed to establish that the assumptions of the theory of forms (suitably elaborated) entail that each form is many. In the Whole-Part Dilemma, the multiplicity of each form is the result of its having many parts. In the TMA, the multiplicity of each form is the result of its partaking of many other forms. Fourth (and this is something I have not yet pointed out in previous comments on this blog), my gloss brings out the parallel between the TMA and the first argument of the First Deduction at the beginning of Part II. There Parmenides argues that since ONENESS is one, it can't be many, and hence can't have parts. There is simply no way to make sense of this argument on the standard supposition that "ONENESS is many" means the same as "there are many ONENESSES". But the argument makes perfect sense if we suppose (as I do) that something's having parts is sufficient for its being many. Finally, my gloss (as I argue in the paper) provides the key that is needed to unravel the mystery of the dialogue as a whole.

The upshot is this. The standard interpretation of the last line of the TMA does not make sense of the text as written (with or without my gloss). My own interpretation of that line (a) makes sense of the text, and (b) connects it to passages that appear before the TMA (Socrates' Speech, the Whole-Part Dilemma) and passages that appear after the TMA (the First Deduction).

I see a certain irony in the discussion we've been having up till now. It all started when you (as I see it, rightly) criticized Annas for suggesting that analytic approaches to the TMA are not fruitful. But I think Annas did put her finger on something, which is that it is ultimately impossible to know what Plato thought of the TMA without connecting the argument with the rest of the dialogue. As far as this point is concerned, I agree with Annas completely. (In this, I am really following in the footsteps of others, most particularly Constance Meinwald, whose interpretation of the *Parmenides* is the best and most developed published interpretation of the dialogue.) The irony is that Annas's own (standard) interpretation of the last line of the TMA fails to abide by her own recommendation that one not consider arguments in isolation, but rather in context.


Anonymous said...

I wonder whether anyone else is having difficulty understanding Socrates’ unquestioning acceptance of Parmenides’ account of how we are supposed to envision or recognize these new TMA forms: holding simultaneously in the mind’s eye both a collection of sensible particulars & the Form they partake of, and presumably then intuiting some commonality.
This is an unprecedented feat of mental acumen, is it not, on Plato’s psychology? The Parmenides still worries whether we are able to intuit clearly the Forms (in our embodied state). But now we are assumed to be able to simultaneously attend both to a Form and to a collection of sensibles and spontaneously recognize some commonality? I can see the young Socrates saying, “Gee, Parmenides, how do you do that?”
Does the fact that we allow SP for the forms guarantee that we have a commonality sufficient to require a form? “This disc is circular” and “ the Circle Itself is circular” are both allowed, but the second surely is a tautology, vacuously true, whilst the truth condition for tokens of the former depend upon all sorts of observation & measurements. Where is the Form-requiring commonality?
You can’t just assert that there must be a commonality when you license use of a predicate across different Types of objects ( forms & particulars). I can hear Parmenides saying, “the many will no doubt deny it,” but the burden of proof is with those pretending to be able to compare sensibles & a form and extract significant commonalities.
Is there some strong reason Socrates cannot take this line and argue that Parmenides has at least not shown any need to recognize another form based on what may amount to trying to compare incomparables?

Sam Rickless said...

1. We are supposed to attend to the forms with the mind's eye (i.e., reason), not with the senses. Maybe that's difficult to do, but the Socrates of the *Republic* thought it possible. So why not the Socrates of the *Parmenides*?

2. Does the fact that THE CIRCLE is a circle and this disk is a circle guarantee the kind of commonality that will trigger OM? Well, why not? They're both circles. Why isn't that enough? You say (i) that "THE CIRCLE is a circle" is tautologous, while (ii) "this sensible disk is a circle" is not tautologous. I agree with (ii), but I deny (i). "THE F" names whatever it is that is responsible for making F things F. But it is not a tautology to claim that *that* thing, whatever it is, is F.

3. Does the fact that THE CIRCLE and the disk are completely different kinds of objects entail that they can't have properties (such as circularity) in common? No. Things of completely different kinds have properties in common (e.g., the property of being one, the property of being beautiful, the property of being like, and so on), so why not the property of being circular? It is certainly not philosophically disreputable to deny that THE CIRCLE can be a circle in the same sense that the disk is a circle. But I don't see why it would be philosophically disreputable IN PLATO'S DAY to maintain what you deny.

Perhaps you are taking for granted that forms are abstract properties or concepts. But Plato does not say this, or anything approaching this. Forms are abstract, of course, but why assume that they are properties or concepts? Why aren't they abstract particulars, like numbers? (Later in life, if we are to trust Aristotle, Plato thought that the forms were contructed out of THE ONE and THE INDEFINITE DYAD.) As I see it, to assume that forms must be concepts or properties is anachronistic.