12 April 2005

Worth Pausing to Think About

We get Rickless' interpretation by beginning with a statement of the TMA such as in Annas' elegant paragraph, quoted in an earlier post, and then adding some additional claims, which I include in italics:

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 each form in this infinite series is large; it therefore participates in every form above it. But anything that participates in many forms is therefore itself many; and any form that participates in an infinity of forms is infinite in number. So each form in this infinite sequence is infinite in number. Thus, each form of large, which is one, is infinite. ("Each of your forms will no longer be one, but unlimited in multitude.”) This is a contradiction, because whatever is infinite is not one.

The interpretation gets a conclusion that seems to coincide very closely with the stated conclusion of the TMA. But, again, what do we say about this? I have my concerns. What are yours?

6 comments:

Anonymous said...

May I ask a na├»ve question? I’ve have never been able to decide whether self-predication(SP) is an indispensible premise of the TMA.
“Large”, first of all, is concept with too many special problems. May we think instead of “courageous” or “bovine” or, if you require a math concept, “prime”. Now I assume that few of us are strongly tempted to the view that the Form of courage is something courageous, or that the Form of primeness is/ could be prime, etc. Maybe Plato would want to disagree with us at this point and try to defend SP, but my question is whether it is necessary for him to do so to sustain the TMA.
Suppose we have (1) the set C of all particular actions and men and whatever else we’d call courageous, and (2) the Form of courage, by virtue of participating in which everything in (1) is courageous. We define the set C’ as the union of the C and the Form of courage. First point: whether or not we accept that “courageous” is a proper definiens of C’ , C’ is a well-defined set, as is the set C” whose members are just C, and the Form of courage, and the next-order Form in which both C & the Form of courage participate/belong. And similarly for the sets C’” and C”” ad infin.
Second point: IF each these sets corresponds to a legit new definiens of “courageous”, I suppose we get the intra-Form inflation Rickless believes the translation favors, whereas IF we reject SP and insist that C’ et seq are just some new higher order concepts somehow subsuming courage, we get the inflation of many new forms.
So, does this line of reasoning suggest that if we find Plato committed to SP in the Parmenides, this is evidence for Rickless’ construal of the TMA , but if he find him wary of SP,the many new forms version is more likely?

Anonymous said...

You are taking the notion of a set as intuitive and not needing special justification. But from Plato's point of view, I think, we cannot count things as grouped together (in a 'set') except through a Form, the existence of which would need to be established by a One Over Many type argument. So one could not group together the Form of Courage and C, without its being the case that 'there is some one thing which all of these are'. And I don't see what that could possibly be, except courageous . So your hierarchy of well-defined sets can't, I think, be developed independently of SP. 

Posted by Michael Pakaluk

Sam Rickless said...

1. I agree with Michael. The importance of SP is brought out in the text of the TMA. At 132a6, Parmenides says: "And what about the large itself *and the other large things*?" This strongly suggests that "the large itself" is large, in the same sense in which the "other large things" are large.

2. It has worried many that SP seems obviously false. For example, as you say, it seems that courage is not the kind of thing that could be courageous. But here, I think, the English language misleads. In general, Plato speaks of the form corresponding to the predicate F in different ways. Sometimes, as in the case of the predicate "like" he uses the locution: "F-ness" (homoiotes). But sometimes, also as in the case of the predicate "like", he uses the locution: "the F" (to homoion). "Homoiotes" makes us think of what WE would refer to in using the word "likeness". This would be something like an abstract quality or property, perhaps even a concept. But "to homoion" makes us think of something very different, something that is itself like, in fact, as Plato sees it, the perfectly like thing. This is an old debate, really. Should we think of the form corresponding to the predicate "circle" as circularity (i.e., the property or quality of being circular)? If so, then, since circularity is not a circle, SP seems obviously false. Should we think of the form corresponding to the predicate "circle" as THE CIRCLE (i.e., the perfectly circular thing)? If so, then, since THE CIRCLE is clearly a circle, SP seems obviously true. The moral of the story: Don't be misled by the English words that are used to translate the Greek text.

3. SP is entailed by two Platonic doctrines. The first ("Causality") is that the F is what makes F things (other than itself) F. Thus, as Socrates puts it in the Phaedo, the beautiful is what makes beautiful things beautiful (it is by the beautiful that beautiful things are beautiful). The second ("Transmission") is that whatever makes F things F must itself be F. Transmission has an ancient pedigree. As a theory of causation, it takes us at least from Anaxagoras through Plato and Aristotle. So, to use Anaxagoras's own example, whatever makes hot things hot must itself be hot. These two theses, Causality and Transmission, jointly entail SP. If the F is what makes F things F, and whatever makes F things F must itself be F, then the F must itself be F. So, THE HOT is hot, THE LIKE is like, THE BEAUTIFUL is beautiful, and so on. There is nothing mysterious here.

Anonymous said...

Thank you both for your thoughtful replies.
OK, we should accept that SP is a intended premise of the TMA, and that Plato unreluctantly embraces SP, since in fact it is entailed by his principles of causality and transmission. That very perspicuous statement of argument points directly to my second puzzlement here. How can we conceive of another form being the cause of THE CIRCLE being circular?
Surely the essential circularity of THE CIRCLE is self-caused, if "caused" at all.
THE CIRCLE, then, is all we need to explain the circularity that all the worldly circular shapes partake of and the circularity of the Form itself. No additional Form is needed or indicated because of the special condition that one of our enumerated circulars is already causally adequately to explain the circularity of all the rest, including itself. No regress.
How does Plato avoid this obstacle to the regress?

Sam Rickless said...

Dear Anonymous,

The rejection of NI, which you are recommending, is certainly one way out of the TMA. NI can be rendered in different ways: (a) no form partakes of itself, (b) it is not by virtue of partaking of itself that the F is F. You can think of (a) as Non-Self-Partaking, and (b) as Non-Self-Explaining. As I see it, both of these claims (NSP and NSE) follow from the claim (call it "Itselfness") that each form is itself by itself (auto kath auto), a claim that is one of the rock bottom assumptions of the theory of forms. Without getting into the nitty-gritty, I would argue that, in the *Parmenides*, Plato equates a form's being "itself by itself" with its being "separate" (see 129d7-8), and treats a form's being "separate" as amounting (at least) to its being "separate from the things that partake of it" (see 130b1-2), which entails its being not numerically identical to any of the things that partake of it. Thus, from the fact that THE F is itself by itself, Plato infers that THE F is not identical to any of its participants, from which it follows that THE F does not partake of itself (NSP). Hence Itselfness logically entails NSP. [NSE then simply follows from NSP.)

Now towards the end of Part I, after having criticized Socrates' theory of forms, Parmenides says that "only a very gifted man can come to know that for each thing there is some kind, a being itself by itself" (135a7-b1). So Parmenides assumes that, whatever else Socrates should provide in the way of a response to Parmenides' criticisms, he should not give up Itselfness. But if part of Plato's message is that the solution to the problems raised by Parmenides in Part I should not involve abandoning Itselfness, then it doesn't make sense to respond to the TMA by rejecting NI (=NSP), since Itselfness logically entails NI (see above), and hence the rejection of NI would force the rejection of Itselfness.

So, strange as it may seem to say that The Circle is a circle by virtue of partaking of another form of circle, this is what the theory of forms entails. There is no way to stop the regress. And one of the claims that must be given up is the idea that there is exactly one form per predicate.

Anonymous said...

Dear Sam (if I may),

Thank you for taking the time to explain the consequences of rejecting NI. Yes, I certainly don't see Plato moving to reject the "itselfness" of the Forms to answer the TMA.
It does seem quite strange, as you say, that the Circle is circular by virtue of partaking of another form of circularity. But if we accept that the Circle partakes of anything, it seems that it must partake ( by your argument ) of another form of circularity.