According to Rickless, what the text of the Parmenides actually gives, as the conclusion of the TMA, is that each form is unlimited (or infinite) in number. The usual interpretations, he claims, go astray and incorrectly take the conclusion to be, rather, that the number of forms is unlimited (or infinite).
The Greek is: 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.
But I think the usual interpretations are correct, and the Greek should be understood in the way they presume, not as Rickless would have it. Here’s why.
1. The expression ‘each of the Forms’ has a definite and established meaning in Parmenides: it signifies the Forms that Socrates wishes to postulate, for each of the kinds of things that we naturally distinguish. ‘Each of the Forms’, then, indicates distributively Large, Many, One, Good, Beauty, and so on. Here is a passage that clearly shows that this is so:
Socrates, that is because you are trying to mark off something beautiful, and just, and good, and each one of the Forms (e(n e(/kaston tw=n ei)dw=n), too soon…before you have been properly trained. (135c)
Here are other passages which show the same thing.
And yet, Socrates…the Forms inevitably involved these objections and a host of others besides—if there are those characters for things, and a person is to mark off each form as ‘something itself’ (o(riei=tai/ tij au)to/ ti e(/kaston ei)=doj). (135a)
Yet on the other hand, Socrates,…if someone, having an eye on all the difficulties we have just brought up and others of the same sort, won’t allow that there are Forms for things and won’t mark off a Form for each one (mhde/ ti o(riei=tai ei)=doj e(no\j e(ka/stou), he won’t have anywhere to turn his thoughts…(135)
Because I think that you, Socrates, and anyone else who posits that there is for each thing some being, itself by itself (o(/stij au)th/n tina kaq' au(th\n e(ka/stou ou)si/an ti/qetai ei)=nai), would agree, to being with, that none of these beings is in us. (133c)
I assure you,…that you do not yet, if I may put it so, have an inkling of how great the difficulty is if you are going to posit one form in each case every time you make a distinction among things (ei) e(\n ei)=doj e(/kaston tw=n o)/ntwn a)ei/ ti a)forizo/menoj qh/seij). (133b)
2. Relying on this expression, Parmenides sets up the TMA in this way. Socrates wants to say that each of his Forms is one, because he thinks that only one Form should be postulated (i.e only one entity which exists separately from particulars and is ‘itself by itself’) for each kind of thing that we naturally distinguish (oi)=mai/ se e)k tou= toiou=de e(\n e(/kaston ei)=doj oi)/esqai ei)=nai: o(/tan po/ll' a)/tta mega/la soi do/ch| ei)=nai, mi/a tij i)/swj dokei= i)de/a h( au)th\ ei)=nai e)pi\ pa/nta i)do/nti, o(/qen e(\n to\ me/ga h(gh=| ei)=nai). But the TMA shows that there are an infinite number of such things. If it was true to say that “Large is one”, on the grounds that we should postulate just one Form for the large things that we naturally distinguish, then it is true to say that “Large is infinite”, if, as the TMA shows, we should postulate an infinite number of Forms for the large things we naturally distinguish. So ‘each of your Forms’, that is, not simply Large, but also Many, One, Good, Beauty, etc. turns out to be infinite in number, not one.
3. Parmenides expresses this by saying that each of the the Forms will ‘no longer’ be one, but ‘will be’ infinite in number, because he is thinking of the infinite regress of the TMA as the result of a process of postulation, involving an intellectual viewing, as is clear from his language (e)a\n w(sau/twj th=| yuxh=| e)pi\ pa/nta i)/dh|j).
4. It is important, I think, that Parmenides says ‘each of your Forms' (e(/kasto/n soi tw=n ei)dw=n) rather than simply ‘each of the Forms’. This suggests precisely the opposite of what Rickless thinks. Rickless thinks that ‘your’ functions to indicate each of the Forms which Socrates has agreed to exist, in agreeing to the steps of the TMA. But at 131c7 Parmenides uses, rather, ‘our Form’, when he wants to say something about the Forms that is the result of his ad hominem argument against Socrates (to\ e(\n ei)=doj h(mi=n th=| a)lhqei/a| meri/zesqai). If, in the TMA, Parmenides wanted to say that the each member of the infinite hierarchy was infinite in number, presumably he would again have said that ‘each of our Forms is infinitely multiple’. He says, in contrast, ‘each of your Forms’, precisely because he wants to refer to the theory that has been marked out and identified outside the context of the TMA.
5 comments:
Dear Michael,
Thank you for your thoughtful comments. Here's what I would say in reply.
1. With respect to the proper interpretation of the last sentence of the TMA ("Each of your forms will no longer be one, but infinitely many."), your first (and last) point is that the expresssion "each of your forms" indicates distributively all the forms Socrates wishes to postulate, namely The Large, The Many, The One, and so on. I have two reactions to this.
First, the expression "each of your forms" need not have a fixed meaning, even if it appears in various different places with a single meaning. Suppose I tell you the following story. "Noah brought each animal into the ark. Later, when all the primates had finished eating, they got together and had a meeting. Each animal in turn said how thankful she was that she had been spared..." In the first sentence of the story, "each animal" distributively picks out all the animals there are. In the last sentence of the story, "each animal" distributively picks out all the *primates* in the ark. This phenomenon is well known to linguists and philosophers of language: the same quantifier phrase can be restricted in different ways depending on the immediate sentential context in which it appears. There is no reason to think that Plato's use of quantifier phrases is any different. So we cannot infer from the fact that "each of your forms" picks out one set of items in one context that it picks out the same set of items in every context.
Second, let us suppose that you are right to suppose that "each of your forms" distributively picks out all the forms Socrates wishes to postulate. Still, it doesn't follow that my rendition of the argument is incorrect. The text, even as you interpret it, is consistent with the following reconstruction. First, Parmenides shows that there are infinitely many forms of largeness, each of which partakes of infinitely forms of largeness. Second, he (implicitly) allows us to conclude from this that each form of largeness is infinitely many (by virtue of the fact that it partakes of infinitely many things). Third (and this is the important point), since the argument generalizes, it follows (now explicitly, on your view) not only that largeness is infinitely many, but also (by parity of reasoning) that oneness, likeness, and so on, are infinitely many. The only difference between this reading and the one offered in my paper is this: whereas the reading offered in my paper argues that the second step is explicit while the third step is implicit, the reading offered here (accepting your reading of the last line of the TMA for the sake of argument) takes the second step to be implicit while the third step is explicit. That's certainly no skin off my nose. Why? Because, ultimately, what's important about the Third Man, on my view, is that the absurdity generated at the end of the argument depends on the assumption that no form can have contrary properties. On the reading offered in my paper, and also on the reading offered here, it is *this* assumption on which Parmenides relies in inferring that "each of your forms is no longer one" from the fact that "each of your forms is infinitely many".
2. With respect to your suggestion that "F-ness is one" should be understood as "there is just one form of F-ness", and therefore that "F-ness is infinitely many" should be understood as "there are infinitely many forms of F-ness", I reply as follows. If this were correct, then we would expect the sentence "Socrates is one" to mean the same as "there is just one Socrates", and we would expect the sentence "Socrates is many" to mean the same as "there are many Socrateses". But, as Parm. 129c makes clear, this is not how Plato wants us to understand the sentences "Socrates is one" and "Socrates is many". In that passage, Socrates says that he is many by virtue of the fact that he has many parts, and that he is one by virtue of the fact that he is "one among the seven of us". The last sentence of the TMA and this passage from Socrates' speech are quite similar, and this is by design. In the speech, Socrates says that he is happy to accept that sensible things (such as he) are both one and many (in the sense described at 129c). What Socrates says he is NOT happy to accept, and challenges Parmenides and Zeno on several occasions in the Speech to prove, is that FORMS are both one and many in the same sense in which SOCRATES is both one and many. I take Socrates' challenge seriously, seeing as how it frames the entire discussion to follow. As I read the dialogue, Socrates issues a challenge in his Speech, and Parmenides takes up the challenge in the rest of Part I. First, in the Whole-Part Dilemma, Parmenides shows that, whether partaking of a Form is understood as getting the whole Form or only part of it, absurdity follows. [If partaking of the F is understood as getting the whole of the F, then the F turns out to be separate from itself, which is absurd. And if partaking of the F is understood as getting a part of the F, then the F turns out to be divided, i.e., many, and hence not one (131c9-11). Unless, of course, forms can be both one and many (in the sense of 129c).] Next, in the TMA, Parmenides shows that Socrates' reason for thinking that each form is one (namely, that it is one over many) leads to the conclusion that each form is also (infinitely) many. Thus, unless Socrates accepts that each of his forms is both one and many, his theory of forms leads to absurdity. Parmenides has indeed risen to the challenge. This is why, given the evidence from Socrates' speech and the Whole-Part Dilemma, I cannot bring myself to read "largeness is one" as meaning the same as "there is just one form of largeness", and I cannot bring myself to read "largeness is many" as meaning the same as "there are many largenesses".
You might respond to this by saying that, for Plato, the attribution of "one" or "many" to a sensible thing doesn't amount to the same as the attribution of "one" or "many" to a form. When Plato says that Socrates is many he means one thing, but when he says that Largeness is many he means another. My reply to this is that, in the middle period, Plato uses "F-ness is one" to mean something different from "there is just one form of F-ness". For example, consider Rep. 475e-476a, where Socrates argues that since the beautiful and the ugly are two, each is one. In saying that the beautiful is one and the ugly is one, Socrates surely doesn't mean that there is just one form of beauty and just one form of ugliness. All he means is that the beautiful is one thing and the ugly is one thing, so that together they are two. Here, to say that the beautiful is one (among two) is of a piece with saying that Socrates is one (among the seven who are present). So I see no reason to think that Plato means us to understand "F-ness is one" as a kind of attribution whose logical structure is fundamentally different from the logical structure of "Socrates is one". Mutatis mutandis for "F-ness is many" and "Socrates is many".
3. As I argue in the paper, reading the TMA in the way I propose (as a way of meeting the challenge Socrates issued in his Speech) provides us with one of the keys by which we can unlock the whole mystery of the *Parmenides*. If I'm right, the absurdity generated by the TMA relies not just on SP, OM, and NI, but also on the assumption that no form can have contrary properties. The same is true of the absurdity generated by the Whole-Part Dilemma, and by all the other arguments of Part I aside from the Greatest Difficulty (see my paper for details). So if Parmenides can show that forms can and do have contrary properties (as I believe he does in Part II), he will be able to avoid all these absurdities (aside from the Greatest Difficulty) and thereby save Socrates' theory of forms. I take it as a notable advantage of my interpretation that it makes sense of the TMA both considered on its own AND considered in the context of the entire dialogue. Perhaps this is what Annas meant when she said that we should avoid treating arguments in isolation. With this, I am in perfect agreement. But of course it doesn't follow that Vlastos-style logical reconstruction is to be abandoned. It should simply be engaged in with an eye to the larger context in which the reconstructed argument appears.
Sam, thanks.
1. I'm happy if I've shifted the argument now to whether your interpretation is consistent with the text!
2. Attributions of the form 'A is one, not many' can mean either 'A is undivided' or 'A is the only member of its kind'. I agree that context helps us to decide how such attributions are used in the TMA. You wish to go back to 129c and take that to determine the meaning. I say that it's sufficient, and better, to look at the beginning of the argument, where Parmenides says, "I suppose you think each Form is one on the following ground: whenever some number of things seem to you to be large, perhaps there seems to be some one character, the same as you look at them all, and from that you conclude that the large is one." This presumably gives the sense of what 'one' means in the context of the TMA, and the sense of "some one character" here comes from the contrast with "some number of things seem to you to be large". It's the One Over Many Argument, after all, that Parmenides is taking as his target, and the 'One' meant in the title of that argument is: just one thing (of that kind) is the Form.
3. It would of course be a considerable mark in favor of your interpretation, if every other objection to the theory of Forms given in the Parmenides , besides the TMA, was aiming to show that Forms are both one and many (i.e. both undivided and divided). But plainly there are several arguments that don't have this character, e.g. that on the view that a Form is a thought, then things that participate in them are thinking. Doesn't Parmenides seem to bring forward every absurdity involving the Forms that he can devise? It would be odd for him to pass over or give scant attention to an infinite regress difficulty. And yet your interpretation has him doing just that.
Posted by Michael Pakaluk
Dear Michael,
1. I appreciate the care with which you've considered my reconstruction of the TMA. I think this exchange is particularly fruitful, in view of the fact that you are providing what I take to be an excellent summary of the reasons favoring what I think of as the "standard" interpretation of the TMA.
2. I don't think that "A is one" means "A is undivided". If that were true, then it would be a contradiction to say that Socrates is both one and divided. But plainly, as 129c indicates, this is not the case. There, Socrates says (I take it, without contradicting himself) that he is divided (or, at least, divisible) into parts, and yet also one. What he says is that he is one because he is one among many. This is a major clue as to what "A is one" means for Plato.
In order to understand what Plato takes "A is one" to mean, I think it helps to look at the big picture. What, in general, does Plato take "A is F" to mean? Well, it's plain that, in the Phaedo, the fact that A is F relative to B is sufficient for A's being F. For example, the fact that Simmias is tall relative to Phaedo is sufficient for Simmias's being tall. This phenomenon is a constant throughout the Platonic corpus. So, to take another example, in the Hippias Major, the fact that a girl is beautiful relative to a pot is sufficient for the girl's being beautiful, and the fact that the girl is ugly relative to the gods entails that she is ugly. (With respect to the Sophist, there is Lesley Brown's wonderful 1986 "Being in the Sophist" paper, which makes what I take to be a similar point about Plato's use of "A is", namely that it is sufficient for A's being that A is F.)
Let's extrapolate to the case of "A is one" at the beginning of the TMA. You say that there the contrast between the "one" Largeness and the "many" things that partake of it indicates that Parmenides is claiming that there is just one form of Largeness. That's a possible reading. But it's not the only reading consistent with the text. Here's mine. As a general rule, if A is F relative to B then A is F (see above). It follows from this that if A is one *among* many, then A is one. (We find Socrates saying this much at 129c.) It ALSO follows that if A is one *over* many, then A is one. What I claim is that THIS is the import of the passage at the head of the TMA. If I'm right, then, whatever "A is one" means, the passage at the head of the TMA need not be read in the way you propose.
3. You are right that, apart from the Greatest Difficulty, there are a few arguments in Part I that are not based on the assumption (I call it "Radical Purity") that no form can have contrary properties (or the more specific instance of that claim, namely that no form can be both one and many). One example is the little argument at 132c9-11. Another is the pair of little arguments at 131c12-d5. But these arguments are clearly afterthoughts in the scheme of the Part I project as a whole. The main arguments are the ones discussed in my paper (the Whole-Part Dilemma, the TMA, the Anti-Noematic Argument, the Likeness Regress, and the Greatest Difficulty). Of these, as I argue, only the Greatest Difficulty does not assume Radical Purity. The fact that a few subsidiary arguments are based on assumptions that do not include Radical Purity is not sufficient to establish that the main thrust of Parmenides' criticisms is not designed to put pressure on Radical Purity.
What would be the possible rationale for postulating an infinite number of Forms of circularity? I’m trying to understand why Plato came to believe this objection ( TMA) important enough to present, and what’s really at issue in our discussion.
May we ( with egregious anachronism ) think of the Form of the Circularity as having its familiar math description in 2D Cartesian space. Then any sensible circular object “participates” in this Form by trying to approximate this description to the limits of measurement ( but falls short because the x and y coefficient are not quite the same).
We could, I suppose, postulate an unlimited number of circular forms corresponding to every real value of r ( the radius). But why invoke all of these instantiation of the general formula? And how are we ever going to match them with particular circular shapes? Is every sensible circle trying to be not just a perfect circle, but a perfect circle of some determinate radius? Surely it is enough to say all sensible circles try to approximate the general formula?
Now—another issue-- what form are we ever going to be able to come up with that all our sensible circles and our general formula both “participate” in? And remember, this higher order form is going to have to be the cause of the common circularity of sensibles and the Form ( which is circular by SP ). I can’t see how we are going to think of a ( higher order?) form being the cause of the circularity of the self-sufficient and perfect Form of Circularity.
Dear Anonymous,
Plato does not *postulate* an infinite number of forms of F-ness. He finds himself compelled to accept their existence, and this because of the TMA. If you accept, as he does, OM, SP, and NI, then you have no choice but to accept that the number of forms corresponding to any given predicate is infinite.
With respect to the second issue, OM simply requires that, for any group of circles (no matter whether the group is comprised of sensibles or forms), there is a form by virtue of partaking of which each member of the group is a circle. You don't have to *think* of a particular form to do the job. OM *guarantees* the existence of such a form.
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