16 April 2005

Recourse to the Philebus

Rickless' implicit argument depends crucially on the claim that something of which many things can be predicated is itself multiple. Where does this claim come from? Rickless finds it in the Philebus, as he indicates in his 1998 Phil Review article:

Socrates has already acknowledged that something is many if it has multiple parts, and there is evidence in the Philebus that he accepts that something is many if many predicates are true of it. (522)

It should be noted that, in the Philebus, Socrates accepts not only that a man’s being many follows from his having many parts (14d-e), but also that a man’s being many follows from the fact that many predicates are true of him (14c-d). (513)

But there are at least three difficulties with this.

1. It's not clear that Plato even endorses the relevant principle in the Philebus. In 14c-15c, Socrates distinguishes two sorts of problems involving one and many. He dismisses the first sort as merely eristic and "no longer even worth touching; they are considered childish and trivial but a serious impediment to argument if one takes them on". The second sort he takes seriously: "But when someone tries to posit man as one, or ox as one, or the beautiful as one, and the good as one, zealous concern with divisions of these unities and the like gives rise to controversy". The latter sort seems to correspond to the kinds of difficulties that are raised in the first half of the Parmenides. (Look here to follow out the text, if you wish.) But it's within the first group, the sort that 'is not worthy of scrutiny', that one finds the eristic argument that Rickless is appealing to, that "there are many 'me's' , and even contrary ones, when [someone] treats me, who am one and the same, as tall and short, heavy and light, and endless other such things". The passage hardly gives us grounds for holding that Plato was sympathetic to such arguments or accepted Rickless' key premise.

2. But even if Plato was endorsing the principle in the Philebus (which I don't grant), why would we be justified in presuming that he endorsed it when he was putting forward, as Rickless calls it, the "Middle Period Theory of Forms"? That seems an unjustified leap.

3. But even if one could infer that the principle was at work in Plato's "Middle Period Theory of Forms", because of something said in the Philebus (which I don't grant), it's not clear that the principle would be relevant, when the many predicates involved are all the same! On Rickless' understanding of the TMA, each Form of Large participates in an infinite number of Forms of Large, and, because of this, multiple predicates become true of each Form. However, each of these multiple predicates is, simply, 'large'. Thus, on Rickless' interpretation, the important point is that we can say of the first Form, as well as each of the others: "This is large, and large, and large, etc." ad infinitum. But it's at least not clear that our being able to assert multiple predicates in this way would imply multiplicity, on the same grounds that saying 'tall' and 'short', or 'heavy' and 'light', might be taken to imply multiplicity. (Oh, sure, one might want to maintain that each predication of 'large' is distinct: ‘This is Large1, and Large2, and Large3, etc.’ But then that argument has to be implicit in the passage as well!)


Anonymous said...

is it possible to read the whole Rickless' article?

Michael Pakaluk said...

I obtained it online from JStor. If you're unable to do that, then write to me, and I'll e-mail you my copy as a PDF attachment. It's an interesting piece and very much worth studying, I think.

Sam Rickless said...

I really like these objections. Each one seems better than the last. But I still don't buy them. Here's why.

(1) I affirm, as part of my reconstruction of the TMA, that Plato endorses the claim (call it (C)) that something of which many things are (truly) predicated is itself many. I find evidence that Plato endorsed (C) in the post-middle period in the *Philebus* (at 14c-e). You say now that the relevant *Philebus* passage is one in which Plato describes (C) as "childish", "trivial", and "not worthy of scrutiny". But I think we should be careful not to overinterpret here. What Socrates describes as "childish" and "commonplace" at 14d is the claim that PROTARCHUS is one and many (one, presumably because he is one of many human beings, and many, because many predicates are true of him). And at 14e, Socrates also finds "unworthy" the "quibble" that arises from the fact that a PERSON is one and many (one, presumably because, as above, he is one of many, and many, because he has many limbs and parts). It does not follow from this, I claim, that Socrates finds childish (unworthy, commonplace, or what have you) the claim that a FORM is both one and many. In fact, at 14e5-15a2, Socrates explicitly announces that the kind of one-many puzzle that has NOT yet become commonplace concerns something that "is not taken from the things that come to be or perish, as we have just done in our example".

Here, then, is how I read Philebus 14c-15c. Socrates tells us, on the one hand, that one-many puzzles concerning SENSIBLES are commonplace and childish, but, on the other, that one-many puzzles concerning FORMS are not commonplace and far from childish. The latter puzzles are, as Socrates puts it at 14b8-15c2, "problems of the one and many...that cause all sorts of difficulties if they are not properly settled, but promise progress if they are".

The relevance of this passage to the TMA is this. The TMA, as I read it, is meant to establish that each form of largeness generated by the regress is many because it has been pluralized by its many predicates. But OM, which contributes to the regress, also establishes that each form of largeness is one because it is one *over* its many participants. The problem, then, is that the premises of the TMA entail that each form of largeness generated by the regress is both one and many. This is a one-many puzzle about FORMS, not a one-many puzzle about SENSIBLES. Consequently, if we are to take Philebus 14c-15c seriously, we should read Plato as recommending there that we take the TMA (as I have reconstructed it) seriously. This involves taking seriously the premise that a FORM is pluralized by its many predicates, even as one dismisses as commonplace the claim that a SENSIBLE is pluralized by its many predicates.

(2) Even if I am right about the Philebus passage, you claim that it is an "unjustified leap" to attribute to the Socrates of the *Parmenides* (or to the Socrates of the middle dialogues) a principle that is taken seriously by the Socrates of the *Philebus*. I imagine you think this because there are two different dialogues in play here.

In reply, I admit that I am making an inference here, but I deny that the inference is an "unjustified leap". The entire tenor of Philebus 14c-15c is vritually identical to the tenor of Socrates' speech in the *Parmenides*. In the speech Socrates finds COMMONPLACE the claim that HE is both one and many (one because he is one among many, many because he has many parts). As he puts it there (129c4): "But if someone should demonstrate that I am one thing and many, what's astonishing about that?" This is echoed at Philebus 14c-d and 14e (see above). In the speech Socrates finds FAR FROM COMMONPLACE the claim that FORMS are both one and many. As he puts it there (129c2-3): "If [someone] could show that the kinds and forms themselves have in themselves these opposite properties [such as one and many], that would call for astonishment." This is again echoed at Philebus 14e-15c (see above). It is frankly inconceivable to me that Plato did not see the connection between these dialogues when he wrote the *Philebus* (which, many acknowledge, post-dates the *Parmenides*). So if the Socrates of the *Philebus* thinks that forms are pluralized by virtue of having many predicates, and Plato is virtually quoting Socrates' speech from the *Parmenides* in the relevant portion of the *Philebus*, then it is far from an "unjustified leap" to attribute to the Socrates of the *Parmenides* the claim that forms are pluralized by virtue of having many predicates.

(3) You say that, even if Plato accepts that a form is pluralized by its having many predicates, there is only one predicate at issue in the TMA, namely "large". This poses a problem for me, and I answer it as follows. The TMA establishes a hierarchy of forms of largeness, L1, L2, L3, L4, etc. such that L1 partakes of L2, L3, L4, and so on, L2 partakes of L3, L4, and so on, etc...In short, every form in the sequence partakes of the forms that appear later in the sequence. This means that L1 partakes of L2, partakes of L3, partakes of L4, and so on. Thus, many predicates are true of L1: "partakes of L2", "partakes of L3", "partakes of L4", etc... And similarly for all the other forms in the sequence. Thus, it is a consequence of the TMA assumptions that each form in the hierarchy has many DIFFERENT predicates.

I could also answer it by giving up on the idea that the TMA assumes that a form is pluralized by its predicates, and insisting that the TMA assumes instead (see previous comments) that a form is pluralized by its parts. The reasoning would go as follows. OM, SP, and NI entail that L1 partakes of L2, L3, L4, and so on. But what is the relevant conception of partaking governing the TMA? Arguably it is the same conception of partaking that is at issue in the Whole-Part Dilemma (which comes just before the TMA), namely that for X to partake of Y is for Y (or a part of Y) to be in (i.e., to be a part of) X. If this is correct, then it follows from the fact that L1 partakes of L2, L3, L4, etc.. that L2 (or part of L2), L3 (or part of L3), L4 (or part of L4), etc... are all parts of L1. Hence, L1 has many parts. If a form is pluralized by its parts, then it follows directly that L1 is many. Mutatis mutandis for L2, L3, L4, etc... So even if you are right that there is only one predicate at issue in the TMA, there is good reason to believe that Plato would still want to insist that the assumptions of the TMA are sufficient to conclude that each form generated by the regress is infinitely many.