Saturday, December 09, 2006

The Problem of the Many, Supervaluations, and the Sorites

(Cross-posted at The bLOGOS.)

These days I am revising this paper, once again :-(! There I argue against the so-called ‘supervaluationist’ solution to the problem of the many, which is often the one favored by fellow defenders of the view of vagueness as semantic indecision.

In a nutshell, I claim that the feature of precisifications that such a solution requires—selecting just one of the many candidate-mountains in the vicinity of paradigmatic mountain Kilimanjaro—render them inadmissible. In my paper I focus on the penumbral truth that if something is a paradigmatic mountain, and something else is very similar to the former in that which is required for something to be a mountain, then the latter is also a mountain. One other main difficulty, emphasized by McGee 1998, is that such precisifications fail to preserve clear cases of application of the predicate, in that there is no entity that is determinately a mountain—at least, on standard ways of characterizing what it is for something to satisfy a 'determinately'-involving matrix.

In Williams 2006, Robbie claims that, in virtue of nothing determinately satisfying ‘is a mountain,’ the solution undermines the explanation offered by defenders of the view of vagueness as semantic indecision such as Keefe 2000 of the persuasiveness that the (false) sorites premise certainly has. According to her,

“Our belief that there is no true instance of the quantification gets confused with a belief that the quantified statement is not true. … The confusion … is a confusion of scope, according to whether the truth predicate appears inside or outside the existential quantifier” (Keefe 2000, 185).

Insofar as I can see, however, the difference in scope in truth- (or determinate-) involving existential statements appealed to here is compatible with nothing determinately satisfying ‘is a mountain’—disturbing as the latter might be for other reasons, of course.


Anonymous said...

Hi dan.

The worry isn't that the sentence that Keefe uses to explain the seductiveness of the sorites--- ~(Ex)D(Mx&~Mx')--- is false. It's that it's trivially true and thus can't explain the data. E.g. we find the major premise of a standard sorites series on 'mountain' compelling. Not so the same sentence in application to the two element series consisting of kilimanjaro and small hummock. But Keefe's sentence has the same value in each case. So it doesn't explain our contrasting attitudes to the two cases.

all best

Dan López de Sa said...

Hi Robbie! Thanks very much for your response.

I take your point here is the one you also make in your paper, in the paragraph starting with “An even more serious consequence of the ‘sane’ view is that…” (Williams 2006, p. 6). This I think is closely connected to the McGee’s point about the disturbance of having entities in the “clear” region and not only those in the “borderline” borderline wrt ‘is a mountain,’ and I fully agree.

I was concerned, however, about the point you make before that in the previous paragraph: “This result, if sustained, completely undermines the confusion hypothesis outlined earlier” (ibid), i.e., Keefe’s.

I took them to be two separate independent points, hence my worry. Now I think that maybe you see the first as part of the second, “McGeeian” concern, is this right?

Dan López de Sa said...

Apologies! I was so far relying on the version available from your website, which, as you warn, is not the ultimate one. I’ve now just checked the published PAS version, and the relevant passages read somehow differently, in a way that clarifies, I think, my confusion.

There are two ways, you say (p. 415), in which the result undermines the confusion hypothesis. The first way is probably one you would not use against the confusion hypothesis as defended by Keefe, given that for her the confusion is one about scope, not about interaction between ‘determinately’-free and -involving fragments. The second way is the one you mention in your response here, connected with the general “McGeeian” worry, but specifically addressing consequences involved in the confusion hypothesis, and fairly so. If this is right, then I fully agree. Sorry if I’ve been too slow!

Robbie said...

Hi Dan,

Right, I'd forgotten the modifications. (Actually, I can't get access to the published version from here).

As I read myself in the earlier version, though, I still think I'm right! A few points:

(1) Keefe formulates the confusion hypothesis in terms of the scope of "is true that". She says we confuse "~(Ex) True[Mx&~Mx']" and "True[~(Ex)(Mx&~Mx')]". I tend to formulate it in terms of scope of a "determinately" operator: "~(Ex) Determinately[Mx&~Mx']" with "Determinately[~(Ex)(Mx&~Mx')]". I was taking these to be notational variants. (In fact, the only way I see to give an exact treatment of "it is true that", allowing for quantification in, etc, is just to give it the same semantics as "determinately"!) Can you expand on why you think it makes a difference? I'm just not seeing it.

(2) I am assuming more than Keefe explicitly commits herself to, I think. I'm assuming that the confusion here is systematic: if we are apt to confuse "~(Ex) True[Mx&~Mx']" and "True[~(Ex)(Mx&~Mx')]", we'll also be apt to confuse "(Ex) True[Mx&~Mx']" and "True[(Ex)(Mx&~Mx')]"; and also "(Ex) True[Mx]" and "True[(Ex)(Mx)]". I suppose you might think there's something very special about the form of words used in the major premise of the sorites that induces confusion, not present in the latter cases. But surely that's totally implausible! So I was taking it that the confusion *has* to be a systematic one.

(3) I then had two arguments that confusion hypothesis is in tension with the supervaluational treatment of POM. The first point is supposed to be a matter of false predictions. Given the above, when we utter "there are mountains", we should feel this to be false, since we are (scope) confused and hear it as committing us to: "(Ex) True[Mx]". The second point (the "even worse" one) is that not only does the confusion hypothesis generate false predications in this way, but it also means that it doesn't explain the contrastive facts about our intuitions in the sorites case vs. the clear-cut-off series.

Does McGee talk about the confusion hypothesis at all? I didn't see that in his stuff at all. The way it went when I was writing this stuff, was that I noticed that POM would render quantification into "definitely" contexts trivial in relevant cases, and then cast around for theoretical costs that this might bring. Issues with the confusion hypothesis seemed the way to bring this out. I later read the McGee, and saw that he noted the fact that POM will trivialize quantification-in. But I didn't think he really put any weight on that observation (of course, he's got all sorts of other interesting things to say about supervaluations and POM in that paper).

Dan López de Sa said...

Hi Robbie!

Re (1): Yes, I was also assuming 'it is true that' and 'determinately' to be here interchangeable. My point was to distinguish (i) the claim that we confuse 'determinately'/'it is true'-involving fragments with 'determinately'/'it is true'-free fragments from (ii) the claim that we confuse different readings due to scope interaction between 'determinately'/'it is true' and (say) the existential quantifier within 'determinately'/'it is true'-involving fragments.

Re (2): Yes, I also agree that plausibly the confusion phenomenon would be more general that just targeting cases like those involved around the Sorites premise.

Re (3): Your first point is the only place where perhaps we disagree, and I take it to be really minor. You say: "Given the above, when we utter "there are mountains", we should feel this to be false, since we are (scope) confused and hear it as committing us to: "(Ex) True[Mx]."" But I was taking the confusion hypothesis as defended by Rosanna to consist in the confusion (i) of (1). For your first point to stand you need, in addition to the above, the generality of (2) to be large enough and also the further confusion (ii) of (1) (so as to confuse first 'there are mountains' with 'deffo there are mountains' and then confuse this with 'there are deffo mountains').

Re McGee: Yes, again, I agree. McGee didn't put much weight on his observation, although it does suffice for the disturbing consequence that both "clear" and "borderline" cases turn out to be borderline wrt 'is a mountain.' And I think this is fairly and vividly emphasized in your piece, in connection with the issues involved around the confusion hypothesis.

Anonymous said...

Hi Dan! Sounds like we're pretty much in agreement on much of this stuff.

I guess, if you think that by uttering S you're committing yourself to it's truth, then to hear "there are mountains" as committing one to deffo there are mountains, is no confusion. But this is quibbling: there are two moves here, whether or not we think they both equally confusions!

I suppose I'm still not seeing an "out" for Keefe, though (supposing she wanted to have a supervaluationist treatment of the problem of the many). Suppose her story is supposed to explain why we intuitively classify the major premise as true: by confusion the proposition that it is true that p with one where the truth operator takes narrow scope. Then it seems that exactly parallel reasoning with "p"="there are mountains" should lead one to the same result. Anyone who wants to argue that the confusion hypothesis doesn't give false predictions in this case has the burden of pointing to where the parallel breaks down (no matter how, in detail, their story goes).

Happy xmas!

Dan López de Sa said...

Yeah, loads of agreement, and the remaining disagreement is probably not only minor, but tiny! Still... ;-)!

I take your last comment to claim the plausible generality of (2) above to be in effect large enough as to include confusion between ‘deffo there are mountains’ and ‘there are deffo mountains.’ Granted, at least for the sake of discussion. Still, you would need the further confusion (ii) of (1) above in order for your first point to stand, no?

In any case, minuscule disagreement. More so when I am fully convinced by your second point (and my related different consideration) that there is really no “out” for Keefe, is she really wants a so-called "supervaluationist" solution to the problem of the many, as she seems to do in her book.

Hope you enjoy holydays!