Monday, December 11, 2006

Vagueness and Supervaluationism

One of the standard objections to supervaluationist views concerning vagueness is that if they are true, then there are true existential generalizations that lack true instances and true disjunctions none of whose disjuncts are true. However, I wonder if this is an essential feature of supervaluationist views. In particular, mightn't a supervaluationist say the following:

a. An atomic sentence S is true iff it is true under all precisifications, and
b. A non-atomic sentence S is true iff there are some true atomic sentences that entail it?

Anyway, I know this isn't worked out very well or anything, but it does seem to me that making this move allows the supervaluationist to avoid one of the major objections to his view. What do the rest of you think? And do you know if a move like this has been made by any supervaluationists in the literature?

5 Comments:

Blogger Chris Tillman said...

Might Bruan and Sider accept your (a) and (b)? Also, though it has been mentioned as a liability, some supervaluationists (like Fine and van Fraassen (I think)) have touted the preservation of e.g. LEM as true (supertrue) as a virtue of their view. So I'm not sure whether such supervaulationists would want your "help". One key concern would be viability of the resultant view as a response to the sorities in all its flavors. Here would you follow Bruan/Sider or did you have something else in mind?

1:18 PM  
Blogger avwake said...

On the view you're suggesting, what do we say about universally quantified claims?

2:45 PM  
Blogger Joshua said...

Does it seem too ad hoc-y for greg to simply say that LEM is true. What is so special about LEM being supertrue. I thought that what F and VanF liked about the fact that LEM is supertrue is that it preserved out intuitions that LEM is true. But now Greg can preserve those intuitions too.

Also, how about this as an amendment to the view.

For any S, if S is atomic, then S is true iff it is supertrue.

For any S1 and S2, 'S1 and S2' is true iff S1 is true and S2 is true.

etc etc.

for any PHI, AxPHIx is true iff for any object o, PHIo is true.

This would solve Andrew's worry. This method uses the same idea that Greg had that supertruth applies to atomic sentences and something else is going on with non-atomic ones. But it also takes care of Andrew's worry. It is a strange semantics for vague sentences. But it gets the results we would like (I think).

I wonder what kind of things such a view would say about higher order vagueness.

7:23 PM  
Blogger rock* said...

Chris,

I'm not sure about the supposed parallels you draw between the view I am accepting and Braun and Sider's view. I would have thought that Braun and Sider take a to be false because they hold (I thought):

B&S: For all sentences S, if S contains a vague expression, then S lacks truth value (and so is neither true nor false).

Thus, although 'Jesse Ventura is bald' is an atomic sentence that is true under all precisifications (and therefore true according to (a)), because Braun and Sider accept (B&S) they will hold that 'Jesse Ventura is bald' lacks truth value. Thus, Braun and Sider reject (a).

5:55 AM  
Blogger rock* said...

[Whoops! When I wrote 'accepting' in my previous comment, I meant to write 'proposing'. I do not accept the view proposed in my post, since I don't know enough about vagueness and I'm not sure how attractive I find supervaluationism anyway. I'm merely presenting the view as an option for supervaluationists.]

Chris wonders about LEM and Andrew asks about what someone who accepts the view I am suggesting will say about universally quantified claims. Surprisingly, these worries are connected. Strictly speaking, my suggestion (b) concerning when non-atomic sentences are true tells us that every negation and universally quantified sentence is not true because no atomic sentences entail a negation or a universally quantified sentence. For this reason, I think that someone who is inclined towards something like the view I proposed ought to give recursive truth conditions for non-atomic sentences of the sort suggested by Joshua.

Now the supervaluationist of the stripe I am suggesting has options. For instance, he or she may accept the following truth conditions for negation:

(N1) For any S, 'not-S' is true iff S is not true.

If he or she does this, then he or she can preserve excluded middle, since for any sentence atomic sentence S, either S is supertrue or it is not. If S is supertrue, then (by (a)), it is true. On the other hand, if S is not supertrue, then (by (a) and (N1)), not-S is true.

Unfortunately, one who thinks that (N1) gives the correct truth-conditions for negation will not be able to hold (for instance) that in a standard Sorites series for 'bald', there are some cases in which neither 'He is bald' nor 'He is not bald' come out true. So, one who is a Greg-flavored supervaluationist might instead accept:

(N2) For all sentences S, 'not-S' is true iff S is false,

where an atomic sentence is false iff it is superfalse (i.e., true under no precisification). But such a supervaluationist will have to say that 'He is bald or he is not bald' is not true in some cases in a standard Sorites series and so must reject LEM.

(I think this is right. Do any of you have any doubts? Am I confusing the law of excluded middle with some other principle?)

6:28 AM  

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