Wednesday, July 12, 2006

Quine and Vague Existence Again

The Joint Session was fun, although it was a shame that lots of the accommodation was so far from the conference venue - strolling in across the common was nice in the morning sunshine but at 2am it was less appealing to walk back.

Like last year, I thought the open sessions were in need of some degree of refereeing. Still, I very much enjoyed giving my paper in one of them, on ontological commitment and vague existence. The purpose of this paper (which is a much improved version of this post) is to present the following argument and then wonder what should be done about it:

1 (Quinean premise): One is committed to Fs iff there are Fs among the range of the quantifiers appearing in one's best theory.
2 (Assumption): We think it's a vague matter whether there are any Fs (and that's all we have to say on the question of whether Fs exist or not).
3 (From 2): We are not committed to there being any Fs.
4 (Contraposing on the right-to-left direction of 1, then MPP using 3): There are no Fs among the range of the quantifiers appearing in our best theory.
5 (Premise): Our quantifiers are precisely those which appear in our best theory.
6 (From 4 and 5): There are no Fs among the range of our quantifiers.
7 (From 6): We can truly assert 'There are no Fs'.
8 (From 7, disquoting): It is not a vague matter whether there are any Fs: it is settled that there are no Fs.
9 (From 2 and 8): We are mistaken.
10 (Discharging 2, using 9): If we think it's a vague matter whether there are any Fs (and that's all we have to say on the question of whether Fs exist or not), then we are mistaken.

Some members of the audience suggested that rejecting contraposition was the best thing to do, a response I've not come across before. (Although as Daniel pointed out to me later, we really only need modus tollens. But maybe the people who'd want to reject contraposition would want to reject MTT too, for similar reasons?)

5 comments:

Istvan said...

Maybe we can deny (3), and say that all that follows from (2) is that it is a vague matter whether we are committed to there being any Fs. Then (7) would be replaced by: "we can truly assert 'It is a vague matter whether there are Fs'", which is incompatible with (8).

Carrie Jenkins said...

Hi Istvan,

Yes, that seems to be one of the popular responses (in fact, probably the most popular so far). For myself, I think it is hard to deny that attributing indeterminacy is a paradigm way of remaining *non*-committal. And I'm not quite sure what vague commitment is supposed to be! But you aren't alone in thinking that's the way to go.

Robbie said...

Just on the contraposition point: dropping contraposition is a familiar part of the Lewis-Stalnaker conditional logics: it's got lots of intuitive counterexamples. But dropping modus tollens isn't, and doesn't, as far as I know (though maybe you could use the McGee anti-modus ponens stuff to this effect).

If people get worried about that, why can't you just restate the argument without using conditionals, but just conjunctions, disjunctions and negation though? (Equivalently, just insist that you're using material conditionals). Revising the logic of those babies looks a much bigger bullett...

Or were you in the presence of those nasty australians who want to mess around even with the mat cond?

Carrie Jenkins said...

Hi Robbie,

Yeah, much as it distresses me, I think the material conditional is supposed to be up for this sort of malarkying too on this response. (John Broome suggests something like this as a response to Evans in his analysis paper from 1984.)

I should say that the people who proposed this response on Sunday weren't Australians!

istvan said...

There is a more sophisticated reply, I think, which would go as follows.

Premise (5) creates a context in which all we assert or have asserted so far has to be compatible with our best theory. But supposedly it is part of what makes our theory the best one that it is precise (e.g. for Quine it is microphysics). If this is so, then (2) is not assertible in this context, because we are not supposed to have vague matters if speaking from within our best theory.