In 'Against Vague Existence', Ted Sider argues that our quantifiers cannot be vague, because it is impossible to characterize semantic vagueness in our quantifiers in the usual way; that is, in terms of multiple admissible precisifications. Sider considers as a test case whether it could be indeterminate, due to vagueness in the existential quantifier, whether the following was true:
(E): Ex (x is composed of the F and the G).
Sider claims that the ‘familiar model’ for spelling out how such indeterminacy comes about would apply to this case as follows:
(P1): ‘E’ has at least two precisifications, call them E1 and E2. There is an object, x, that is in E1’s domain but not in E2’s domain, and which is composed of the F and the G. Thus, (E) is neither definitely true nor definitely false.
But, as Sider points out, ‘the defender of vague existence thinks that it is not definitely true that there is something composed of the F and the G ... She will therefore not make this speech’ (p. 139).
Sider proceeds to offer three options to the defender of vague existence: rejecting the need to non-vaguely describe the precisifications, using vague quantifiers to non-vaguely describe them, and finding non-quantificational non-vague language to describe them. None of these is my preferred way of resisting Sider’s argument. Nor do I wish to resist (here) his two presuppositions: that the indeterminacy of (E) would have to be semantic (as opposed to ontic), and that this means we need to explain it in terms of multiple admissible precisifications of the existential quantifier.
Instead, I propose we investigate how much can be achieved through paying careful attention to scope in describing the relevant precisifications. Instead of (P1) above, perhaps we can appeal to:
(P2): ‘E’ has at least two precisifications. On the first precisification, there is an object, x, which is composed of the F and the G. But on the second precisification, there is no such object. Thus, (E) is neither definitely true no definitely false.
Note that, now, the existential quantifiers appearing in the account of why (E) is neither definitely true nor definitely false occur within the scope of the operators ‘on the first precisification’ and ‘on the second precisification’. Hence there is no need for any metalanguage commitment to an object which is composed of the F and the G.
(P2) seems to do what Sider requires: it talks about two precifications for ‘E’, and explains what it is about these two precisifications which results in the indeterminacy of (E). So what’s wrong with (P2)?
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4 comments:
Thanks for posting this, Carrie. My response is that what you said doesn't count as "describing" the precisifications (though I certainly was not clear enough about what I meant by that in my paper). You speak of what is true "on a precisification". Now, to say "on presification P, S" is to say that P counts S as true. But I want to know: *how* does P count S as true? What kind of semantic value is P, and what about P makes S count as true relative to it? When we're dealing with 'bald', it's easy to answer these questions: the presifications are sets, and for a precisification P to count a certain person as bald (i.e., for it to be true that: on P, the person is bald) is for the person to be a member of P. What I'm demanding is that one be able to tell that kind of story when the precisifications are precisifications of the quantifiers.
Incidentally, my own conception of how people like Hirsch should answer this sort of challenge is to deny the need for "stating" or "describing" the precisifications. Hirsch should just say that there exists a certain space of quantifier meanings. What are the points in this space? The only answer one can give are: things with respect to which quantificational sentences are true or false. Not wholly satisfying, but the best he can do, I suspect. I describe this in more detail in a paper I recently posted on my web site: http://fas-philosophy.rutgers.edu/sider/papers/neofregeanism_and_quantifier_variance.pdf
Thoughts?
Ted Sider
Thanks - that does help make clearer what you're after and why you think we can't get it. However, I'm not sure how the fact that we can't get *that* could be taken to show that the quantifiers are not vague.
I wonder whether there is an analogy between the difficulty of doing what you describe and the difficulty of saying what it would be for all quantification to be restricted.
My instinctive response to the latter problem is to say it's one of expressibility, and therefore doesn't show that the thing we're having trouble expressing is false. I have a similar instinctive response to your argument.
Hi Carrie,
that's a neat comparison to the thing about restricted quantification. I have your reaction to that argument too (though I'm a fan of unrestricted quantification), but not to my argument against vague existence (surprise, surprise). The argument against the view that all quantification is restricted, at least as put forward by Williamson, points out a difficulty with describing the view *in general*. Whereas my argument is trying to show that we don't really have a sense of what the precisifications of quantifiers are supposed to be at all. It's a much more basic problem. Still, I do agree that my argument doesn't show that the quantifiers couldn't have precisifications.
Note that my argument's ambitions were fairly modest; it was supposed to show that if quantifiers do have precisifications, the situation is at least somewhat unlike that of other familiar vague terms (which have precisifications whose natures are unproblematic and which can be easily "described".) I probably overstated my case in the paper, making it sound like quantifier precisifications would be NOTHING like familiar precisifications.
Interesting story you got here. It would be great to read a bit more about this matter. Thank you for posting this material.
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