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Thursday, October 26, 2006

Schlenker on Quantifiers

It is widely agreed that the truth-conditions for sentences with quantified noun phrases must reflect our use of them. If we are talking about my logic class, and I say 'some student failed', then my utterance of 'some student failed' may be false even if some student in the universe failed. The question is, how do we account for the apparent context-sensitivity of quantified noun phrases?

Jason Stanley and Zoltan Szabo (2000) argue that there are implicit indexical variables in the sentence structure. Such variables are either bound by higher operators or assigned values by context.

Philippe Schlenker (forthcoming) has a different proposal. To see what the proposal is, let us briefly look at how quantifiers were treated pre-Stanley/Szabo and pre-generalized quantifier theory. Here is how we used to give truth-conditions for existentially quantified sentences.

'Ex(Fx & Gx)' is true at a sequence of evaluation s iff for some individual d in the domain fixed by the sequence, 'Fx & Gx' is true at s for the assignment of d to x.

For example, 'some boy is hungry' is true at s iff for some individual d in the domain, 'x is a boy and x is hungry' is true at s for the assignment of d to x.

Schlenker suggests that we make the following amendments.

'Ex(Fx & Gx)' is true at s iff for some individual d in the domain satisfying certain conditions determined by an accessibility relation R, 'Fx & Gx' is true at s for the assignment of d to x.

Suppose I utter 'some student failed' and intend it to mean that some student in my logic class failed. Treating the tensed verb as if it were tenseless, 'some student failed' is true at the domain of individuals assigned by the sequence of evaluation iff for some individual d satisfying 'x is in Brit's logic class' at the domain for the assignment of d to x, 'x is a student and x failed' is true at the domain of individuals for the assignment of d to x.

Note that all of this is stated in the meta-language, just as we do it in modal logic. So, context determines an accessibility relation, and the accessibility relation determines the conditions an individual in the domain must satisfy for it to be relevant in the context. So, on Schlenker's proposal, quantified noun phrases have the same semantic values in all contexts: they are not context-sensitive, and there are no implicit domain variables in the sentence structure of sentences with quantified noun phrases. What varies with context is the relevance relation (or accessibility relation) and so also which individuals in the domain of the sequence are deemed relevant.

I think Schlenker's suggestion is very interesting. Only drawback: it seems to presuppose pre-generalized quantifier theory, and so I do not see at this point how it would deal with determiners such as 'most', 'more than half' and the like.

References:
Schlenker, P. forthcoming. "Ontological Symmetry in Language: A Brief Manifesto", Mind & Language.
Stanley, J. and Szabo, Z. 2000. "On Quantifier Domain Restriction", Mind and Language 15: 219-261.

(Thanks to Francois Recanati for recommending Schlenker's article)

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