A remark on collective quantification

Journal of Logic, Language and Information 17 (2):131-140 (2008)
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Abstract

We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective quantification in natural language.

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2009-01-28

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Jakub Szymanik
University of Amsterdam

References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Oxford, England: Clarendon Press.
Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Oxford, England: Oxford University Press UK.

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