A Remark on Collective Quantification

Authors:
Juha Kontinen;Jakub Szymanik
Affiliations:
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland 00014;Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands and Institute of Philosophy, Warsaw University, Warsaw, Poland
Venue:
Journal of Logic, Language and Information
Year:
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.