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Journal of Philosophical Logic

, Volume 31, Issue 6, pp 499–526 | Cite as

Standard Quantification Theory in the Analysis of English

  • Stephen Donaho
Article
  • 41 Downloads

Abstract

Standard first-order logic plus quantifiers of all finite orders (“SFOLω”) faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOLω models. The typed structure of SFOLω models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is removed. The models of this class permit definitions of the quantifiers which allow a desirable flexibility in fixing the domain of quantification. Certain SFOLω type restrictions are thereby avoided. The resulting models of English validate all of the standard first-order logical truths and are free of the four deficiencies of SFOLω models.

quantification theory quantifiers semantics type-free logic type theory 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Stephen Donaho
    • 1
  1. 1.Normandale College and General CollegeUniversity of MinnesotaMinneapolisU.S.A.

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