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hal-00607678, version 1

Quantification in ordinary language

Michele Abrusci 1, Christian Retoré (, http://www.labri.fr/perso/retore/) 2, 3

14TH CONGRESS OF LOGIC, METHODOLOGY AND PHILOSOPHY OF SCIENCE (2011) http://www.univ-nancy2.fr/poincare/documents/CLMPS2011ABSTRACTS/14thCLMPS2011_C2_Abrusci-Retore.pdf

Abstract: We firstly show that the standard interpretation of natural quantification in mathematical logic does not provide a satisfying account of its original richness. In particular, it ignores the difference between generic and distributive readings. We claim that it is due to the use of a set theoretical framework. We therefore propose a proof theoretical treatment in terms of proofs and refutations. Thereafter we apply these ideas to quantifiers that are not first order definable like "the majority of".

  • 1:  Università degli studi Roma III
  • Università degli studi Roma III
  • 2:  Laboratoire Bordelais de Recherche en Informatique (LaBRI)
  • CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II
  • 3:  SIGNES (INRIA Bordeaux - Sud-Ouest)
  • INRIA – CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – Université Michel de Montaigne - Bordeaux III – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)
  • Domain : Mathematics/Logic
    Humanities and Social Sciences/Philosophy
    Humanities and Social Sciences/Linguistics
 
  • hal-00607678, version 1
  • http://hal.archives-ouvertes.fr/hal-00607678
  • oai:hal.archives-ouvertes.fr:hal-00607678
  • From: Christian Retore <>
  • Submitted on: Sunday, 10 July 2011 19:35:37
  • Updated on: Sunday, 10 July 2011 21:20:35