Quantification in ordinary language: from a critique of set-theoretic approaches to a proof-theoretic proposal
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19 juillet 2011
- handle: 10670/1.94j0eq
- hal: hal-00607678
- ARXIV: 1107.1883
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info:eu-repo/semantics/altIdentifier/arxiv/1107.1883
info:eu-repo/semantics/OpenAccess
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Michele Abrusci et al., « Quantification in ordinary language: from a critique of set-theoretic approaches to a proof-theoretic proposal », HAL-SHS : linguistique, ID : 10670/1.94j0eq
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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".