Quantification in ordinary language

Details Quantification in ordinary language Quantification in ordinary language

2011-07-10

arxiv.org/abs/1107.1883v1

Mathematics

Logic

14TH Congress of Logic, Methodology and Philosophy of Science, Nancy : France (2011)

Scientific paper

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".

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