Some proof theoretical remarks on quantification in ordinary language

Abstract

This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for a different view based on proof theory, which on many aspects gets closer to the language itself. We stress the importance of Hilbert's oper- ator epsilon and tau for, respectively, existential and universal quantifications. Indeed, these operators help a lot to construct semantic representation close to natural language, in particular with quantified noun phrases as individual terms. We also define guidelines for the design of the proof rules corresponding to generalised quantifiers

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References found in this work

The Development of Logic.William Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press.
Reference and Generality.P. T. Geach - 1962 - Ithaca: Cornell University Press.
The Development of Logic.William Kneale & Martha Kneale - 1962 - Philosophy 40 (151):79-83.
The Development of Logic.Benson Mates - 1962 - Journal of Symbolic Logic 51 (2):476.

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