Quantification in ordinary language and proof theory

Michele Abrusci

Fabio Pasquali

Christian Retoré

pp. 185-205

in: Le Kantisme hors des écoles kantiennes, Philosophia Scientiae 20 (1), 2016.

Abstract

This paper gives an overview of the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this usual general framework represents a departure from empirical linguistic data. We briefly sketch a different idea for proof theory which is closer to the language itself than standard approaches in many aspects. We stress the importance of Hilbert’s operators—the epsilon-operator for existential and tau-operator for universal quantifications. Indeed, these operators are helpful in the construction of a semantic representation which is close to natural language in particular with quantified noun phrases as individual terms. We also define guidelines for the design of proof rules corresponding to generalized quantifiers.