Can majority be supervalued?

Katarzyna Kijania-Placek

pp. 67-75

in: Jaakko Hintikka, Tadeusz Czarnecki, Tomasz Placek, Artur Rojszczak (eds), Philosophy and logic in search of the Polish tradition, Berlin, Springer, 2003

Abstract

This paper addresses the question of whether it is possible to build a superval-uational semantics for the language of first order predicate logic with an added binary majority quantifier in such a way that a counterpart of the monotonicity condition is satisfied. I will show that this is not possible in the general case (for all partial models) and will propose a definition of a class of semipartial models for which it can be done. These remarks can be generalized at least to all binary quantifiers that are not left-monotone.