Journal of Philosophical Logic

, Volume 33, Issue 3, pp 237-260

First online:

A Modal Sortal Logic

  • Max A. FreundAffiliated withDepartamento de Filosofía, Universidad Nacional Apdo

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An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.

conceptualism count nouns modal logic non-standard semantics for predicates sortals