Modality and Logic

Abstract

The chapter begins with a brief historical survey of the development of the formalization of modalities in logic in the 20th century, focusing on the work by Lewis, Carnap and Quine. Then what seems to be one of the main limitative results on modal predicates, Montague’s theorem, is presented and critically discussed. It is shown how such paradoxes can be avoided by placing constraints on the interpretation of the non-semantic terms. To this end a construction by Gupta is extended to the setting of multiple modal predicates. Furthermore it is shown that the operator approach is also affected by semantic paradoxes if the expressive strength of the framework is increased. It is then argued that such greater expressive strength is desirable from a philosophical perspective because it is required to capture some important features of the modal notions from natural language.