Free Logic and Quantification in Syntactic Modal Contexts

Abstract

The field of modal logic spans a very wide range of philosophical notions and motivations, with the result that to construct any particular formal system will require that a number of choices be made between alternative intuitions and goals. This is particularly true of quantified modal logic, since here disparate modal notions combine with alternative interpretations of quantification to produce a labyrinth of technical possibilities. Unfortunately, even though the number of possibilities is large, the theoretical ingredients seem to interact in ways which force internal compromises. For example, choices in favor of standard first-order logic conflict with modal intuitions about assertions involving possible objects, while the “primary” reading of necessity as logical validity runs up against the problem of not being recursively axiomatizable.