In Defense of the Simplest Quantified Modal Logic

Abstract

By combining the laws of classical quantification theory with the modal propositional logic K in the most direct manner, one produces the simplest Quantified Modal Logic. The models of this simple QML relativize predication to possible worlds and interpret the quantifiers as ranging over a single, fixed domain. But simple QML has many controversial features, not the least of which are that it validates the Barcan formula and appears to require quantification over possibilia. Whereas possibilists employ distinctions that render these features of simple QML unobjectionable,I actualists find the distinctions and the controversial features difficult to accept. Many thought that Kripke-models, with their varying domains and restricted quantifiers, promised to rid QML of the Barcan formula, quantification over possibilia, and other objectionable features we haven't yet described. Unfortunately, Kripke-models themselves have features at which actualists balk, and so these philosophers have had to modify (our understandingo f) Kripke-modelst o find an acceptable QML.