On McKinsey's syntactical characterizations of systems of modal logic

Abstract

In [1] McKinsey gives a method of defining possibility in terms of “substitutions”, or transformations of one sentence into another. Roughly, the motivation is that a sentence be possible if a sentence of “like form”, i.e. a transformation of it, is true.The purpose of this paper is to show that the two systems given in [1], shown by McKinsey to be at least as strong as Lewis' systems S4 and S5, do exactly characterize S4 and S5, and that the system given by omitting rule A4 from the first system exactly characterizes von Wright's system M.1