Modal Tic-Tac-Toe

Abstract

The work we are doing began as an attempt to find a formal definition of truth for a limited class of English sentences. Guided by Tarski’s definition of truth for formalised languages, and by Chomsky’s conception of natural language syntax, we wanted to take a subset of English suitable for discussing a model universe, and to define in a intuitively satisfying way what it would mean for a sentence to be true of that universe, in terms of the syntactic structure of the sentence and the referents of the individual words. We did not feel committed to any specific grammar of English, but we were — and are — strongly prejudiced to the view that English syntax must serve some purpose in the process of communication, and we wanted our scheme to assign some function to as much as possible of the syntax we would use.