Truth and Satisfaction in Chihara’s Model-theoretic Actualism

Abstract

In The Worlds of Possibility (1998), Charles Chihara presents an actualistic model-theoretic semantics for S5 modal quantificational logic. It is actualistic in the sense that it does not carry any ontological implications of the existence of merely possible entities. The paper aims to provide detailed analyses, interpretations, and reformulations of the notions of truth and satisfaction in Chihara’s semantics, with which we can solve several problems that can be raised against his semantics. The main points are that the truth predicate in Chihara’s system should be understood to be not monadic but dyadic and the satisfaction relation to be triadic, relativized both by the reference point where semantic machinery lies and by the evaluation point where the truth values of sentences in question are evaluated.