Abstract

This chapter initially describes possible-worlds semantics, which was first introduced by Rudolf Carnap in 1946 in terms of his state-description semantics, for sentential modal logic. Carnap was not concerned with different notions of necessity and possibility, but only with logical necessity and logical possibility. He proposed a criterion of adequacy that any formal semantics for these notions must satisfy in his account of logical necessity and logical possibility. The authors construct a formal semantics and modal logic that satisfies Carnap's criterion in terms of the ontology of logical atomism — an ontology that was implicit in Carnap's state-description semantics.