3 - Entailment and Possible Worlds

Summary

One difficulty with Lewis’s logics favourite systems, S1–S3, is that they have no intuitive semantics or proof theory. Another approach to constructing a logic of entailment is to begin with a semantic intuition and then adopt the logic characterized by the semantics. This is the approach of Carnap’s Meaning and Necessity. On Carnap’s view, entailment is just strict implication in the sense of the logic S5. The chapter examines Carnap’s semantics and its successor developed by Nino Cocchiarella, and finds that whereas they may give a good representation of the notion of logical truth, they do not provide an adequate analysis of entailment. Once again, the problem of implosion and nested entailments are problematic. This chapter also looks at attempts to solve these difficulties using worlds at which the logical truths differ, and raises philosophical worries about them.