Title: Counterfactual Logics via Comparative Possibility
Abstract:
In 1973, C. I. Lewis published a landmark text developing a theory of counterfactual logics. The primary goal of the text was in providing a logical framework where one could reason about sentences of the form: “if P were true, then Q would be true”. Such sentences were handled with a new connective and the majority of his text explores the semantics and behavior of this new connective. More general semantics and other connectives were introduced as well and briefly discussed, including a comparative possibility relation. It isn’t until the last chapter of his book that Lewis actually described the syntax for the logics, a reformulation of the semantics, soundness and completeness theorems, and a list of axioms, among other things. This final chapter is unusual for many reasons, the logic and semantics rely on the comparative possibility relation instead of the counterfactual relation and all of the proofs and definitions are written in extremely terse prose. Moreover, this chapter discusses a large family of logics as well as their related modal logics.
In this talk we’ll first go over the sort of counterfactual logic and semantics that Lewis is primarily interested in. Then we’ll discuss the semantics and logic in terms of the comparative possibility relation. Finally, we’ll give an overview of how the soundness and completeness proofs work and where the difficulties lie.
