Conjunctions, Disjunctions and Lewisian Semantics for Counterfactuals

AbstractConsider the reasonable axioms of subjunctive conditionals (1) if pq1 and pq2 at some world, then p (q1 & q2) at that world, and (2) if p1q and p2q at some world, then (p1 ∨ p2) q at that world, where pq is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably false. I will then show how Lewisian semantics can be modified so as to assure (1) and (2) even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then.