 Could we introduce a new connective with a different semantics than \(\supset\) that would do better? A striking theorem discovered by Lewis (1976) suggests not. The theorem relies on an assumption posited by Stalnaker (1970): that the probability of “If \(A\) then \(B\)” is the same as the conditional probability, \(p(B\mid A)\). Let’s use \(A \rightarrow B\) as shorthand for the English, “If \(A\) then \(B\)”: