Multidimensional Possible-world Semantics for Conditionals

Adams’ Thesis the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents – has proven impossible to accommodate within orthodox possible worlds semantics. This paper considers the approaches to the problem taken by Jeffrey and Stalnaker (1994) and by McGee (1989), but rejects them on the grounds that they imply a false principle, namely that probability of a conditional is independent of any proposition inconsistent with its antecedent. Instead it is proposed that the semantic contents of conditionals be treated as sets of vectors of worlds, not worlds, where each coordinate of a vector specifies the world that is or would be true under some supposition. It is shown that this treatment implies the truth of Adams’ Thesis whenever the mode of supposition is evidential.