 Bradley’s account can be seen as a modification of Stalnaker’s (1968) theory discussed in §4.1: consider a possible world in which \(A\) is true, and otherwise differs minimally from the actual world; “If \(A\), then \(B\)” is true just in case \(B\) is true in that possible world. First modification: Bradley abandons the notion of similarity, or of minimal difference, in favour of a probability distribution over the candidate A-worlds. The example of the short straws in §4.1 shows that this is a good idea. Second modification: conditionals are not propositions. This is a suppositional theory. Conditionals involve two propositions which play different roles, one a supposition, one a judgement within its scope. They cannot be represented by the set of worlds in which they are true. Indeed, conditionals are not ingredients of worlds—they are cross-world entities. Bradley proposes that the conditional “if \(A, B\)” can be represented by the set of pairs of worlds, \(\langle w_i, w_j\rangle\) such that, if \(w_i\) is actual, and \(w_j\) is the “nearest” \(A\)-world, i.e. the world that would be actual if \(A\) were true, the conditional would be true (because \(B\) is true at \(w_j)\). Note: “nearest” does not mean “most similar”. There is no ordering of worlds for similarity. It means the world that would be actual if \(A\) were true. Often, we do not know which world that is—hence the probability distribution over candidates. Sometimes it might even be indeterminate which world that is, but reflection again on the “short straws” example in §4.1 shows that the probabilities are still in order.