 This is a remarkable achievement. Probability is probability of truth. Validity is necessary preservation of truth, and so Adams’s probabilistic criterion of validity is demonstrable. If B is true/false at all \(A\)-worlds, \(A\Rightarrow B\) is straightforwardly true/false. Plenty of others may be straightforwardly true/false, whether or not we know this. The many uncertain conditionals come out with the right probability—the conditional probability of \(B\) given \(A\). The construction is not easy to work with, but it is a sort of possibility proof—that the embeddings objection can be met. (Bradley also has a suggested approach to conditionals within conditionals, but this has not been worked out in detail.)