 The if-clause refers to “admissible” propositions, which are roughly propositions that give no more information about whether or not \(E\) is true than is already contained in \(\Ch(E) = c\). To see why we need the qualification imposed by the if-clause, suppose for instance that the event \(E\) is “the coin will land heads the next time it is tossed”. If the conditioning proposition \(A\) is “the coin is fair”, it is a paradigmatic example of an “ordinary” proposition. This reproduces the Coin Case, with the conditional credence being the chance 0.5. Alternatively, if the conditioning proposition \(A\) is the conjunction of “the coin is fair” and \(E\), then the conditional credence \(\Cr(E \mid A)\) should be 1 rather than the 0.5 chance of \(E\) that \(A\) entails. After all, to be given this \(A\) is to be given a lot of information, which entails \(E\). So this case is supposed to be ruled out by an account of “admissible” propositions. Lewis (1980) initiates a systematic quest for such an account, which has invited counterexamples and responses. See Joyce (2011: sec. 4.2) for a survey.