Putting the irrelevance back into the problem of irrelevant conjunction

Naive deductive accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H & X, for any X-even if X is utterly irrelevant to H (and E). Bayesian accounts of confirmation also have this property (in the case of deductive evidence). Several Bayesians have attempted to soften the impact of this fact by arguing that-according to Bayesian accounts of confirmation-E will confirm the conjunction H & X less strongly than E confirms H (again, in the case of deductive evidence). I argue that existing Bayesian resolutions of this problem are inadequate in several important respects. In the end, I suggest a new-and-improved Bayesian account (and understanding) of the problem of irrelevant conjunction.