The Bayesian explanation of transmission failure

Even if our justified beliefs are closed under known entailment, there may still be instances of transmission failure. Transmission failure occurs when P entails Q, but a subject cannot acquire a justified belief that Q by deducing it from P . Paradigm cases of transmission failure involve inferences from mundane beliefs (e.g., that the wall in front of you is red) to the denials of skeptical hypotheses relative to those beliefs (e.g., that the wall in front of you is not white and lit by red lights). According to the Bayesian explanation, transmission failure occurs when (i) the subject’s belief that P is based on E, and (ii) P (Q|E) < P (Q). But there are compelling cases of transmission failure where P (Q|E) > P (Q). No modifications of the Bayesian explanation are capable of accommodating such cases, so the explanation must be rejected as inadequate. Alternative explanations employing simple subjunctive conditionals are fully capable of capturing all of the paradigm cases, as well as those missed by the Bayesian explanation. 1 transmission failure You can often enlarge your set of justified beliefs by deduction alone. Glancing at the table, I see my wife’s keys. I justifiably believe that her keys are on the table, and then come to believe (1) by a straightforward deductive inference: (1) She doesn’t have the keys in her purse. Thus do I acquire a justified belief in (1). But while (2) also follows from my belief that my wife’s keys are on the table, it doesn’t seem that I could come to justifiably believe it in the same way: