  Consider a more mundane case. Jack hears a bump in the night and irrationally thinks there is an intruder in his house (he has long had three cats and two dogs, so he should know by now that bumps are usually caused by his pets; further, he has been a house owner long enough to know full well that old houses like his make all sorts of odd noises at night, pets or no). Jack has irrational belief \(B\): there is an intruder upstairs or there is an intruder downstairs. Then after searching upstairs he learns that there is no intruder upstairs. Clearly, the reasonable thing for him to do is infer that there is an intruder downstairs—that’s the epistemically reasonable cognitive move to make in response to the new information, given—despite the fact that the new belief ‘There is an intruder downstairs’ is irrational in an evidential sense.