Bayesian treatment of auxiliary hypotheses rests on a misinterpretation of Strevens's central claim about the negligibility of certain small probabilities. The present paper clarifies and proves a very general version of the claim. The project Clarifications The negligibility argument Generalization and proof.

This paper examines the standard Bayesian solution to the Quine–Duhem problem, the problem of distributing blame between a theory and its auxiliary hypotheses in the aftermath of a failed prediction. The standard solution, I argue, begs the question against those who claim that the problem has no solution. I then provide an alternative Bayesian solution that is not question-begging and that turns out to have some interesting and desirable properties not possessed by the standard solution. This solution opens the way (...) to a satisfying treatment of a problem concerning ad hoc auxiliary hypotheses. (shrink)