Synthese: an International Journal for Epistemology, Methodology and Philosophy of Science vol:193 issue:4 pages:1225-1250
We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called openminded Bayesianism challenges the assumption —implicit in standard Bayesianism— that the correct empirical hypothesis is among the ones currently under consideration. It requires the inclusion of a catch-all hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catch-all is decomposed into a new empirical hypothesis and a new catch-all. As will be seen, this motivates a second update rule, besides Bayes’ rule, for updating probabilities in light of a new theory. This rule conserves probability ratios among the old hypotheses. This framework allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context. The result is a version of Bayesianism that, in the words of Earman, “keep[s] an open mind, but not so open that your brain falls out”.