Probability and Confirmation

In 1945, Carl Hempel proposed a simple theory of confirmation that eventually came to be seen as unacceptably unsophisticated: it failed to incorporate the impact of epistemic context, of the "superempirical virtues" such as simplicity and explanatory elegance, and it was purely qualitative, determining when a piece of evidence supported a hypothesis but not by how much. I propose that Hempel's theory, precisely because it has these properties, comes much closer to capturing the handling of evidential support in the official channels of scientific communication -- in the journals -- than is commonly supposed. I comment on the reasons for this.

My goal here is to explain why it is harder than one might expect to find a satisfying package that combining the Best System Account of chance and the Principal Principle. One can show that for a certain prima facie attractive version of the Best System Account of chance, the only priors that satisfy the Principal Principle are non-computable. So fans of the Lewisian package must either find a more suitable version of the Best System Account, weaken the Principal Principle, or maintain that rationality requires us to perform tasks beyond the capability of any Turing machine.

There are major three schools of thought in statistics: frequentism, Bayesianism, and likelihoodism. They are often thought to be in fundamental disagreement, but I don't think so. My goal is to develop a simultaneous unification of the three camps, and defend it against the most urgent of the alleged conflicts, including especially Lindley's paradox and the actualism debate.

In a Bayesian framework, Goodman's `New Riddle of Induction' boils down to the choice of priors. I argue that if we assume random sampling, we should assign a low prior probability to all emeralds being grue. This is because random sampling and the observation-independence of green and blue imply that our prior should be *exchangeable* with respect to green and blue.