The Problem of the Priors, or Posteriors?

The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the challenge of identifying norms that directly govern one's posterior credences, which then induce constraints on the priors via the diachronic requirement of conditionalization. This forward-looking approach can be summarized as: Think ahead, work backward. Although this idea can be traced to Freedman (1963), Carnap (1963), and Shimony (1970), it has received little attention in philosophy. In this paper, I initiate a systematic defense of forward-looking Bayesianism, addressing potential objections from more traditional views (both subjectivist and objectivist) and arguing for its advantages. In particular, I develop a specific approach to forward-looking Bayesianism -- one that treats the convergence of posterior credences to the truth as a fundamental rather than derived normative requirement. This approach, called convergentist Bayesianism, is argued to be crucial for a Bayesian foundation of Ockham's razor and related inference methods in statistics and machine learning.