Bayesian Convergence for Computably Bounded Agents

ABSTRACT In this article, we pursue two goals. First, we argue that computable probability theory offers a fitting framework for modeling the credences of computably bounded—and, thus, more realistic—Bayesian reasoners. Second, we develop a Bayesian perspective on algorithmic randomness: a branch of computability theory that provides a formal account of what it takes for a sequence of observations (a data stream) to be probabilistically typical in an algorithmically specifiable way. In particular, we argue that adopting such a perspective leads to novel insights for one of the pillars of Bayesian epistemology: Bayesian convergence to the truth. In a companion article, we showed that, for Bayesian agents whose credences are given by computable probability measures, the data streams that guarantee convergence to the truth coincide with the algorithmically random ones. Here, we put these results to use to counter various skeptical arguments which target the philosophical significance of Bayesian convergence‐to‐the‐truth theorems.