Fundamentals of Bayesian Epistemology 1

Abstract

This book introduces readers to the fundamentals of Bayesian epistemology. It begins by motivating and explaining the idea of a degree of belief (also known as a “credence”). It then presents Bayesians’ five core normative rules governing degrees of belief: Kolmogorov’s three probability axioms, the Ratio Formula for conditional credences, and Conditionalization for updating credences over time. After considering a few proposed additions to these norms, it applies the core rules to confirmation and decision theory. The book then details arguments for the Bayesian rules based on representation theorems, Dutch Books, and accuracy measures. Finally, it looks at objections and challenges to Bayesian epistemology. It presents problems concerning memory loss, self-location, old evidence, logical omniscience, and the subjectivity of priors. It considers the rival statistical paradigms of frequentism and likelihoodism. Then it explores alternative Bayesian-style formalisms involving comparative confidence rankings, credences ranges, and Dempster-Shafer functions.