"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"-- Bayesian ideas have recently been applied across such diverse fields as philosophy, statistics, economics, psychology, artificial intelligence, and legal theory. Fundamentals of Bayesian Epistemology examines epistemologists' use of Bayesian probability mathematics to represent degrees of belief. Michael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implicationsVolume 1 begins by motivating the use of degrees of belief in epistemology. It then introduces, explains, and applies the five core Bayesian normative rules: Kolmogorov's three probability axioms, the Ratio Formula for conditional degrees of belief, and Conditionalization for updating attitudes over time. Finally, it discusses further normative rules (such as the Principal Principle, or indifference principles) that have been proposed to supplement or replace the core five.Volume 2 gives arguments for the five core rules introduced in Volume 1, then considers challenges to Bayesian epistemology. It begins by detailing Bayesianism's successful applications to confirmation and decision theory. Then it describes three types of arguments for Bayesian rules, based on representation theorems, Dutch Books, and accuracy measures. Finally, it takes on objections to the Bayesian approach and alternative formalisms, including the statistical approaches of frequentism and likelihoodism. Fundamentals of Bayesian Epistemology provides an accessible introduction to the key concepts and principles of the Bayesian formalism. This volume introduces degrees of belief as a concept in epistemology and the rules for updating degrees of belief derived from Bayesian principles. Autorid: Michael G. Titelbaum
