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Formal methods are changing how epistemology is being studied and understood. A Critical Introduction to Formal Epistemology introduces the types of formal theories and logic being used and explains how they are shaping the subject. Beginning with the basics of probability and Bayesianism, it applies the techniques to beliefs and shows how they inform central debates in justification and knowledge. As well as discussing the main challenges to Bayesianism, induction and the paradox of confirmation, this comprehensive overview covers the new riddle of induction and the Paradox of the Ravens. Subjecting each position to a critical analysis, it explains the main issues in formal epistemology and provides the sense of an on-going conversation. Written in an accessible language and supported by summaries, study questions, guides to further reading and a glossary, each chapter takes care to place developments in an historic context. As the first epistemological account of formal methods, A Critical Introduction to Formal Epistemology is an invaluable resource for students and scholars of contemporary epistemology.