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This book introduces students and researchers to the philosophical issues at play in the growing field of formal (or Bayesian) epistemology. It focuses not on how to do particular calculations but instead on the philosophical foundations at the convergence of belief and mathematical representation. Its central questions are: What is the nature of quantifying belief? What is the source of its norms? How is it reasonable to represent belief numerically? Accessible to those without any mathematical background, this book will become a much used classic in the field.