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Our beliefs come in degrees. I'm 70% confident it will rain tomorrow, and 0.001% sure my lottery ticket will win. What's more, we think these degrees of belief should abide by certain principles if they are to be rational. For instance, you shouldn't believe that a person's taller than 6ft more strongly than you believe that they're taller than 5ft, since the former entails the latter. In Dutch Book arguments, we try to establish the principles of rationality for degrees of belief by appealing to their role in guiding decisions. In particular, we show that degrees of belief that don't satisfy the principles will always guide action in some way that is bad or undesirable. In this Element, we present Dutch Book arguments for the principles of Probabilism, Conditionalization, and the Reflection Principle, among others, and we formulate and consider the most serious objections to them. --

Probabilities --- Knowledge, Theory of --- Philosophy --- Probabilities - Philosophy --- Probabilities. --- Bayesian statistical decision theory. --- Knowledge, Theory of. --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Epistemology --- Theory of knowledge --- Psychology --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

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Theory of knowledge --- Mathematical statistics

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"Logical methods are used in all areas of philosophy. By introducing and advancing central topics in the discipline, The Bloomsbury Companion to Philosophical Logic emphasizes the crucial role logic plays in understanding philosophical problems. Covering stages in the history of logic and of modern logic, this comprehensive Companion looks ahead to new areas of research and explores issues relating to classical logic and its rivals, semantics and the application of logic in the theory of rationality. Written by experts in the field, chapters offer excellent encyclopaedias of results in each area together with philosophical discussions surveying a range of philosophical positions. To facilitate further study, this volume also includes a series of research tools such as a detailed index, an up-to-date list of resources and an annotated bibliography. Balancing technical exposition with philosophical discussion, The Bloomsbury Companion to Philosophical Logic not only provides students and lecturers with the basis of a course in philosophical logic, it offers anyone working in this key area of contemporary philosophy a valuable research guide"--Back cover.

Logic --- Philosophy.

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