Book contents
- Lotteries, Knowledge, and Rational Belief
- Lotteries, Knowledge, and Rational Belief
- Copyright page
- Contents
- Contributors
- Introduction
- Chapter 1 Rational Belief and Statistical Evidence
- Chapter 2 Knowledge Attributions and Lottery Cases
- Chapter 3 The Psychological Dimension of the Lottery Paradox
- Chapter 4 Three Puzzles about Lotteries
- Chapter 5 Four Arguments for Denying that Lottery Beliefs Are Justified
- Chapter 6 Rethinking the Lottery Paradox
- Chapter 7 Rational Belief in Lottery- and Preface-Situations
- Chapter 8 Stability and the Lottery Paradox
- Chapter 9 The Lottery, the Preface, and Epistemic Rule Consequentialism
- Chapter 10 Beliefs, Probabilities, and Their Coherent Correspondence
- Chapter 11 The Relation between Degrees of Belief and Binary Beliefs
- Bibliography
- Index
Chapter 10 - Beliefs, Probabilities, and Their Coherent Correspondence
Published online by Cambridge University Press: 29 January 2021
- Lotteries, Knowledge, and Rational Belief
- Lotteries, Knowledge, and Rational Belief
- Copyright page
- Contents
- Contributors
- Introduction
- Chapter 1 Rational Belief and Statistical Evidence
- Chapter 2 Knowledge Attributions and Lottery Cases
- Chapter 3 The Psychological Dimension of the Lottery Paradox
- Chapter 4 Three Puzzles about Lotteries
- Chapter 5 Four Arguments for Denying that Lottery Beliefs Are Justified
- Chapter 6 Rethinking the Lottery Paradox
- Chapter 7 Rational Belief in Lottery- and Preface-Situations
- Chapter 8 Stability and the Lottery Paradox
- Chapter 9 The Lottery, the Preface, and Epistemic Rule Consequentialism
- Chapter 10 Beliefs, Probabilities, and Their Coherent Correspondence
- Chapter 11 The Relation between Degrees of Belief and Binary Beliefs
- Bibliography
- Index
Summary
There appear to be two sorts of doxastic attitudes, propositional beliefs in the traditional sense (belief that your shoes are tied) and Bayesian credences (degree of belief .998 that your shoes are tied). Deductive consistency and closure traditionally define coherence for belief.Probability theory traditionally defines coherence for degrees of belief. That leaves open the question how propositional and probabilistic beliefs should cohere with one another. We refer to that as the problem of doxastic coherence. We explicate doxastic coherence in terms of rationality constraints on doxastic correspondences that map propositional belief states to Bayesian credal states. Of particular interest is the principle that doxastic correspondences should preserve diachronic coherence. By way of application, we propose a concrete family of coherent doxastic correspondences. Furthermore, we show that the familiar Lockean proposal that one should believe the propositions that pass a credal threshold is incoherent in a number of important respects.
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- Lotteries, Knowledge, and Rational BeliefEssays on the Lottery Paradox, pp. 185 - 222Publisher: Cambridge University PressPrint publication year: 2021
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