Lotteries, Knowledge, and Rational Belief: Essays on the Lottery Paradox

Half title
Title page
Imprints page
Contents
Contributors
Introduction
	Overview of the Contributions
Chapter 1 Rational Belief and Statistical Evidence
	Introduction: The Lottery Paradoxes and Statistical Evidence
	Bias and Belief
	The Proof Paradox and the Law
	Blame
	Conclusion
Chapter 2 Knowledge Attributions and Lottery Cases
	Introduction
	Experiment
		Method
		Results
	Conclusion
	Appendix
Chapter 3 The Psychological Dimension of the Lottery Paradox
	Shifting and Controversial Intuitions
	Speaking of Believing and Thinking
	The Difficulty of Belief Attributions and Beliefs Themselves
	Intuitive and Reflective Cognition
	The Knowledge Version of the Paradox
	The Belief Version of the Problem
	Kyburg’s Sunrise and the Problem of Avoiding Skepticism
Chapter 4 Three Puzzles about Lotteries
	Introduction
	Solutions to Kyburg’s Lottery Puzzle that Modify the Threshold Constraint
		The Odds Threshold Rule
		The Stability Theory
	Two More Puzzles
		The Harman–Vogel Paradox
		The Statistical Evidence Problem
	What’s Left of the Simple Threshold Thesis?
	Conclusion
Chapter 5 Four Arguments for Denying that Lottery Beliefs Are Justified
	Introduction
	Justification and Knowledge
	Justification and Surprise
	Justification, Risk, and Normic Support
	Justification and Epistemic Resilience
	Conclusion
Chapter 6 Rethinking the Lottery Paradox
	Introduction
	The Lottery Paradox: A Troubled Past
		The End?
	Is the Mind One and Undivided?
	Some Psychological Evidence
	The Remaining Connection
Chapter 7 Rational Belief in Lottery- and Preface-Situations
	Introduction: Rational Belief – Qualitative and Quantitative
	The Lottery Paradox and the Preface Paradox
	Impossibility Results for Rational Belief
	Impossibility Results for Cautious Versions of Locke’s Condition
		Locke’s Condition with Differentiated Bounds
		Defeater Restrictions of Locke’s Condition
		Contextualist Accounts of Belief
	Two Ways Out of the Inconsistency
		Practical Contexts: Probabilistically Safe Restrictions of Conjunctive Closure Combined with Reliability Enhancement
		Belief in Approximate Truth in Epistemic Contexts
	Conclusion
Chapter 8 Stability and the Lottery Paradox
	Introduction
	Stability
	The Poss-Variant of the Humean Thesis and the Lottery Paradox
	The Bel-Variant of the Humean Thesis and the Lottery Paradox
Chapter 9 The Lottery, the Preface, and Epistemic Rule Consequentialism
	Introduction
	The Lottery Paradox
	Douven-Style Epistemic Rule Consequentialism
		Douven-Style Rule Consequentialism in Trouble
		A Knowledge-Centric Version of Epistemic Rule Consequentialism
	The Preface Paradox
		A Rule Consequentialist Solution to the Preface
		An Objection and Reply
	Conclusion
Chapter 10 Beliefs, Probabilities, and Their Coherent Correspondence
	Introduction
	The Setting
	Belief
		Synchronically Coherent Belief
		Diachronically Coherent Belief
	Credence
	Synchronically Coherent Credence
	Diachronically Coherent Credence
	Doxastic Correspondence
		Basic Correspondence Principles
		Coherence Preservation Principles
		Odds Threshold Correspondences
		Flattened Odds Threshold Correspondences
	Lockean Coherence Principles
		Uniform Lockeanism
		Content-Dependent Lockeanism
		Closed Lockeanism
		Credence-dependent Lockeanism
	Neo-Lockeanism
	Conclusion
Chapter 11 The Relation between Degrees of Belief and Binary Beliefs
	Introduction
	The Formalism
	A General Impossibility Result
	The Special Case of Functionality
	Escape Routes from the Impossibility
		The First Route: Relaxing Universality
		The Second Route: Relaxing Belief Consistency and Deductive Closure
		The Third Route: Relaxing Propositionwise Certainty Preservation
		The Fourth Route: Relaxing Nonlooseness
		The Fifth and Most Compelling Route: Relaxing Locality
			Holistic Threshold Relations
			Relations with Partially Complete Binary Beliefs
			Distance-Based Relations
			Stability-Theoretic Relations
	A Further Generalization
	Concluding Remarks
	Appendix
		Appendix 1: Negation-Connected Agendas
		Appendix 2: Proofs
			Reducing the Relational Theorem to the Functional Theorem
			Proof of Proposition 1
			Proof of Theorem 2*: Sufficiency
			Proof of Theorem 2*: Necessity
Bibliography
Index