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

Description

We talk and think about our beliefs both in a categorical (yes/no) and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious, near-platitudinous claim is known to give rise to a paradox commonly known as the 'lottery paradox' – at least when it is coupled with some further seeming near-platitudes about belief. How to resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject, all of which provide compelling reasons for rethinking many of the fundamentals of the debate. 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