The stability of belief : how rational belief coheres with probability / Hannes Leitgeb.

Format:

Book

Author/Creator:

Leitgeb, Hannes, author.

Language:

English

Subjects (All):

Probabilities.

Epistemic logic.

Belief and doubt.

Physical Description:

x, 365 pages : illustrations ; 24 cm

Edition:

First edition.

Place of Publication:

Oxford, United Kingdom : Oxford University Press, 2017.

Summary:

In everyday life we normally express our beliefs in all-or-nothing terms: I believe it is going to rain; I don't believe that my lottery ticket will win. In other cases, if possible, we resort to numerical probabilities: my degree of belief that it is going to rain is 80 per cent; the probability that I assign to my ticket winning is one in a million. It is an open philosophical question how all-or-nothing belief and numerical belief relate to each other, and how we ought to reason with them simultaneously. The Stability of Belief develops a theory of rational belief that aims to answer this question. Hannes Leitgeb puts forward a joint normative theory of all-or-nothing belief and numerical degrees of belief. While rational all-or-nothing belief is studied in traditional epistemology and is usually assumed to obey logical norms, rational degrees of belief constitute the subject matter of Bayesian epistemology and are normally taken to conform to probabilistic norms. One of the central open questions in formal epistemology is what beliefs and degrees of belief have to be like in order for them to cohere with each other. The answer defended in this book is a stability account of belief: a rational agent believes a proposition just in case the agent assigns a stably high degree of belief to it. Leitgeb determines this theory's consequences for, and applications to, learning, suppositional reasoning, decision-making, assertion, acceptance, conditionals, and chance. The volume builds new bridges between logic and probability theory, traditional and formal epistemology, theoretical and practical rationality, and synchronic and diachronic norms for reasoning. Book jacket.

Contents:

1 Introduction 1

1.1 The Nature of Belief 2

1.2 Concepts of Belief 8

1.3 Elimination, Reduction, Irreducibility 11

1.3.1 The Elimination (without Reduction) Option (i): At Least One of the Two Concepts of Belief is Empty 13

1.3.2 The Reduction Option (ii): Both Concepts of Belief Refer, and they Refer to the Same Phenomenon 16

1.3.3 The Irreducibility Option (iii): Both Concepts of Belief Refer, But Not to the Same Phenomenon 20

1.4 Norms for Belief: How Should Beliefs Cohere? 27

1.5 The Route to an Answer 32

1.6 Bridge Principles for Rational Belief and Rational Degrees of Belief 41

1.6.1 The Certainty or Probability 1 Proposal 42

1.6.2 The Lockean Thesis 44

1.6.3 Decision-Theoretic Accounts 45

1.6.4 The Nihilistic Proposal 47

1.7 What is to Come 48

Appendix A The Review Argument: On the Diachronic Costs of Not Closing Rational Belief under Conjunction 54

A.1 Closing Rational Belief under Conjunction 54

A.2 The Argument 55

A.3 A Variation 63

A.4 Conclusions 65

2 The Humean Thesis on Belief 69

2.1 Introduction 69

2.2 Explicating the Humean Thesis 73

2.3 The Consequences of the Humean Thesis 89

2.3.1 Consequence 1: Doxastic Logic 89

2.3.2 Consequence 2: The Lockean Thesis 96

2.3.3 Consequence 3: Decision Theory 100

2.4 Conclusions 104

Appendix B Where Does Stability Come from? Stability through Repetition 106

3 Logical Closure and the Lockean Thesis 112

3.1 The Lockean Thesis and Closure of Belief under Conjunction 112

3.2 P-Stability 117

3.3 The Theory and its Costs 127

3.4 Application to the Lottery Paradox 148

3.5 A First Shot at the Preface Paradox 151

3.6 An Application in Formal Epistemology 153

3.7 Summary 157

4 Conditional Belief and Belief Dynamics 159

4.1 A Stability Theory of Conditional Belief and Belief Dynamics: Introduction and Synopsis 160

4.1.1 Conditional Probability and Conditionalization 160

4.1.2 Conditional Belief and Belief Revision 162

4.1.3 Conditionalization vs Belief Revision: A Preview 171

4.1.4 Some Closely Related Theories 176

4.2 A Stability Theory of Conditional Belief and Belief Dynamics: The Formal Details 179

4.2.3 Probabilistic Postulates 180

4.2.2 Restricted Conditional Belief and a Bridge Postulate 181

4.2.3 Conditional Belief in General 214

4.3 Some Examples with a Concrete Interpretation 225

Appendix C Does Rational Belief Reduce to Subjective Probability? Dots it Supervene? 230

C.1 The First Argument Against Supervenience 232

C.2 The Second Argument Against Supervenience 234

5 Stability and Epistemic Decision Theory 237

5.1 Belief's Aiming at the Truth 240

5.2 Belief's Aiming at Subjective Probability 250

5.2.1 Probabilistic Order vs Doxastic Order over Worlds 250

5.2.2 Accuracy for Orders over Worlds 256

5.2.3 Error-Free Doxastic Orders of Worlds 260

5.2.4 Conclusions on Rational Belief 262

6 Action, Assertability, Acceptance 265

6.1 Action 267

6.2 Assertability 274

6.3 Acceptance 302

6.4 The Preface Paradox Reconsidered 313

Appendix D On Counterfactuals and Chance 319

D.1 A New Paradox 320

D.2 The Derivation 324

D.3 Related Arguments 325

D.4 Diagnosis 330

D.5 A New Way Out 335

D.6 Evaluation and Prospects 344.

Notes:

Includes bibliographical references (pages 349-360) and index.

ISBN:

0198732635

9780198732631

OCLC:

949911860