Quitting certainties : a Bayesian framework modeling degrees of belief.

Format:

Book

Author/Creator:

Titelbaum, Michael G.

Language:

English

Subjects (All):

Belief and doubt--Mathematical models.

Belief and doubt.

Bayesian statistical decision theory.

Mathematical models.

Physical Description:

xii, 345 pages ; 24 cm

Edition:

First edition.

Place of Publication:

Oxford : Oxford University Press, 2013.

Summary:

Michael G. Titelbaum presents a new Bayesian framework for modeling rational degrees of belief, called the Certainty-Loss Framework. Subjective Bayesianism is epistemologists' standard theory of how individuals should change their degrees of belief over time. But despite the theory's power, it is widely recognized to fail for situations agents face every day; cases in which agents forget information, or in which they assign degrees of belief to self-locating claims. Quitting Certainties argues that these failures stem from a common source-the inability of Conditionalization (Bayesianism's traditional updating rule) to model claims going from certainty at an earlier time to less-than-certainty later on. It then presents a new Bayesian updating framework that accurately represents rational requirements on agents who undergo certainty loss. Titelbaum develops this new framework from the ground up, assuming little technical background on the part of his reader. He interprets Bayesian theories as formal models of rational requirements, leading him to discuss both the elements that go into a formal model and the general principles that link formal systems to norms. By reinterpreting Bayesian methodology and altering the theory's updating rules, Titelbaum is able to respond to a host of challenges to Bayesianism both old and new. These responses lead in turn to deeper questions about commitment, consistency, and the nature of information. Quitting Certainties presents the first systematic, comprehensive Bayesian framework unifying the treatment of memory loss and context-sensitivity. It develops this framework, motivates it, compares it to alternatives, then applies it to cases in epistemology, decision theory, the theory of identity, and the philosophy of quantum mechanics. Book jacket.

Contents:

Part I Going Modeling

1 Introduction 3

1.1 What's to come 7

1.2 Notes on the text 10

2 Models and norms 11

2.1 Bridge principles 12

2.2 What we need to go modeling 17

2.3 Our modeling methodology 24

Part II Elements of CLF

3 The modeling framework and what models represent 31

3.1 Stories and claims 32

3.2 Formal elements and representation scheme 37

3.2.1 Time sets, languages, and credence functions 37

3.2.2 Extrasystematic constraints 40

3.2.3 A sample model 43

3.2.4 Systematic constraints 45

3.2.5 Consequences of these constraints 47

3.3 Updating by Conditionalization 50

4 Applying CLF models to stories 55

4.1 The standard interpretation's application scheme 56

4.2 The evaluative standard 60

4.2.1 Constraints as necessary conditions 60

4.2.2 What the standard requires 62

4.2.3 The nature of the evaluation 67

4.2.4 The strength of the evaluation 70

4.3 Model theory and alternative interpretations 75

4.3.1 A model theory for CLF 75

4.3.2 Ranged attitudes 79

4.3.3 Further interpretations 82

5 Three common objections to Bayesian frameworks 84

5.1 Counterexamples and modeling 84

5.2 Judy Benjamin and expanding doxastic space 88

5.2.1 The Judy Benjamin Problem 88

5.2.2 The problem of new theories 92

5.3 Ratio Formula objections 96

5.3.1 Regularity and infinity 97

5.3.2 Undefined conditional credences 100

5.3.3 Other domain limitations 104

5.4 Logical omniscience 106

5.4.1 Accommodating non-omniscience 108

5.4.2 The costs of non-omniscience 110

Part III Memory Loss

6 Generalized Conditionalization 117

6.1 Updating rules 118

6.1.1 Memory-loss objections 118

6.1.2 Limited Conditionalization 123

6.1.3 (GC) 127

6.2 Applications of (GC) 129

6.2.1 The lottery 129

6.2.2 (GC) and Reflection 131

7 Suppositional consistency 137

7.1 The basic idea 138

7.2 The synchronic solution 141

7.2.1 Credal Uniqueness and conditional structure 141

7.2.2 Conditional structure and interpersonal relations 147

7.3 Diachronic doxastic commitments 149

7.3.1 Denying Credal Uniqueness 150

7.3.2 Making a commitment 152

7.3.3 The structure of doxastic commitments 155

7.4 Objections to (GC) 157

7.4.1 Unique updates 157

7.4.2 Re-evaluating evidence 161

7.4.3 Changing your mind 162

7.4.4 Forgetting an earlier assignment 164

7.5 (GC) and CLF's domain of applicability 166

Part IV Context-Sensitivity

8 The Proper Expansion Principle 171

8.1 The problem 172

8.1.1 Context-sensitivity and Conditionalization 172

8.1.2 A strategy for Sleeping In 179

8.1.3 Non-monotonicity under language change 181

8.2 (PEP) 187

8.2.1 Perfect expansions 187

8.2.2 Proper expansions 191

8.3 The Sarah Moss Problem 195

9 Applying (PEP) 201

9.1 Straightforward applications of (PEP) 203

9.1.1 Self-location and The Die 203

9.1.2 Shangri La internalized 205

9.1.3 John Collins's prisoner example 207

9.2 The Sleeping Beauty Problem 210

9.2.1 Lewis's analysis 211

9.2.2 Elga's analysis 212

9.2.3 The solution 215

9.2.4 Objections to this solution 217

9.2.5 Modeling strategies 219

9.3 Technicolor Beauty 223

9.3.1 Analysis 223

9.3.2 An objection to this solution 226

10 Alternative updating schemes 230

10.1 Halpern and Meacham 230

10.2 Moss 238

10.3 Stalnaker 243

11 Indifference principles and quantum mechanics 250

11.1 The Indifference Principle 251

11.1.1 Elga's argument 251

11.1.2 CLF and Duplication 254

11.1.3 Colored papers overdrive 259

11.1.4 Weatherson's objections 263

11.2 Fission and cloning 266

11.2.1 Fission and diachronic consistency 266

11.2.2 Three metaphysical accounts 268

11.2.3 Cloning 271

11.3 Quantum mechanics 273

11.3.1 Everettian interpretations 273

11.3.2 Everett and Bayes 275

11.3.3 Solutions 278

Part V Conclusion

12 A few loose ends 285

12.1 Dutch Books 285

12.1.1 Dutch Books and context-sensitivity 286

12.1.2 Dutch Books and memory loss 287

12.2 Jeffrey Conditionalization 289

12.2.1 (JC) and memory loss 292

12.2.2 (JC) and context-sensitivity 294

12.3 Defeaters 296

13 The advantages of modeling 299.

Notes:

Includes bibliographical references (pages [332]-338) and index.

ISBN:

9780199658305

0199658307

OCLC:

832825636