Hume's problem solved : the optimality of meta-induction / Gerhard Schurz.

Format:

Book

Author/Creator:

Schurz, Gerhard, 1956- author.

Language:

English

Subjects (All):

Hume, David, 1711-1776.

Hume, David.

Induction (Logic).

Physical Description:

1 online resource (320 pages)

Other Title:

MIT Press CogNet.

Place of Publication:

Cambridge : MIT Press, 2019.

System Details:

text file

Summary:

A new approach to Hume's problem of induction that justifies the optimality of induction at the level of meta-induction. Hume's problem of justifying induction has been among epistemology's greatest challenges for centuries. In this book, Gerhard Schurz proposes a new approach to Hume's problem. Acknowledging the force of Hume's arguments against the possibility of a noncircular justification of the reliability of induction, Schurz demonstrates instead the possibility of a noncircular justification of the optimality of induction, or, more precisely, of meta-induction (the application of induction to competing prediction models). Drawing on discoveries in computational learning theory, Schurz demonstrates that a regret-based learning strategy, attractivity-weighted meta-induction, is predictively optimal in all possible worlds among all prediction methods accessible to the epistemic agent. Moreover, the a priori justification of meta-induction generates a noncircular a posteriori justification of object induction. Taken together, these two results provide a noncircular solution to Hume's problem. Schurz discusses the philosophical debate on the problem of induction, addressing all major attempts at a solution to Hume's problem and describing their shortcomings; presents a series of theorems, accompanied by a description of computer simulations illustrating the content of these theorems (with proofs presented in a mathematical appendix); and defends, refines, and applies core insights regarding the optimality of meta-induction, explaining applications in neighboring disciplines including forecasting sciences, cognitive science, social epistemology, and generalized evolution theory. Finally, Schurz generalizes the method of optimality-based justification to a new strategy of justification in epistemology, arguing that optimality justifications can avoid the problems of justificatory circularity and regress.

Contents:

1 The Problem of Induction p. 1

1.1 The Notion of Induction: Conceptual Clarifications p. 1

1.2 David Hume and the Problem of Justifying Induction p. 5

2 On Failed Attempts to Solve the Problem of Induction p. 11

2.1 Can Induction Be Avoided? p. 11

2.2 Is Induction Rational "by Definition"? Rationality and Cognitive Success p. 13

2.3 Can Induction Be Justified by Assumptions of Uniformity? p. 16

2.4 Can Circular Justifications of Induction Have Epistemic Value? p. 18

2.5 Can Induction Be Justified by Abduction or Inference to the Best Explanation? p. 22

2.6 The Role of Induction and Abduction for Instrumentalism and Realism p. 24

3 The Significance of Hume's Problem for Contemporary Epistemology p. 27

3.1 The Aims of Epistemology p. 27

3.2 Foundation-Oriented Epistemology and Its Main Problems p. 29

3.3 Coherentism and Its Shortcomings p. 35

3.4 Externalism and Its Shortcomings p. 38

3.5 The Necessity of Reliability Indicators for the Social Spread of Knowledge p. 43

3.6 Conclusion: A Plea for Foundation-Oriented Epistemology p. 44

4 Are Probabilistic Justifications of Induction Possible? p. 47

4.1 Why Genuine Confirmation Needs Induction Axioms p. 47

4.2 Digression: Goodman's Paradox and the Problem of Language Relativity p. 52

4.3 Statistical Principal Principle and Narrowest Reference Classes p. 57

4.4 Statistical Principal Principle and Exchangeability as Weak Induction Axioms p. 61

4.5 Indifference Principle as an Induction Axiom p. 68

4.6 Inductive Probabilities without the Principle of Indifference? p. 72

4.7 Is Skepticism Unavoidable? p. 75

5 A New Start: Meta-Induction, Optimality Justifications, and Prediction Games p. 77

5.1 Reichenbach's Best Alternative Approach p. 77

5.2 Reliability Justifications versus Optimality Justifications p. 78

5.3 Shortcomings of Reichenbach's Best Alternative Approach p. 81

5.4 Object-Induction versus Meta-Induction p. 82

5.5 Prediction Games p. 85

5.6 Classification of Prediction Methods and Game-Theoretic Reflections p. 90

5.7 Definitions of Optimality, Access-Optimality, and (Access-) Dominance p. 94

5.8 Three Related Approaches: Formal Learning Theory, Computational Learning Theory, and Ecological Rationality Research p. 99

5.9 Simple and Refined (Conditionalized) Inductive Methods p. 102

6 Kinds of Meta-Inductive Strategies and Their Performance p. 109

6.1 Imitate the Best (ITB): Achievements and Failures p. 110

6.2 Epsilon-Cautious Imitate the Best (eITB) p. 122

6.3 Systematic Deception: Fundamental Limitations of One-Favorite Meta-Induction p. 126

6.3.1 General Facts about Nonconverging Frequencies p. 126

6.3.2 Nonconvergent Success Oscillations and Systematic Deceivers p. 127

6.3.3 Limitations of One-Favorite Meta-Induction p. 129

6.4 Deception Detection and Avoidance Meta-Induction (ITBN) p. 131

6.5 Further Variations of One-Favorite Meta-Induction p. 135

6.6 Attractivity-Weighted Meta-Induction (AW) for Real-Valued Predictions p. 138

6.6.1 Simple AW p. 140

6.6.2 Exponential AW p. 144

6.6.3 Access-Superoptimality p. 145

6.7 Attractivity-Weighted Meta-Induction for Discrete Predictions p. 147

6.7.1 Randomized AW Meta-Induction p. 149

6.7.2 Collective AW Meta-Induction p. 153

6.8 Further Variants of Weighted Meta-Induction p. 156

6.8.1 Success-Based Weighting p. 157

6.8.2 Worst-Case Regrets and Division of Epistemic Labor p. 161

7 Generalizations and Extensions p. 163

7.1 Bayesian Predictors and Meta-Inductive Probability Aggregation p. 163

7.2 Intermittent Prediction Games p. 169

7.2.1 Take the Best (TTB) p. 172

7.2.2 Intermittent AW p. 177

7.3 Unboundedly Growing Numbers of Players p. 180

7.3.1 New Players with Self-Completed Success Evaluation p. 181

7.3.2 Meta-Induction over Player Sequences p. 183

7.4 Prediction of Test Sets p. 186

7.5 Generalization to Action Games p. 188

7.6 Adding Cognitive Costs p. 191

7.7 Meta-Induction in Games with Restricted Information p. 194

8 Philosophical Conclusions and Refinements p. 197

8.1 A Noncircular Solution to Hume's Problem p. 197

8.1.1 Epistemological Explication of the Optimality Argument p. 197

8.1.2 Radical Openness and Universal Learning Ability p. 203

8.1.3 Meta-Induction and Fundamental Disagreement p. 204

8.1.4 Fundamentalists Strategies and the Freedom to Learn p. 206

8.1.5 A Posteriori Justification of Object-Induction p. 208

8.1.6 Bayesian Interpretation of the Optimality Argument p. 210

8.1.7 From Optimal Predictions to Rational (Degrees of) Belief p. 212

8.2 Conditionalized Meta-Induction p. 215

8.3 From Optimality to Dominance p. 222

8.3.1 Restricted Dominance Results p. 222

8.3.2 Discriminating between Inductive and Noninductive Prediction Methods p. 224

8.3.3 Bayesian Interpretation of Dominance p. 228

9 Defense against Objections p. 233

9.1 Meta-Induction and the No Free Lunch Theorem p. 233

9.1.1 The Long-Run Perspective p. 235

9.1.2 The Short-Run Perspective p. 245

9.2 The Problem of Infinitely Many Prediction Methods p. 260

9.2.1 Infinitely Many Methods and Failure of Access-Optimality p. 260

9.2.2 Restricted Optimality Results for Infinitely Many Methods p. 262

9.2.3 Defense of the Cognitive Finiteness Assumption p. 266

9.2.4 The Problem of Selecting the Candidate Set p. 268

9.2.5 Goodman's Problem at the Level of Prediction Methods p. 270

10 Interdisciplinary Applications p. 273

10.1 Meta-Induction and Ecological Rationality: Application to Cognitive Science p. 273

10.2 Meta-Induction and Spread of Knowledge: Application to Social Epistemology p. 284

10.2.1 Prediction Games in Epistemic Networks p. 287

10.2.2 Local Meta-Induction and Spread of Reliable Information p. 289

10.2.3 Imitation without Success Information: Consensus Formation without Spread of Knowledge p. 293

10.3 Meta-Induction, Cooperation, and Game Theory: Application to Cultural Evolution p. 297

11 Conclusion and Outlook: Optimality Justifications as a Philosophical Program p. 305

11.1 Optimality Justifications as a Means of Stopping the Justificational Regress p. 305

11.2 Generalizing Optimality Justifications p. 307

11.2.1 The Problem of the Basis: Introspective Beliefs p. 307

11.2.2 The Choice of the Logic p. 307

11.2.3 The Choice of a Conceptual System p. 310

11.2.4 The Choice of a Theory p. 310

11.2.5 The Justification of Abductive Inference p. 311

11.3 New Foundations for Foundation-Oriented Epistemology p. 314

12 Appendix: Proof of Formal Results p. 315.

Notes:

OCLC-licensed vendor bibliographic record.

ISBN:

9780262352444

0262352443

OCLC:

1082521677

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Restricted for use by site license.

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