Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory
Earman (John)
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BOOK ABSTRACT:

Preface

  1. Philosophers of science can be justifiably proud of the progress achieved in their discipline since the early days of logical positivism. A glaring exception concerns the analysis of the testing of scientific hypotheses and theories, an exception that threatens to block further progress toward a central goal not only of the logical positivists but also of their predecessors and heirs. That goal is the understanding of “the scientific method”. Whatever else this method involves, its principal concern is with the issue of how the results of observation and experiment serve to support or undermine scientific conjectures. Not only does contemporary philosophy of science fail to provide a persuasive analysis of this issue, there are even rumblings to the effect that a search for an “inductive logic” or “theory of confirmation” is a fruitless quest for a nonexistent philosopher’s stone. The principal difficulty here, it should be emphasized, does not derive from Kuhnian incommensurability and its fellow travellers, for the issue has resisted resolution even for cases that do not stray near the frontiers of scientific revolutions.
  2. This work explores one dimension of this impasse by providing a critical evaluation of the approach I take to provide the best good hope for a comprehensive and unified treatment of induction, confirmation, and scientific inference: Bayesianism. It is intended for students of the philosophy of scientific methodology, where ‘student’ is used in the broad sense to include advanced undergraduates, graduate students, and professional philosophers. It is also intended to annoy both the pro- and contra-Bayesians. To fling down the gauntlet, the critics of Bayesianism have generally failed to get the proper measure of the doctrine, while the Bayesians themselves have failed to appreciate the pitfalls and limitations of their approach. And to add insult to insult, neither side has appreciated the source of the doctrine — the Reverend Bayes's essay. Nor is there much appreciation of what the new discipline of formal learning theory has to tell us about the latent assumptions responsible for the apparent reliability of Bayesian methods. If the annoyance serves as a spur to further progress, I will count this book a success.
  3. I want to emphasize as strongly as I can that this work is not intended as a comprehensive review of the pros and cons of Bayesianism. Issues and points of views on issues have been selected with an eye to giving the reader a sense of the strengths and weaknesses of the Bayesian approach to confirmation, and my selections should be judged on that basis.

Contents
  1. Bayes’s Bayesianism – 7
    1. Bayes's Problem – 7
    2. Bayes’s Two Concepts of Probability – 8
    3. Bayes’s Attempt to Demonstrate the Principles of Probability – 9
    4. Bayes’s Principle-of-Insufficient-Reason Argument – 14
    5. Choosing a Prior Distribution – 16
    6. Proxy Events and the Billiard-Table Model – 20
    7. Applications of Bayes’s Results – 24
    8. Conclusion – 26
      Appendix: Bayes’s Definitions and Propositions – 27
  2. The Machinery of Modem Bayesianism – 33
    1. The Elements of Modern Bayesianism – 33
    2. The Probability Axioms – 35
    3. Dutch Book and the Axioms of Probability – 38
    4. Difficulties with the Dutch Book Argument – 40
    5. Non-Dutch Book Justifications of the Probability Axioms – 44
    6. Justifications for Conditionalization – 46
    7. Lewis’s Principal Principle – 51
    8. Descriptive versus Normative Interpretations of Bayesianism – 56
    9. Prior Probabilities – 57
    10. Conclusion – 59
      Appendix 1: Conditional Probability – 59
      Appendix 2: Laws of Large Numbers – 61
  3. Success Stories – 63
    1. Qualitative Confirmation: The Hypothetico-Deductive Method – 63
    2. Hempel’s Instance Confirmation – 65
    3. The Ravens Paradox – 69
    4. Bootstrapping and Relevance Relations – 73
    5. Variety of Evidence and the Limited Variety of Nature – 77
    6. Putnam and Hempel on the Indispensability of Theories – 79
    7. The Quine and Duhem Problem – 83
    8. Conclusion - 86
  4. Challenges Met – 87
    1. The Problem of Zero Priors: Carnap’s Version – 87
    2. The Problem of Zero Priors: Jeffrey’s Version – 90
    3. The Problem of Zero Priors: Popper’s Versions – 92
    4. The Popper and Miller Challenge – 95
    5. Richard Miller and the Return to Adhocness – 98
    6. Grunbaum’s Worries – 102
    7. Goodman’s New Problem of Induction – 104
    8. Novelty of Prediction and Severity of Test – 113
    9. Conclusion – 117
  5. The Problem of Old Evidence – 119
    1. Old Evidence as a Challenge to Bayesian Confirmation Theory – 119
    2. Preliminary Attempts to Solve or Dissolve the Old-Evidence Problem – 120
    3. Garber’s Approach – 123
    4. Jeffrey’s Demonstration – 126
    5. The Inadequacy of the Garber, Jeffrey, and Niiniluoto Solution – 130
    6. New Theories and Doubly Counting Evidence – 132
    7. Conclusion: A Pessimistic Resolution of the Old-Evidence Problem – 133
  6. The Rationality and Objectivity of Scientific Inference – 137
    1. Introduction – 137
    2. Constraining Priors – 139
    3. The Washing Out of Priors: Some Bayesian Folklore – 141
    4. Convergence to Certainty and Merger of Opinion as a Consequence of Martingale Convergence – 144
    5. The Results of Gaifman and Snir – 145
    6. Evaluation of the Convergence-to-Certainty and Merger-of-Opinion Results – 147
    7. Underdetermination and Antirealism – 149
    8. Confirmability and Cognitive Meaningfulness – 153
    9. Alternative Explanations of Objectivity – 154
    10. The Evolutionary Solution – 155
    11. Modest but Realistic Solutions – 156
    12. Non-Bayesian Solutions – 158
    13. Retrenchment – 158
    14. Conclusion – 160
  7. A Plea for Eliminative Induction – 163
    1. Teaching Dr. Watson to Do Induction – 163
    2. The Necessity of the Eliminative Element in Induction – 163
    3. Salmon’s Retreat from Bayesian Inductivism – 171
    4. Twentieth-Century Gravitational Theories: A Case Study – 173
    5. Conclusion – 180
  8. Normal Science, Scientific Revolutions, and All That: Thomas Bayes versus Thomas Kuhn – 187
    1. Kuhn’s Structure of Scientific Revolutions – 187
    2. Theory-Ladenness of Observation and the Incommensurability of Theories – 189
    3. Tom Bayes and Tom Kuhn: Incommensurability? – 191
    4. Revolutions and New Theories – 195
    5. Objectivity, Rationality, and the Problem of Consensus 198
    6. A Partial Resolution of the Problem of Consensus – 201
    7. Conclusion – 203
  9. Bayesianism versus Formal-Learning Theory – 207
    1. Putnam’s Diagonalization Argument – 207
    2. Taking Stock – 209
    3. Formal-Learning Theory – 210
    4. Bayesian Learning Theory versus Formal-Learning Theory – 211
    5. Does Formal Learning Have an Edge over Bayesian Learning? – 212
    6. The Dogmatism of Bayesianism – 215
    7. In What Sense Does a Formal Learner Learn? – 218
    8. Putnam’s Argument Revisited – 220
    9. Conclusion – 222
  10. A Dialogue – 225
  11. Notes – 237
    References – 253
    Index – 265

BOOK COMMENT:



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