Probability

4.95 MB·English

by  Darrell P. Rowbottom

Key Concepts in Philosophy Page: ii
Title page Page: iii
Copyright page Page: iv
Dedication Page: v
Contents Page: vii
Preface Page: ix
1: Probability: A Two-Faced Guide to Life? Page: 1
1 Why Care about Probabilities? Page: 1
2 The Two Faces of Probability Page: 3
3 Monism or Pluralism Page: 7
4 Laplace’s Demon: A Thought Experiment Page: 9
5 Interpretations of Probability: An Initial Taxonomy Page: 10
2: The Classical Interpretation Page: 12
Further Reading Page: 18
3: The Logical Interpretation Page: 19
1 A Brief Introduction to Conditional Probabilities Page: 19
2 What Are Logical Probabilities? Page: 20
3 Conditional and Unconditional Probabilities in the Logical Interpretation Page: 23
4 Logical Probabilities and Beliefs Page: 24
5 Measuring Logical Probabilities Page: 26
6 Problems with the Logical Interpretation Page: 29
7 Partial Entailment vs. Partial Content Page: 36
Further Reading Page: 37
4: The Subjective Interpretation Page: 38
1 Dutch Books and Gambling Behaviour Page: 39
2 Problems with the Dutch Book Argument Page: 42
3 Measurement and ‘Degrees of Belief’ Page: 46
4 An Alternative to Gambling Scenarios for Measuring Degree of Belief: Scoring Rules Page: 50
5 Objections to the Subjective View of Probability Page: 52
6 Subjective Monism and Independence Page: 56
Further Reading Page: 60
5: The Objective Bayesian Interpretation Page: 61
1 Extra Constraints on Degrees of Belief Page: 62
2 Objective Bayesianism in Action: A Further Illustration Page: 64
3 Is Objective Bayesianism an Interpretation of Probability? Page: 66
4 Objections to Objective Bayesianism Page: 68
5 Objective Bayesianism vs. the Logical Interpretation Page: 70
6 From Subjectivism to Objective Bayesianism: A Spectrum Page: 75
Further Reading Page: 76
6: Group Level Interpretations Page: 77
1 Group Dutch Books Page: 78
2 Group Dutch Books and Rationality Page: 78
3 The Intersubjective View: Gillies on Group Degrees of Belief and Consensus Page: 81
4 My Alternative View: Consensus on Using Betting Quotients Page: 84
5 Gillies vs. Rowbottom: A Dialogue Page: 86
6 From Intersubjective to Interobjective Probabilities: Another Spectrum Page: 90
Further Reading Page: 91
7: The Frequency Interpretation Page: 92
1 Finite Empirical Collectives and Actual Relative Frequencies Page: 93
2 Infinite Empirical Collectives and Actual Frequencies in the Limit Page: 96
3 Hypothetical Frequentism and von Mises’s Relative Frequency Interpretation Page: 99
4 The Empirical Laws: Stability and Randomness Page: 101
5 Initial Criticisms of Hypothetical Frequentism Page: 105
6 More Criticisms of Hypothetical Frequentism: Single Cases, Reference Classes, and Sequence Orderin Page: 108
7 A Brief Sympathetic Conclusion Page: 112
Further Reading Page: 112
8: The Propensity Interpretation Page: 113
1 Probabilities as Dispositions Page: 114
2 Single Case Propensities (Popper) Page: 115
3 Single Case Propensities vs. Long Run Propensities Page: 117
4 Single Case and Long Run Propensities: What’s the Relationship? Page: 120
5 The Reference Class Problem Again Page: 123
6 A Final Objection to Probabilities as Single Case Propensities: Humphrey’s Paradox Page: 125
7 A Brief Conclusion on Propensities Page: 126
Further Reading Page: 127
9: Fallacies, Puzzles, and a Paradox Page: 128
1 The Gambler’s Fallacy and the ‘Law’ of Averages Page: 128
2 The Base Rate Fallacy Page: 132
3 The Inverse Fallacy Page: 134
4 The Conjunction Fallacy Page: 135
5 The Monty Hall Paradox Page: 137
Further Reading Page: 142
10: Probability in the Humanities, Natural Sciences, and Social Sciences Page: 143
1 Confirmation Theory Page: 143
2 Mendelian Genetics Page: 147
3 Game Theory Page: 151
4 Quantum Theory Page: 155
5 The Final Curtain Page: 159
Further Reading Page: 159
Appendices Page: 161
A: The Axioms and Laws of Probability Page: 161
B: Bayes’s Theorem Page: 164
References Page: 167
Index Page: 171
EULA Page: A1