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