What is included with this book?
Preface | p. xiii |
Intuitive Definitions | p. 1 |
Motivating Examples | p. 3 |
Free Will and Determinism | p. 5 |
Can Free Choice Be Predicted? | p. 5 |
Is the World Deterministic? | p. 6 |
Is Free Will Observable? | p. 6 |
The Problem of Free Will | p. 7 |
A Rational Illusion | p. 10 |
Free Will and the Decision Matrix | p. 12 |
The Principle of Indifference | p. 14 |
Will a Canonical Space Help? | p. 14 |
The Canonical State Space | p. 14 |
Difficulties with a Uniform Prior on [0, 1] | p. 15 |
Conclusion | p. 16 |
What's Special about the Coin? | p. 17 |
Symmetry | p. 17 |
Smooth Beliefs | p. 18 |
Relative Frequencies | p. 20 |
The Law of Large Numbers | p. 20 |
The Problem of Induction | p. 21 |
Hume's Critique | p. 21 |
Goodman's Grue-Bleen Paradox | p. 22 |
Kolmogorov Complexity and Its Dependence of Language | p. 23 |
Grue-Bleen Again | p. 26 |
Evolutionary Explanations | p. 31 |
Problems with the Frequentist Approach | p. 34 |
Subjective Probabilities | p. 37 |
Linda the Bank Teller | p. 37 |
Pascal's Wager | p. 38 |
Classical versus Bayesian Statistics | p. 40 |
Basic Definitions | p. 40 |
The Gambler Fallacy | p. 41 |
Exchangeability | p. 42 |
Confidence Is Not Probability | p. 44 |
Classical Statistics Can Be Ridiculous | p. 45 |
Different Methods for Different Goals | p. 46 |
Behavioral Definitions | p. 49 |
A Case Study | p. 51 |
A Characterization Theorem for Maximization of Utility | p. 51 |
Proof | p. 53 |
Interpretations | p. 55 |
A Few Definitions | p. 56 |
A Meta-Scientific Interpretation | p. 59 |
A Normative Interpretation | p. 62 |
A Descriptive Interpretation | p. 63 |
Limitations | p. 64 |
Semiorders | p. 65 |
Other Ways to Measure Utility | p. 71 |
The Role of Theories | p. 72 |
Theories Are Always Wrong | p. 72 |
Theories and Conceptual Frameworks | p. 74 |
Logical Positivism as a Metaphor | p. 76 |
Von Neumann-Morgenstern's Theorem | p. 78 |
Background | p. 78 |
The Theorem | p. 79 |
Proofs | p. 83 |
The Algebraic Approach | p. 83 |
A Geometric Approach | p. 84 |
A Separation Argument | p. 85 |
The Three Interpretations | p. 86 |
De Finetti's Theorem | p. 89 |
Motivation | p. 89 |
The Theorem | p. 90 |
A Proof | p. 91 |
The Three Interpretations | p. 92 |
Savage's Theorem | p. 94 |
Background | p. 94 |
States, Outcomes, and Acts | p. 96 |
Axioms | p. 97 |
P1 | p. 97 |
P2 | p. 97 |
Notation | p. 99 |
Null Events | p. 99 |
P3 | p. 100 |
P4 | p. 102 |
P5 | p. 102 |
P6 | p. 103 |
P7 | p. 104 |
The Result for a Finite Outcome Set | p. 105 |
Finitely Additive Measures | p. 105 |
Nonatomic Measures | p. 107 |
The Theorem | p. 108 |
The Case of a General Outcome Set | p. 108 |
Interpretations | p. 109 |
The Proof and Qualitative Probabilities | p. 110 |
The Definition of States | p. 113 |
Causality | p. 113 |
Newcomb's Paradox | p. 113 |
States as Functions from Acts to Outcomes | p. 114 |
A Problem | p. 115 |
Hempel's Paradox of Confirmation | p. 116 |
Are All Ravens Black? | p. 116 |
A State-Space Formulation | p. 117 |
What Is a Confirmation? | p. 117 |
A Resolution | p. 118 |
Good's Variation | p. 118 |
What Do We Learn from This? | p. 119 |
Monty Hall Three-Door Game | p. 120 |
A Critique of Savage | p. 123 |
Criticizing Critiques | p. 123 |
An Example | p. 123 |
The General Lesson | p. 124 |
Critique of P3 and P4 | p. 125 |
Example | p. 125 |
Defense | p. 126 |
State-Dependent Utility | p. 127 |
The Definition of Subjective Probability | p. 128 |
When Is State Dependence Necessary? | p. 129 |
Critique of P1 and P2 | p. 130 |
The Basic Problem | p. 130 |
Reasoned Choice versus Raw Preferences | p. 131 |
Schmeidler's Critique and Ellsberg's Paradox | p. 132 |
Observability of States | p. 136 |
Problems of Complexity | p. 137 |
Objectivity and Rationality | p. 138 |
Subjectivity and Objectivity | p. 138 |
Objective and Subjective Rationality | p. 139 |
Anscombe-Aumann's Theorem | p. 142 |
Alternative Behavioral Theories | p. 145 |
Choquet Expected Utility | p. 147 |
Schmeidler's Intuition | p. 147 |
Choquet Integral | p. 149 |
Comonotonicity | p. 150 |
Axioms and Result | p. 151 |
Prospect Theory | p. 154 |
Background | p. 154 |
Gain-Loss Asymmetry | p. 154 |
Distortion of Probabilities | p. 156 |
Rank-Dependent Probabilities and Choquet Integration | p. 158 |
Maxmin Expected Utility | p. 160 |
Convex Games | p. 160 |
A Cognitive Interpretation of CEU | p. 161 |
Axioms and Result | p. 163 |
Interpretation of MMEU | p. 163 |
Generalizations and Variations | p. 165 |
Bewley's Alternative Approach | p. 165 |
Combining Objective and Subjective Rationality | p. 166 |
Applications | p. 168 |
Cognitive Origins | p. 171 |
Case-Based Qualitative Beliefs | p. 173 |
Axioms and Result | p. 173 |
Four Known Techniques | p. 175 |
The Combination Axiom in General Analogical Reasoning | p. 177 |
Violations of the Combination Axiom | p. 179 |
Frequentism Revisited | p. 180 |
Similarity-Weighted Empirical Frequencies | p. 180 |
Intuition | p. 181 |
Axiomatization | p. 182 |
Empirical Similarity and Objective Probabilities | p. 184 |
Future Research | p. 188 |
References | p. 191 |
Index | p. 199 |
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