## The Logic of Decision"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, Journal of Philosophy |

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### Contents

A Bayesian Framework | 3 |

12 Desirabilities and Probabilities | 4 |

13 Summary and Rationale | 7 |

14 Incompletely Specified Desirabilities | 8 |

15 Dominance and a Fallacy | 10 |

16 Problems | 12 |

17 Rat if lability | 17 |

18 Notes and References | 22 |

72 Determining Ratios of Probabilities | 120 |

73 A Probability Scale for Indifferent Propositions | 124 |

74 Nullity | 125 |

75 A General Technique | 127 |

76 Measuring Probabilities of Indifferent Propositions | 128 |

77 Problems | 131 |

8 Uniqueness | 134 |

81 Uniqueness of Probabilities | 135 |

Equivalent Scales | 28 |

21 Equivalent Desirability Matrices | 29 |

22 Conventions about Probabilities | 33 |

23 A General Desirability Transformation | 34 |

24 A Special Desirability Transformation | 36 |

25 Problems | 41 |

Ramseys Theory | 43 |

32 From Probabilities to Desirabilities | 44 |

33 The von NeumannMorgenstern Method | 46 |

34 Ethical Neutrality Probability 12 | 48 |

35 Calibrating the Desirability Scale | 51 |

36 Measuring Probabilities | 52 |

37 Conclusion | 53 |

38 Problems | 55 |

39 Notes and References | 57 |

4 Prepositional Attitudes | 61 |

42 Justifying the Special Addition Law | 62 |

43 Remarks on Fairness | 63 |

44 Desirability | 64 |

45 Sentences and Propositions | 66 |

46 Notation | 67 |

47 Belief versus Assent | 70 |

48 Problems | 72 |

49 References and Solutions | 74 |

Preference | 76 |

52 The Propositions T and F | 78 |

54 Computing Desirabilities | 80 |

55 The Probability and Desirability Axioms | 82 |

56 Good Bad Indifferent | 83 |

57 Preference between News Items | 84 |

58 Acts as Propositions | 85 |

59 Desirabilities Determine Probabilities | 87 |

510 Problems | 89 |

511 Notes and References | 93 |

Equivalence Perspectives Quantization | 97 |

61 Bolkers Equivalence Theorem | 98 |

62 Zero and Unit | 101 |

63 Bounds on Desirabilities | 102 |

64 Bounds on c | 104 |

65 Perspective Transformations of Desirability | 105 |

66 Probability Quantization | 108 |

67 Problems | 113 |

68 Acknowledgment | 114 |

From Preference to Probability | 115 |

71 The Existence Closure G and Splitting Conditions | 118 |

82 A Scale of Desirabilities between 0 and 1 | 136 |

83 Uniqueness of the Scale | 138 |

84 Uniqueness of Desirabilities in the Unit Interval | 139 |

85 Uniqueness of Negative Desirabilities | 141 |

86 Completing the Uniqueness Proof | 142 |

87 Problems | 143 |

88 Notes and References | 144 |

Bolkers Axioms | 146 |

92 Prospects as Propositions | 147 |

93 Averaging Nullity and Impartiality | 148 |

94 Completeness Atomlessness Continuity | 149 |

95 Notes and References | 151 |

10 Boundedness Causality | 152 |

101 The St Petersburg Paradox | 153 |

102 Resolving the Paradox | 156 |

103 Gambles as Causal Relationships | 158 |

104 Our Theory Is Noncausal | 159 |

105 Further Comparison with Ramseys Theory | 160 |

106 Justifying Quantization | 163 |

107 Notes and References | 164 |

Probability Kinematics | 166 |

112 The Problem | 168 |

113 Solution for n 2 | 170 |

114 Relevance | 172 |

115 Comparison with Conditionalization | 173 |

116 Solution for Finite n | 174 |

117 Origination Closure | 175 |

118 The Continuous Case | 177 |

119 Probabilistic Acts Trying | 179 |

1110 Observation Meaning | 181 |

1111 Notes and References | 182 |

Induction and Objectification | 186 |

122 Bayess Theorem | 187 |

123 Simple Induction | 189 |

124 Confirming Generalizations | 192 |

125 Objectivity and Learning | 197 |

126 De Fincttis Representation Theorem | 201 |

127 Objectification | 204 |

128 Conclusion | 210 |

129 Notes and References | 213 |

Preference among Preferences | 216 |

Notes and References | 226 |

231 | |

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### Common terms and phrases

agent's belief function agent's preference ranking Akrates Bayesian belief function prob Bolker's card is drawn Carnap change from prob chapter choice conditionalization conjunction consequences corresponding decision decision theory define degree of belief denial desirability assignment desirability matrix determined disjunction dollars Donald Davidson entry equation equiprobable equivalent estimated desirability ethically neutral example expected desirability expression fact false finite gamble implies incompatible indifferent induction infimum infinite interval Logic necessary proposition negative Newcomb's problem notion null objective observation option ositions partitioning Patrick Suppes Petersburg paradox Port-Royal Logic positive number possible worlds pref prob A(n prob A/B prob G prob X probability and desirability probability assignment probability axioms probability matrix probability measure problem rain Ramsey's theory relevant rows Rudolf Carnap satisfied sense sentences sequence smoking subjective probability suppose supremum takes theory of preference tosses transformation true truth tuna uniqueness theorem whale steak

### Popular passages

Page 1 - In order to judge," they say, "of what we ought to do in order to obtain a good and to avoid an evil, it is necessary to consider not only the good and evil in themselves, but also the probability of their happening and not happening, and to regard geometrically the proportion which all these things have, taken together.