Probability: A Philosophical Introduction

Probability: A Philosophical Introductionpresents the basic concepts of probability to philosophy students who are new to this area of the subject. Probability plays an important part in many areas of philosophy, such as causation in metaphysics, induction in philosophy of science, and belief and justification in epistemology. This book: * assumes no mathematical background and keeps the technicalities to a minimum * explains the most important applications of probability theory to philosophy * outlines the different kinds of probability and assesses the strengths and weaknesses of each * introduces and discusses key terms such as propensity, frequency, evidence and credence D.H. Mellor presents and compares theories of probability in a simple and impartial way, makingProbability: A PhilosophicalIntroductionessential reading for any philosophy student confronted with probability for the first time.

Preface

xi

Introduction and Summary

Introduction

1

(2)

Summary

3

(4)

Kinds of Probability

Introduction

7

(2)

Chances

9

(1)

Epistemic Probabilities

10

(1)

Credences

11

(1)

How Kinds of Probability Differ

12

(1)

Probabilities of Complex Propositions

13

(1)

Conditional Probabilities

14

(1)

Numerical Probabilities

15

(3)

Pure and Applied Probability

18

(3)

Classical Probabilities

Introduction

21

(1)

Two Kinds of Possibility

22

(1)

Credences

23

(1)

Sample Spaces

24

(2)

Infinite Sample Spaces

26

(1)

Indifference

27

(2)

Chances

29

(3)

Frequencies

Credences

32

(1)

Epistemic Probabilities

33

(2)

Humean Chances

35

(3)

Frequentism and Classicism

38

(2)

Limiting Frequencies

40

(2)

Hypothetical Frequencies

42

(3)

Possibilities and Propensities

Modal Chances

45

(4)

Propensities

49

(2)

Dispositions

51

(2)

Dispositional Chances

53

(5)

Chance and Necessity

58

(3)

Modality versus Propensity

61

(1)

The Existence of Chances

62

(3)

Credence

Degrees of Belief

65

(2)

Betting and Belief

67

(2)

Coherence

69

(2)

Approximate Credences

71

(3)

Decision Theory

74

(5)

Confirmation

Measuring Evidential Support

79

(1)

Epistemic and Other Probabilities

80

(2)

Inductive Logic

82

(2)

Chances as Evidence

84

(3)

Confirmation Relations

87

(3)

Conditionalisation

Conditional Probability

90

(1)

The Pro Rata Rule

91

(2)

Epistemic Probabilities

93

(1)

Problems with Priors

94

(2)

Prior Credences

96

(1)

Bayes's Theorem

97

(2)

Bayesianism

99

(2)

Input Credences

Perception

101

(2)

Consistency

103

(2)

Reliability

105

(3)

Uncertain Evidence

108

(4)

Questions for Bayesians

Sample Spaces

112

(2)

Bayes's Proposition 3

114

(2)

Decisions and Credences

116

(3)

Conditional Bets

119

(2)

Imaging

121

(1)

Non-Bayesian Behaviour

122

(3)

Conclusion

125

(2)

Chance, Frequency and Credence

The Straight Rule

127

(2)

The Large Numbers Link

129

(2)

Independence

131

(2)

Chances and Estimates

133

(1)

Exchangeability

134

(1)

Frequencies and Credences

135

(3)

Subjectivism

138

(4)

References

142

(5)

Index

147

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Probability: A Philosophical Introduction

Summary

Table of Contents

Supplemental Materials

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Summary

Table of Contents

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