CSLI, 2005 eISBN: 978-1-57586-797-7 | Paper: 978-1-57586-490-7 | Cloth: 978-1-57586-489-1 Library of Congress Classification BC141.G35 2005 Dewey Decimal Classification 121.63

ABOUT THIS BOOK | TOC

ABOUT THIS BOOK

Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. A Philosophical Introduction to Probability showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's “classical” interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability.

TABLE OF CONTENTS

Contents
Introductory remarks 1
1 The notion of probability
1.1 A historical sketch 7
The birth of probability 7
The dual character of probability 12
Jakob Bernoulli and direct probability 13
Nikolaus and Daniel Bernoulli 15
Thomas Bayes and inverse probability 17
Probability and social mathematics: Condorcet and Quetelet 18
The rise of contemporary statistics: Galton, Pearson, Fisher 21
The advent of probability in physics 25
1.2 Probability and induction 27
Francis Bacon 28
Induction as ampliative inference 29
Hume's problem of induction 31
Mill, Herschel, Whewell 34
2 The laws of probability
2.1 The fundamental properties of probability 39
2.2 Bayes' rule 47
2.3 Kolmogorov's axiomatization 52
3 The classical interpretation
3.1 Laplace and the Principle of insufficient reason 57
Determinism 57
The 'Principle of insufficient reason' 60
The 'Rule of succession' 62
Expectation and certainty 64
3.2 Problems of the classical definition 66
4 The frequency interpretation
4.1 Robert Leslie Ellis 71
4.2 John Venn 74
Probability as limiting frequency 74
Criticism of the rule of succession 77
Probability and belief 78
4.3 Richard von Mises and the theory of 'collectives' 81
Von Mises' approach 81
Collectives 83
Randomness 85
Collective-based probability 87
Applications to science 89
4.4 Hans Reichenbach's probabilistic epistemology 91
Reichenbach's frequentism 91
The theory of posits 95
The justification of induction 98
Causality 99
4.5 Ernest Nagel's 'truth-frequency' theory 101
5 The propensity interpretation
5.1 Peirce, the forerunner 105
5.2 Popper's propensity interpretation 106
Falsificationism 106
The propensity interpretation of probability 109
A world of propensities 112
5.3 After Popper 114
Single-case and long-run propensity theories 114
Humphrey's paradox 118
Propensity as an ingredient of the description of chance
phenomena 121
5.4 Digression on chance and randomness 125
Historical remarks 125
Poincare's views on chance 126
The riddle of randomness 128
Is chance objective? 132
6 The logical interpretation
6.1 Beginnings 135
6.2 The nineteenth century English Logicists 136
Augustus De Morgan 136
George Boole 138
William Stanley Jevons 141
6.3 John Maynard Keynes 144
Probability as a logical relation 144
Rationality and the role of intuition 147
Analogy, relevance and weight 149
Ramsey's criticism 152
6.4 William Ernest Johnson 153
6.5 Viennese logicism: Wittgenstein and Waismann 158
Ludwig Wittgenstein 158
Friedrich Waismann 161
6.6 Rudolf Carnap's inductive logic 164
Two concepts of probability 164
The logic of confirmation 169
The turn of the Sixties 174
6.7 Harold Jeffreys between logicism and subjectivism 178
Bayesianism 178
The interpretation of probability 181
Probabilistic epistemology 184
7 The subjective interpretation
7.1 The beginnings 189
William Donkin 189
Emile Borel 191
7.2 Frank Plumpton Ramsey and the notion of coherence 194
Degrees of belief and consistency 194
Ramsey, Keynes and Wittgenstein 200
Belief, frequency and 'probability in physics' 202
7.3 Bruno de Finetti and exchangeability 208
De Finetti's radical probabilism 208
Subjective Bayesianism 215
Criticism of other interpretations of probability 220
Indeterminism 223
7.4 Some recent trends 225
Richard Jeffrey's radical probabilism 225
Patrick Suppes' probabilistic empiricism 230
Closing remarks 235
References 239
Index 261

Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. A Philosophical Introduction to Probability showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's “classical” interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability.

TABLE OF CONTENTS

Contents
Introductory remarks 1
1 The notion of probability
1.1 A historical sketch 7
The birth of probability 7
The dual character of probability 12
Jakob Bernoulli and direct probability 13
Nikolaus and Daniel Bernoulli 15
Thomas Bayes and inverse probability 17
Probability and social mathematics: Condorcet and Quetelet 18
The rise of contemporary statistics: Galton, Pearson, Fisher 21
The advent of probability in physics 25
1.2 Probability and induction 27
Francis Bacon 28
Induction as ampliative inference 29
Hume's problem of induction 31
Mill, Herschel, Whewell 34
2 The laws of probability
2.1 The fundamental properties of probability 39
2.2 Bayes' rule 47
2.3 Kolmogorov's axiomatization 52
3 The classical interpretation
3.1 Laplace and the Principle of insufficient reason 57
Determinism 57
The 'Principle of insufficient reason' 60
The 'Rule of succession' 62
Expectation and certainty 64
3.2 Problems of the classical definition 66
4 The frequency interpretation
4.1 Robert Leslie Ellis 71
4.2 John Venn 74
Probability as limiting frequency 74
Criticism of the rule of succession 77
Probability and belief 78
4.3 Richard von Mises and the theory of 'collectives' 81
Von Mises' approach 81
Collectives 83
Randomness 85
Collective-based probability 87
Applications to science 89
4.4 Hans Reichenbach's probabilistic epistemology 91
Reichenbach's frequentism 91
The theory of posits 95
The justification of induction 98
Causality 99
4.5 Ernest Nagel's 'truth-frequency' theory 101
5 The propensity interpretation
5.1 Peirce, the forerunner 105
5.2 Popper's propensity interpretation 106
Falsificationism 106
The propensity interpretation of probability 109
A world of propensities 112
5.3 After Popper 114
Single-case and long-run propensity theories 114
Humphrey's paradox 118
Propensity as an ingredient of the description of chance
phenomena 121
5.4 Digression on chance and randomness 125
Historical remarks 125
Poincare's views on chance 126
The riddle of randomness 128
Is chance objective? 132
6 The logical interpretation
6.1 Beginnings 135
6.2 The nineteenth century English Logicists 136
Augustus De Morgan 136
George Boole 138
William Stanley Jevons 141
6.3 John Maynard Keynes 144
Probability as a logical relation 144
Rationality and the role of intuition 147
Analogy, relevance and weight 149
Ramsey's criticism 152
6.4 William Ernest Johnson 153
6.5 Viennese logicism: Wittgenstein and Waismann 158
Ludwig Wittgenstein 158
Friedrich Waismann 161
6.6 Rudolf Carnap's inductive logic 164
Two concepts of probability 164
The logic of confirmation 169
The turn of the Sixties 174
6.7 Harold Jeffreys between logicism and subjectivism 178
Bayesianism 178
The interpretation of probability 181
Probabilistic epistemology 184
7 The subjective interpretation
7.1 The beginnings 189
William Donkin 189
Emile Borel 191
7.2 Frank Plumpton Ramsey and the notion of coherence 194
Degrees of belief and consistency 194
Ramsey, Keynes and Wittgenstein 200
Belief, frequency and 'probability in physics' 202
7.3 Bruno de Finetti and exchangeability 208
De Finetti's radical probabilism 208
Subjective Bayesianism 215
Criticism of other interpretations of probability 220
Indeterminism 223
7.4 Some recent trends 225
Richard Jeffrey's radical probabilism 225
Patrick Suppes' probabilistic empiricism 230
Closing remarks 235
References 239
Index 261