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