Philosophical Introduction to Probability
Maria Carla Galavotti
Not limited to merely mathematics, probability has a rich and
controversial philosophical aspect. Philosophical Introduction to
Probability showcases lesserknown 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, including Pierre Simon de Laplace's “classical”
interpretation of probability, the frequency interpretation of
Richard von Mises, the subjectivism of Frank Ramsey and Bruno de
Finettit, and 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.
Maria Carla Galavotti is professor of philosophy of science at the
University of Bologna.
Translated into Japanese.
Copyright page iv (corrected)
Contents pages viix (corrected)
 Opening Remarks
 1. The notion of probability
 1.1 A historical sketch
 The probability
 The dual character of probability
 Jakob Bernoulli and direct probability
 Nikolaus and Daniel Bernoulli
 Thomas Bayes and inverse probability
 Probability and social mathematics: Condorcet Quetelet
 The rise of contemporary statistics: Galton, Pearson, Fisher
 The advent of probability in physics
 1.2 Probability and induction
 Francis Bacon
 Induction as ampliative inference
 Hume's problem of induction
 Mill, Herschel, Whewell
 2. The laws of probability
 2.1 The fundamental properties of probability
 2.2 Bayes' rule
 2.3 Kolmogorov's axiomatization
 3. The classical interpretation
 3.1 Laplace and the Principle of insufficient reason
 Determination
 The ‘Principle of insufficient reason’
 The ‘Rule of succession’
 Expectation and certainty
 3.2 Problems of the classical definition
 4. The frequency interpretation
 4.1 Robert Leslie Ellis
 4.2 John Venn
 Probability as limiting frequency
 Criticisms of the rule of succession
 Probability and belief
 4.4 Richard von Mises and the theory of ‘collectives’
 Von Mises' approach
 Collectives
 Rondomness
 Collectivebased probability
 Applications to science
 4.4 Hans Reichenbach's probabilistic epistemology
 Reichenbach's frequentism
 The theory of posits
 The justification of induction
 Causality
 4.5 Ernst Nagel's ‘truthfrequency’ theory
 5. The propensity interpretation
 5.1 Peirce, the forerunner
 5.2 Popper's propensity interpretation
 Falsification
 The propensity interpretation of probability
 A world of propensities
 5.3 After Popper
 Singlecase and longrun propensity theories
 Humphrey' paradox
 Propensity as an ingredient of the description of chance phenomena
 5.4 Digression on chance and radomes
 Historical remarks
 Poincaré's views on chance
 The riddle of randomness
 Is chance objective?
 6. The logical interpretation
 6.1 Beginnings
 6.2 The nineteenth English Logistics: De Morgan, Boole, Jevons
 Augustus De Morgan
 George Boole
 William Stanley Jevons
 6.3 John Maynard Keynes
 Probability as a logical relation
 Rationality and the role of intuition
 Analogy, relevance and weight
 Ramsey's criticism
 6.4 William Ernest Johnson
 6.5 Viennese logicism: Wittgenstein and Waismann
 Ludwig Wittgenstein
 Friedrich Waismann
 6.6 Rudolf Canarp's inductive logic
 Two concepts of probability
 The logic of confirmation
 The turn of the Sixties
 6.7 Harold Jeffreys between logicism and subjectivism
 Bayesianism
 The interpretation of probability
 7. The subjective interpretation
 7.1 The beginnings
 William Donkin
 Émile Borel
 7.2 Frank Plumpton Ramsey and the notion of coherence
 Degrees of belief and consistency
 Ramsey, Keynes and Wittgenstein
 Belief, frequency and ‘probability in physics’
 7.3 Bruno de Finetti and exchangeability
 De Fintetti' radical probabilism
 Subjective Bayesianism
 Criticism of other interpretations of probability
 Undeterminism
 7.4 Some recent trends
 Richard Jeffrey's radical probabilism
 Patrick Suppes' probabilistic empiricism
 Closing Remarks
 References
 Index
March 2009
ISBN (Paperback): 1575864908 (9781575864907)
ISBN (Electronic): 1575867974 (9781575867977)

Distributed by the University of Chicago Press
