Philosophical Introduction to Probability

Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. 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, 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.

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
  - Collective-based 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 ‘truth-frequency’ 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
  - Single-case and long-run 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)

Philosophical Introduction to Probability

Contents