Key Figures
A compact reference to the principal contributors, with the claim each is cited for in this section. Ordered chronologically.
The founders
Blaise Pascal (1623–1662) — with Fermat, the 1654 correspondence on the division of stakes that founded the calculus. The Wager is the first decision-theoretic argument; see pragmatic arguments.
Christiaan Huygens (1629–1695) — the first textbook (1657); expectation as the primary notion.
Jacob Bernoulli (1655–1705) — Ars Conjectandi (1713): the first law of large numbers, and the first clear statement of the aleatory/epistemic distinction that became the chance/credence divide. Saw that his theorem addressed the inverse problem only indirectly.
Thomas Bayes (1701–1761) — the posthumous Essay (1763) solving a version of the inverse problem; an early recognition that the prior requires justification.
Pierre-Simon Laplace (1749–1827) — the classical interpretation in canonical form; the Principle of Indifference; a determinist for whom probability is entirely epistemic.
The nineteenth-century critics
George Boole (1815–1864) — the circularity objection to equipossibility.
John Venn (1834–1923) — The Logic of Chance (1866): frequentism and a sustained attack on indifference.
Charles Sanders Peirce (1839–1914) — an early propensity theorist: a die's probability is a "would-be", a disposition of the object.
Ludwig Boltzmann (1844–1906) — the statistical account of entropy; the origin of the problems treated in statistical mechanics.
Henri Poincaré (1854–1912) — the method of arbitrary functions, explaining why symmetric mechanical devices produce stable frequencies whatever the input distribution. The best vindication of the classical intuition, and relevant to deterministic chance.
The interpretation-builders
John Maynard Keynes (1883–1946) — A Treatise on Probability (1921): the logical interpretation, with probability as a primitive logical relation, and the admission that some probabilities are merely ordinal or incomparable.
Richard von Mises (1883–1953) — rigorous frequentism: collectives, limiting frequencies, and the axiom of randomness via place selection. Accepted that single-case probability is meaningless.
Frank Ramsey (1903–1930) — "Truth and Probability" (1926): the subjectivist foundation, the first Dutch-book argument, and the joint derivation of probability and utility from preference. Written against Keynes.
Bruno de Finetti (1906–1985) — "probability does not exist"; the representation theorem for exchangeable sequences; the rejection of countable additivity.
Harold Jeffreys (1891–1989) — invariant priors; the Jeffreys prior; the bridge from logical probability to objective Bayesianism.
Andrey Kolmogorov (1903–1987) — the measure-theoretic axiomatisation (1933), whose philosophical significance is its neutrality among interpretations. Also the founder of algorithmic randomness.
Rudolf Carnap (1891–1970) — Logical Foundations of Probability (1950) and the -continuum; the most systematic inductive logic, and the most instructive failure.
Hans Reichenbach (1891–1953) — frequentism; the pragmatic vindication of induction; the common-cause principle and screening off.
Karl Popper (1902–1994) — falsificationism; the propensity interpretation, introduced for single-case quantum probabilities.
Richard Cox (1898–1991) — the derivation of the probability axioms from structural desiderata on plausible reasoning.
Leonard Savage (1917–1971) — The Foundations of Statistics (1954): the definitive representation theorem; the sure-thing principle, relevant to Simpson's paradox.
The modern period
Nelson Goodman (1906–1998) — grue and the new riddle of induction; the demonstration that no purely formal confirmation theory can succeed.
E. T. Jaynes (1922–1998) — maximum entropy and transformation groups; the invariance resolution of Bertrand's paradox.
Wesley Salmon (1925–2001) — statistical-relevance and causal-mechanical accounts of explanation; objective homogeneity as an answer to the reference-class problem.
Richard Jeffrey (1926–2002) — Jeffrey conditionalization for uncertain evidence; radical probabilism.
John Bell (1928–1990) — Bell's theorem: the empirical refutation of local common-cause explanations of quantum correlations.
Patrick Suppes (1922–2014) — the probabilistic theory of causation in its systematic form.
David Lewis (1941–2001) — the Principal Principle; best-system chance; Humean supervenience and the discovery of the Big Bad Bug; the diachronic Dutch book. The single most influential figure in the contemporary debate.
Nancy Cartwright (b. 1943) — contextual unanimity in probabilistic causation; scepticism about universal laws.
Clark Glymour (b. 1942) — the old-evidence problem; with Spirtes and Scheines, causal discovery algorithms.
Judea Pearl (b. 1936) — causal models, the do-operator, the back-door criterion, and the ladder of causation.
Deborah Mayo (b. 1947) — error statistics and the severity requirement; the principal alternative to Bayesian evidence.
Alan Hájek (b. 1962) — the systematic catalogue of objections to each interpretation; the criteria of adequacy used throughout this section; the generality of the reference-class problem; the case for pluralism.
James Joyce (b. 1959) — the accuracy-dominance argument for probabilism, replacing pragmatic Dutch books with an epistemic argument.
Adam Elga (b. 1971) — Sleeping Beauty and the thirder argument; self-locating belief.
Nick Bostrom (b. 1973) — Anthropic Bias: the Self-Sampling and Self-Indication assumptions; the presumptuous philosopher; the systematic treatment of anthropic reasoning.
Barry Loewer (b. 1942) — the Mentaculus; the best-system treatment of statistical-mechanical probability.
David Wallace (b. 1976) — with Deutsch, the decision-theoretic derivation of the Born rule in Everettian quantum mechanics.
Jon Williamson (b. 1971) — the three-norm formulation of objective Bayesianism.
Peter Walley (b. 1946) — the theory of lower previsions and imprecise probability.
Paul Humphreys (b. 1950) — Humphreys' paradox: propensities are asymmetric, probabilities invert, so propensities are not probabilities.