Philosophical Lectures on Probability

Bruno de Finetti (1906–1985) is one of the most important mathematicians of XX century. He is considered the founder of the subjective interpretation of probability, together with the British philosopher F. P. Ramsey. Graduated in Mathematics at Milan Polytechnic in 1927, he served as actuary at Assicurazioni Generali Venezia and as a mathematician (1927–1931) at the National Central Bureau in Rome. In 1936 de Finetti won a competition for a chair at the University of Trieste but, according to Fascist laws in force, his appointment was not implemented, since he was not married. Only in 1950 he became full professor at the University of Trieste. From 1954 he taught at the University of Rome up to 1976, when he retired. During his life de Finetti received numerous prizes and acknowledgments for his exceptional scientific contributions. In particular, he was prized from the Accademia dei Lincei in 1964, the Swiss Association of Actuaries in 1978 and the French Statistical Society in 1979. In April 1981 an International Conference on "Exchangeability in Probability and Statistics" was organised in Rome (the related Proceedings were published by North-Holland in 1982). Several celebrations and books were devoted to his memory after his death. The Italian government declared the years 2005 and 2006 "Definettian biennium", to celebrate together the 20th anniversary after his death and the first centenary after his birth. A long series of international conferences were organised in Rome, Trieste, Bologna and Milan in his honour, and several books by de Finetti were reprinted in Italy. Beyond his fundamental studies on the logic of probability and expectation, de Finetti gave imperishable contributions to the theory of probability, to econometric, to financial and actuarial mathematics. He forerun by a dozen years Markowitz (who received the Nobel Prize for this contribution) discovery of the mean-variance method. In the field of Probability theoryhe introduced the central notion of infinitely divisible distribution and of exchangeability and proved the celebrated De Finetti’s Representation theorem, which is of both mathematical and philosophical outstanding relevance and plays a crucial role in modern Bayesian statistics. Alberto Mura, Ph.D. is associate professor of Logic and Philosophy of Science. He was student of de Finetti at the National Institute for Advanced Mathematics in Rome. His interests include Foundations of Probability, Decision theory, Induction, Causality and Bayesian Law of Evidence. Among his publications are the books "La sfida scettica" (The sceptical challenge), Pisa, 1992 e "Dal noto all’ignoto: Causalità e induzione nel pensiero di David Hume" (From the Known to the Unknown: Causality and Induction in the thought of David Hume), Pisa 1996 and several papers, in particular When Probabilistic Support is Inductive, Philosophy of Science 1990, Hume’s Inductive Logic, Synthese 1998, and Deductive Probability, Physical Probability, and Partial Entailment (in Popper Philosopher of Science, Rubbettino 2006).

Introductory Lecture.- Decisions and Proper Scoring Rules.- Geometric Representation of Brier’s Rule.- Bayes’ Theorem.- Physical Probability and Complexity.- Stochastic Independence and Random Sequences.- Superstition and Frequentism.- Exchangeability.- Distributions.- The Concept of Mean.- Induction and Sample Randomization.- Complete Additivity and Zero Probabilities.- The Definitions of Probability.- The Gambler’s Fallacy.- “Facts” and “Events”.- “Facts” and “Events”: An Example.- Prevision, Random Quantities, and Trievents.- Désir André’s Argument.- Characteristic Functions.