Un “Probabilista neoclassico”: Francesco Paolo Cantelli

Abstract

For some decades F. P. Cantelli (1875–1966) was one of the most prominent Italian contributors to the mathematical theory of probability. Although his name is frequently connected with the name of E. Borel, Cantelli's approach to probability is very different from that of Borel. This paper looks at F. P. Cantelli's contributions to the development of the calculus of probability during the years of the earlier axiomatic formulations, with particular emphasis on Cantelli's point of view on the foundations of probability. After a brief biographical sketch, I emphasize the relation between Cantelli's papers of the years 1916–1917 and the debate among some Italian mathematicians about the possibility of defining probability in terms of relative frequencies. Some of the most important mathematical results are recalled and related to other researches on the calculus of probability during the period 1920–1930. Cantelli's conception of the foundations of probability is analyzed and compared with that of R. von Mises, as presented in 1936 during a debate published in the Giornale dell'Istituto Italiano degli Attuari.