On some French probabilists of the twentieth century: Fréchet, Borel, Lévy

In the first half of the Twentieth century a number of authors active in distant parts of Europe and in different areas of scientific research shared a probabilistic approach to science and knowledge in general, albeit embracing different interpretations of probability. My “Probabilistic Epistemology: a European Tradition” focussed on the work of Polish logician Janina Hosiasson, British mathematician Frank Plumpton Ramsey and geophysicist Harold Jeffreys, Italian statistician Bruno de Finetti, and German philosopher of science Hans Reichenbach, arguing that one can speak of a European tradition in probabilistic epistemology. To clarify the matter, by probabilistic epistemology I mean the view that probability is an essential ingredient of knowledge, and that induction is a fundamental component of the scientific method. Such a view is grounded in the conviction that certainty of knowledge and completeness of information are unachievable. The purpose of this paper is to expand on my earlier work by adding to the picture the French mathematicians Maurice Fréchet, Émile Borel and Paul Lévy, all of whom advocated a probabilistic approach to epistemology, bringing new evidence that probabilistic epistemology was widespread throughout Europe in the first half of the Twentieth century. Apart from that, the philosophy of probability embraced by such outstanding mathematicians seems worthy of attention in itself. Given the scant literature on the topic, confined to its technical aspects, the present analysis will broaden the picture of the debate on the foundations of probability.