The Mathematization of Chance in the Middle of the 17th Century

Abstract

In my paper I will give an account of the calculus of games of chance as presented in the correspondence between Pascal and Fermat as well as in Huygens’ little tract De ratiociniis in ludo aleae. Such an account refers especially to the article of Donald Gillies “An empiricist philosophy of mathematics and its implications for the history of mathematics” and to his claim that empirical observations triggered the early development of probability theory as visible in the correspondence between Pascal and Fermat from 1654. Gillies is concerned with such empirical observations because they confirm in his opinion his empiricist philosophy of mathematics. Gillies’ empiricist approach suggests that “some pattern of development which is well-established as characteristic of the growth of theoretical natural science in general” is likely to be found in the history of mathematics. He contends that if every such pattern found in theoretical natural science can also be found somewhere in the development of mathematics then “this would tend to confirm our empiricist view of mathematics” and if, “on the contrary, some patterns of development which are definitely characteristic of theoretical natural science are not to be found in the history of mathematics, this would tend to undermine the present philosophy of mathematics.”