Law and rule in the Essay towards solving a problem in the doctrine of chances.

In his famous Essay towards solving a problem in the doctrine of chances, Bayes calculates probabilities as chances to be in the right in one's guess or as fractions of certainty. He was led to use two schemas. The first one is a monetary schema.

["Secret causes": causality and determinism in the classical age].

The notion of the "secret cause", which appears in many classical texts is tied to a particular practice of science and a conception of its methods where the "law" finds itself at the center of the nexus. If certain phenomena appear to escape the law, one is obliged to amend the law through the introduction of a series of "small equations." If the calculation of probabilities is deployed, this is to precisely reveal causes which are, at their origin, secret, but which will gradually become less so and eventually conform to laws.

[The problem of divisions, wagers, and game theory].

This article looks at the "problem of the divisions" - a dialogue between two persons or more - to bring out its structure, in which religious and ethical elements are intermingled. It then offers a reevaluation of the argument of the wager, which is seen here as a sort of prefiguration of game theory rather than as the solution to a problem of probabilities. Although their correspondence suggests that Fermat and Pascal believed they were offering a solution to the same problem, they were not - as written by Fermat, the problem of divisions is a problem of probabilities, but ultimately Fermat did not solve the same problem as Pascal.