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contrary, accepted indeterminism very well. To sum up, all of these works dealt with

the problem of games and produced a theory of chance, but probability is never men-

tioned, even if the vocabulary used is slightly more epistemological. There was still

significant confusion between statistics and prior knowledge, which led to two classes

of probabilities being confused, based on frequencies (related to statistics) and based

on equiprobable cases (related to prior knowledge).

A.1.2.
Towards the Bayesian mathematical formulation

The first link between game theory and probabilities was given in 1662, when it

was introduced by Arnauld in the
Art of Thinking
. Arnauld established an analogy

between games and everyday life and suggested that an epistemological perspective

of chance made it possible to apply the theory to probabilities (which were still consid-

ered as attributes of opinion). He stopped short of the concept of numerical probability,

but his works clearly mark a milestone in the evolution of the concept of probability.

The analogy between games and life was used up until the end of the 17
th
century by

demographers who calculated life expectancy tables by using game theory, but without

including the concept of probability.

A contribution from an entirely different field came from Leibniz, who suggested

in the
De Conditionibus
(1665) to represent a person's legal rights using numbers.

The absence of law was represented by 0, a pure law by 1 and a conditional law by

a fraction between 0 and 1. This classification of rights relies on the condition upon

which the law is founded: an impossible condition leads to the absence of law, if it is

necessary the law is pure, if it is contingent
2
, the law is conditional. These concepts

of contingency and necessity are also used by Bernoulli regarding the problem of the

combination of testimonies. Leibniz suggests relating the probability for the condition

to exist with the “quantity” of the law and thus seemed to lean towards a numerical

conception of probability, without relying on game theory. He only later becomes

acquainted with this theory. Although his essays on chance provided nothing new

from a mathematical perspective, they acknowledged the link between probability and

game theory.

In the field of the combination of testimonies, the works of Hooper in 1699 (
A Cal-

culation of the Credibility of Human Testimony
) lead to the definition of non-Bayesian

confidence functions, which represent the credibility of a witness, as well as to two

combination rules, one for consecutive testimonies and the other for simultaneous

testimonies. These two rules, which were very popular in the 18
th

century, were com-

pletely abandoned in the 19
th

century.

2. Contingent is used here meaning that something may or may not occur.

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