Probabilities: A Historical Perspective - Information Fusion in Signal and Image Processing - page 253

(apparently) do not follow any law that is predictable or that has been learned. This
third category would seem to rule out any possibility of a mathematical theory for
chance.
These concepts were still very primitive, and no theory had yet been developed.
However, their importance can be disputed, since they are related to the theory of
knowledge, considered to be essential, and the focus of the work of many philoso-
phers. The fact that probability was considered as a “guide to life” by Cicero (60
BC) stands as proof of this. It is difficult to resist the pleasure of repeating these few
sentences by Seneca, quoted in [MAT 78]: “There are differences of interpretation,
however, between our countrymen and the Etruscans, the latter of whom possess con-
summate skill in the explanation of the meaning of lightning. We think that because
clouds collide, therefore lightning is emitted; they hold that clouds collide in order
that lightning may be emitted. They refer everything to the will of God: therefore they
are strong in their conviction that lightning does not give an indication of the future
because it has occurred, but occurs because it is meant to give this indication” (Seneca,
Natural Questions , II, 32).
This passage is a good illustration of the subjective nature of opinion; it is impos-
sible to imagine an experiment that would make it possible to prove or refute either
one of these opinions. This is also an illustration of the difference between causality
and logical links, which are often not distinguished. Probabilities express logical links
but not causality relations [DEM 93].
These epistemological categories later disappeared, for unknown reasons. During
the Renaissance, two completely independent concepts were used: chance, or random-
ness, and probability, which is seen as an attribute of opinion and with no numerical
value attached to it. The concept of chance is strongly related to game theory. Its
premises can be found in Dante's Purgatory (1310), in which he describes the differ-
ent sums that can be obtained from rolling three dice. Game theory was later widely
developed at the end of the 16 th century and during the first half of the 17 th century.
Cardan (1560) and Galileo (1620) compiled the different results that can be obtained
in a game, and counted the number of cases where each of these outcomes occurred.
For the first time, the concept of “equiprobable cases” was mentioned. The origins of
the mathematical probability theory are attributed to Pascal and Fermat (even though
they did not use the word probability), since, in their correspondence (around 1654),
they started solving the first non-trivial problems. In 1657, the first topic on the subject
of game theory, written by Huygens, was published. These three mathematicians and
philosophers tried to solve the “point problem”: a game between two players, which
requires that one player has three points in order to win, remains unfinished; how, then,
should the stakes be equitably divided if one player has one point and the other has
two? They explained with equiprobable cases why proportional frequencies appeared
in a wide series of outcomes. However, they were troubled in solving their problem
because of the determinism imposed on them by Christianity. The Ancients, on the