From Collective to Wager

On Some Recent Theories of Probability


Probability calculus, the extent of its development and the importance of its applications, are still live paradoxes within the system of the sciences. Born of reflections on gambling, a detached branch of combinatory calculus, it will waste no time in making use of mathematical instruments disproportionate to its modest origins, and to the very significance of the results it would claim to achieve. From the eighteenth century, continuous variables were used to represent finite variations; today, following Émile Borel, Paul Lévy and Maurice Fréchet consider as fields of events sets as general as Borel’s, confusing Lebesgue’s integral with mathematical hope. Now, these generalisations, apart from their intrinsic mathematical interest, turn out to have a practical utility: we know the growing role played by probability calculus in the techniques of social economy as much as in physics. Whence an undeniable discomfort: we began with a notion incapable of justifying the practical applications, a notion that is obscure from their point of view—‘the probability of an event, the relation of the number of favourable cases to the number of all possible cases’, according to the definition still adopted by Laplace—limited, so it seems, to the finite; but the outcome is an impressive science, which moves naturally within the infinite, but whose very development brings no clarity as to the possibility of its application to reality…