Inverting Bernoulli's theorem: the original sin

This paper sheds a new light on the gap between a priori and a posteriori probabilities by concentrating on the evolution of the mathematical concept. It identifies the illegitimate use of Bernoulli’s law of large numbers as the probabilists’ original sin. The resulting confusion on the mathematical foundation for statistical inference was detrimental to Laplace’s definition of probability in terms of equi-possible outcomes as well as to von Mises’ frequentist approach. On the opposite, Kolmogorov’s analytical axiomatization of probability theory enables a priori and a posteriori probabilities to relate to each other without contradiction, allowing a consistent mathematical specification of the dual nature of probability. Therefore, only in Kolmorogorov’s formalism is statistical inference rigorously framed.