The problem of probability interpretation was long overlooked before exploding in the 20th
century when the frequentist and subjectivist schools formalized two conflicting conceptions
of probability. Beyond the radical followers of the two schools a circle of pluralist thinkers
tends to reconcile the opposing concepts. The author uses two theorems in order to prove that
the various interpretations of probability do come into opposition and can be used in different
contexts. The goal here is to clarify the multi fold nature of probability by means of a purely
mathematical approach and to show how philosophical arguments can only serve to deepen actual
intellectual contrasts. The book can be considered as one of the most important contributions
in the analysis of probability interpretation in the last 10-15 years.
