On the existence of the true value of a probability. Part 2: The representation theorem and the ergodic theory

Abstract

Some authors, basing their ideas on the exchangeability property, on the postulates of the representation theorem and on its interpretation in the ambit of ergodic theory, believed to find a counterexample to the subjectivist model through the theoretical justification of the existence of an objective probability. As a proof of the inconsistency of this reasoning, the representation theorem allows to assert that the convergence of the relative frequency on a true value of the probability is only a metaphysical illusion motivated by an asymptotic behaviour of the personal assessments of initial probabilities, leading to intersubjective assignment. With regard to the ergodic theory, its assimilation to the propensity model allows the demonstration of its metaphysical character and the resulting subjectivity in the assignment of probabilities