METHODOLOGICAL ANALYSIS OF CONNECTION OF BERNOULLI THEOREM AND KOLMOGOROV’S REQUEST FOR THE NEARNESS OF PROBABILITY AND FREQUENCIES
V. M. Reznikov1,2
1Novosibirsk National Research State University, 2, Pirogov st., Novosibirsk, 630090, Russia
2Institute of Philosophy and Law, SB RAS, 8, Nikolaev st. Novosibirsk, 630090
Keywords: частотная интерпретация, субъективистская интерпретация, теорема Бернулли, близость вероятности и частот, устойчивость частот, принцип Курно, Колмогоров, Мизес, frequency interpretation, subjective interpretation, Bernoulli’s theorem, proximity of probability and frequencies, stability of frequencies, Cournot’s principle, Kolmogorov, Mises, Borel, Frechet, Levy
Abstract
Kolmogorov’s contemporaries Borel, Frechet and Levy believed that Kolmogorov’s request for the proximity of event probability and its frequency characteristics is redundant in the context of applications of mathematics, since it is deduced by means of Bernoulli’s theorem, being its conclusion. The article shows that French mathematicians’ conclusion is restricted by the subjective interpretation of probability theory. Kolmogorov’ recommendations refer to the frequency interpretation in which his «dependent» request is not the conclusion of the theorem, but the precondition of applying Bernoulli’s theorem. A generalized result is that methods used in the subjective interpretation and conclusions based on these methods are of no value in the frequency interpretation and vice versa.
|
