METHODOLOGICAL ANALYSIS OF KOLMOGOROV’S CONDITIONS OF MATHEMATICS APPLICATION
V.M. Reznikov
Institute of Philosophy and Law, SB RAS, 630090, 8 Nikolaeva str., Novosibirsk, Russia
Keywords: принцип Курно, теорема Бернулли, устойчивость частот, субъективистская интерпретация вероятностей, объективистская интерпретация вероятностей, Колмогоров, Cournot’s principle, Bernoulli’s theorem, frequencies stability, subjectivistic interpretation of the probability theory, objectivistic interpretation of the probability theory, Kolmogorov
Abstract
There is a belief that Kolmogorov's condition about the closeness of event probability with frequency characteristics of an event is a conclusion of Bernoulli’s theorem and that if Cournot’s principle is taken into account, the conclusion is true on any typical sampling. The article shows that this assertion is correct within the subjectivistic interpretation of the probability theory. The author proves that in the objectivistic interpretation the closeness of probability and frequencies is understood as the stability of frequencies, i.e. their grouping in a narrow field. He demonstrates that in this interpretation the frequencies stability is a precondition of an application of Bernoulli’s theorem and it depends neither on the theorem nor on the principle.
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