METHODOLOGICAL ANALYSIS OF THE EMPIRICAL INTERPRETATION OF KOLMOGOROV’S CONDITIONS ON THE USE OF MATHEMATICS
V. M. Reznikov
Institute of philosophy and Law SB RAS, Nikolaeva str. 8, Novosibirsk, 630090, Russia
Keywords: принцип Курно, теорема Бернулли, устойчивость частот, субъективная интерпретация вероятностей, объективная интерпретация вероятностей, консервативность математики, Колмогоров, Мизес, Фреше, Борель, Леви, CournotвЂ™s principle, BernoulliвЂ™s theorem, frequencies stability, subjectivistic interpretation of the probability theory, objectivistic interpretation of the probability theory, persistence property of mathematics Kolmogorov, Mises, Frechet, Borel, Levy
Abstract
Kolmogorov’s contemporaries, famous mathematicians Frechet, Borel, Levy supposed that formalization of Kolmogorov’s informal condition about the nearness of a probability event to the frequency characteristics is the same as for the conclusion of Bernoulli’s theorem. So, Kolmogorov’s condition is redundant because it is deduced by means of the theorem. I demonstrate that the informal condition has two different formal descriptions. In the frequency interpretation, the natural formalization consists in the geometrical nearness of the frequencies. In this case, Kolmogorov’s condition isn’t deduced from the theorem, conversely the feasibility of the condition is the precondition of using the theorem. The article shows the inadequacy of the idea of Frechet, Borel and Levy that when using the subjective probability in Bernoulli’s theorem, its conclusion will be objective. I demonstrate that the idea doesn’t agree with persistence property of the mathematical statements.
