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Philosophy of Sciences

2016 year, number 2

METHODOLOGICAL ANALYSIS OF THE EMPIRICAL INTERPRETATION OF KOLMOGOROVS CONDITIONS ON THE USE OF MATHEMATICS

V. M. Reznikov
Institute of philosophy and Law SB RAS, Nikolaeva str. 8, Novosibirsk, 630090, Russia
Keywords: , , , , , , , , , , , Cournot’s principle, Bernoulli’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

Kolmogorovs contemporaries, famous mathematicians Frechet, Borel, Levy supposed that formalization of Kolmogorovs informal condition about the nearness of a probability event to the frequency characteristics is the same as for the conclusion of Bernoullis theorem. So, Kolmogorovs 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, Kolmogorovs condition isnt 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 Bernoullis theorem, its conclusion will be objective. I demonstrate that the idea doesnt agree with persistence property of the mathematical statements.