TOWADS PHILOSOPHICAL PRECONDITIONS IN MATHEMATICAL BATTLES
Vladimir Moiseevich Reznikov1,2
1Institute of Philosophy and Law, SB RAS, 8, Nikolaev st. Novosibirsk, 630090
2Novosibirsk National Research State University, 2, Pirogov st., Novosibirsk, 630090, Russia
Keywords: частотная интерпретация, субъективистская интерпретация, теорема Бернулли, близость вероятности и частот, устойчивость частот, принцип Курно, Колмогоров, Мизес, frequency interpretation, subjective interpretation, Bernoulli theorem, proximity of probability and frequencies, stability of frequencies, Cournot principle, Kolmogorov, Mises
Abstract
By analyzing the critique of Kolmogorov by mathematicians, followers of the subjective interpretation of probability theory I show the importance of philosophical preconditions in scientific research. The critique was targeted at the condition of proximity of probability and frequencies, as according to opponents, the condition coincides with the conclusion of Bernoulli theorem, and therefore it was superfluous. In reality, the critique was directed at the foundations of frequency interpretation, because it was unacceptable for subjectivists, but in the context of applications, the views of Kolmogorov were closely related to those of Mises, the creator of frequency interpretation. The critique of Kolmogorov’s condition was based on the Bernoulli theorem. I show that the condition is formalized on the basis of stability of frequencies, and doesn’t require the theorem for its verification. The theorem is suitable for an introduction of the condition in the field of mathematics; however, it applies only when the stability of frequencies obtains. In any case, in the context of frequency interpretation, the critique misses the target.
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