ON THE RECONSTRUCTION OF THE HISTORICAL, SOCIAL AND SCIENTIFIC FACTORS THAT INFLUENCED THE UNDERSTANDING OF PROBABILITY THEORY AS A PHYSICAL SCIENCE BEFORE HILBERT CREATED THE SCIENTIFIC PROGRAM FOR THE DEVELOPMENT OF MATHEMATICS
V.M. Reznikov
Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Keywords: philosophy of science, mathematics, Bernoulli’s theorem, mathematical statistics, natural science, physics, social epistemology
Abstract
In the well-known literature, questions regarding the status of certain theorems of probability theory often arise. For example, what kind of disciplines do they belong to, namely, mathematics or physics? The most discussed results of this type include theorems frequently used in applications, such as Bernoulli’s theorem, the central limit theorem, and some others. At the same time, the author is not aware of publications that examine the status of probability theory, since almost all researchers believe that it is a completely independent area of research. However, it is known that Hilbert, in the sixth problem of his program for the development of mathematics, proposed axiomatizing probability theory as a physical science. This paper presents a series of arguments demonstrating that Hilbert’s contemporaries had certain grounds for considering probability theory a natural science discipline. Furthermore, as a side effect, the relationship between probability theory and mathematical statistics is clarified, specifically, it is established that some of the apparatus of classical probability theory is a component of mathematical statistics.
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