IS THE PROBABILITY THEORY COMPLETELY FORMAL SCIENCE?
Vladimir Moiseevich Reznikov
Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Keywords: physics, mathematics, probability theory, applied statistics, axiom, independency, causality, artificial intelligence
Abstract
In the 1900s, D. Hilbert formulated his famous problems, and the sixth problem was intended to axiomatize probability theory as a physical science. In 1938, the axiomatics proposed by A.N. Kolmogorov were accepted as a working mathematical science. This raises a question that has been neglected in the established philosophical literature - why did Hilbert consider probability theory a physical science? The main goal of this work was to describe the characteristics of probability theory that are specific to the strong natural sciences. The author first presented some well-known considerations and examples on this subject. They were based on the concept of holism, which held that results, such as those obtained in statistical physics using probability theory, were not separated from probability theory itself. However, they are not sufficiently complete and thorough to consider probability theory a physical science. Then, the author formulated his own arguments. Thus, based on an analysis of the content of Bernoulli’s and Chebyshev’s theorems, he demonstrated that they allow for verification of the conditions of their applicability to the data being studied, and, in principle, a more complex verification of the adequacy of the results proven within them to these data. In addition, he demonstrated that a number of concepts of this science, such as independence and probability, allow for a general scientific interpretation. Therefore, probability theory is a mathematical science, which follows from the formal and abstract nature of its axioms, but it has some features characteristic of strict natural scientific and technical disciplines. The second part of the article is devoted to the study of the reasons for changing the status of applied statistics, since over the past decades in Western universities this science is no longer considered part of mathematics. As a result, on the basis of a substantive analysis of classical statistics, the author has shown that there are far more reasons for this discipline than for probability theory not to be considered an exclusively deductive science.,
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