ON UNIVERSAL APPLICABILITY AND EFFICIENCY OF MATHEMATICS
Vladimir Moiseevich Reznikov
Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Sciences, 8, Nikolaeva str., Novosibirsk, 630090, Russia
Keywords: математика, репрезентация знания, логика, прикладная математика, условия применения математики, базовое свойство, математическая статистика, mathematics, knowledge representation, precision, logic, applied mathematics, application requirements for mathematics, basic property, mathematical statistics
Abstract
The article shows that the formalization method is not universal. Firstly, mathematization does not make it possible to answer certain questions, e.g. those related to the essence of knowledge. Secondly, mathematics is quite suitable for presenting knowledge in the field of exact science but is less adequate for being used in the humanities. Thirdly, not all mathematical disciplines are used in applications; it is rather the task of applied mathematics. Fourthly, even in applied mathematics, not all its branches have a universal application. To determine the applicability of a mathematical result, we introduce the concept of the basic property of the studied object of a mathematical theory. A property is called basic if it is used to prove main results of a mathematical discipline. For example, in the probability theory and classical mathematical statistics, probability distribution and independence function as such properties. Since it is difficult to guarantee the determination and verification of the probability distribution and independence of random variables based on the data under study, the probability theory and classical mathematical statistics are not universally applicable.
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