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No. 1

A systemic approach in philosophical justification of mathematical problem-oriented directions

Liberal Arts in Russia. 2020. Vol. 9. No. 1. Pp. 24-34.
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https://doi.org/10.15643/libartrus-2020.1.3
Mikhailova N. V.
Belarusian National Technical University
65 Nezavisimosti Avenue, 220013 Minsk, Belarus
Email: michailova.n@bntu.by

Abstract

Philosophy of mathematics is the most important section of philosophy of science, which explores the issues of justification of new directions and theories of mathematics, because problem-oriented directions of development of mathematical knowledge do not allow to talk about the final solution of the problem of justification of theoretical and applied mathematics. The cognitive complexity and practical effectiveness of modern mathematical study presupposes methodological demand for a revision of existing conceptual approaches to the concept of mathematical justification. The article focuses on the use of system ideas in the justification of various problem-oriented mathematical directions, as any new philosophical concept of the mathematical justification is not a logical consequence of previous methodological works. In addition, from the point of view of the philosophy of justification of problem-oriented tasks in new mathematical sections, which are based on modern theories of mathematical analysis, a systemic approach in the justification of mathematical development directions, despite their qualitative diversity, is conditioned by the unity of mathematics, based on strict deductive reasoning, and the relationship of all mathematical sections, the inference of mathematical knowledge from axiom systems. The advantage of the idea of systematicity in the new methodological approach to justification is that, in terms of applying mathematical theories, their consistency and visibility becomes a more important criterion than consistency. It actualizes the truth problem in mathematics. At the same time, the axiomatic method that completes the mathematical study, the advantage of the formalism direction, and the hypothetical consistency of theory remain in modern theories the most important components of the creative style of working mathematicians thinking.

Keywords

  • • problems of justification philosophy
  • • system approach
  • • problem-oriented tasks of mathematics

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