2024, no. 2
PHILOSOPHY & SOCIOLOGY

Critical reflection of the system approach to the study of formal logic and justification for mathematics interaction

Natalia V. Mikhailova

DOI 10.20339/am.02-24.018pp. 18–22UDC 167/16880 RUB

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Abstract

It should be noted that many modern works on logical research use a complex technical apparatus, which can only be understood by a well-prepared logic, it is impossible without studying mathematics. On the other hand, feedback from logic in the study of mathematics is important, since logical principles are intrinsically present in the basis constructions of mathematics and in mathematical logic. The principles of logic are adopted in mathematics in order to develop mathematical thinking through critical reflection, although formal logical analysis does not always reflect the real rules of mathematical argumentation. Understanding this contributes to the fundamentality of university mathematical education, as well as the need for a systematic approach to justification for mathematics.

References

  1. Poincaré, A. Intuition and Logic in Mathematics. In: On Science. Moscow, 1983. P. 159–169.

  2. Nepeivoda, N.N. Applied logic. Novosibirsk: Publishing House of Novosibirsk University. 2000. 521 p.

  3. Bocharov, V.A. Logic and Mathematics. Vestnik of Moscow University. Ser. 7. Philosophy. 2012. No. 1. P. 72–80.

  4. Cohen, M, Nagel, E. Introduction to logic and scientific method. Chelyabinsk: Society, 2010. 655 p.

  5. Maiorov, A.A. Logic and informatics. Prospects of science and education. 2015. No. 4. P. 7–12.

  6. Perminov, V.Ya. Philosophy and foundations of mathematics. Moscow: Progress-Tradition, 2001. 320 p.

  7. Uspensky, V.A. Apology of mathematics: Collection of articles. St. Petersburg: Amphora, 2011. 554 p.