The ideas of Brauer in the context of philosophy

Klishina, M. V.; Kazaryan, V. P.

The ideas of Brauer in the context of philosophy

Liberal Arts in Russia. 2018. Vol. 7. No. 2. Pp. 85-96.

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https://doi.org/10.15643/libartrus-2018.2.1

Klishina M. V.

Karaganda Economic University of Kazpotrebsoyuz

9 Akademicheskaya Street, 100009 Karaganda, Kazakhstan

Kazaryan V. P.

Lomonosov Moscow State University

GSP-1, Leninskie Gory, 119991 Moscow, Russia

Email: kazaryanvp@mail.ru

Abstract

The article is devoted to the works of the outstanding Dutch mathematician L. E. Brauer in connection with the anniversary of his idea of the possibility of a new mathematics - intuitionistic mathematics. The authors of the article show the heuristic value of his work, which has created new paths both for the development of science and for understanding the nature of scientific study. In the article, Bauer’s works considered as a unity of strong creative will and logical worldview. The content of the main provisions of intuitionistic mathematics as opposed to classical traditional mathematics is revealed. Attention is drawn to the views of the Brauer on logicism and formalism in the justification of mathematics. His solutions of the problems of the relation of mathematics and language and the interpretation of the nature of mathematical evidence are given. Much attention is paid to Brauer’s intuitionistic approach to the problem of intuition and the role of human nature and personality in mathematical activity. The critical position of K. Popper, highlighting some specific moments in the teachings of Brauer is considered. It is noted that the philosophical ideas of Brauer overlap with the ideas of philosophy of life, phenomenology, existentialism.

Keywords

• mathematics
• intuitionism
• philosophy of mathematics
• mathematics basis
• intuition
• time

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