# The ideas of Brauer in the context of philosophy

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

Get the full text (Russian) 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

#### References

- Brouwer L. E. J. Collected Works. Amsterdam: North-Holland Publishing. 1975. Vol. 1. Pp. 480-494.
- Brouwer L. E. J. Collected Works. Amsterdam: North-Holland Publishing. 1975. Vol. 1. Pp. 102-104.
- Brouwer L. E. J. Collected Works. Amsterdam: North-Holland Publishing. 1975. Vol. 1. Pp. 417-428.
- Brouwer L. E. J. Collected Works. Amsterdam: North-Holland Publishing. 1975. Vol. 1. Pp. 628.
- Brauer L. E. Ya. Vestnik RGGU. Seriya Filosofiya. Sotsiologiya. 2010. No. 13(56). Pp. 249-258.
- Bourbaki N. Ocherki po istorii matematiki [Essays on the history of mathematics]. Moscow: Izdatel'stvo inostrannoi literatury, 1963.
- Weyl H. O filosofii matematiki [On the philosophy of mathematics]. Moscow: Gostekhizdat, 1934.
- Weyl H. O filosofii matematiki [On the philosophy of mathematics]. Moscow: KomKniga, 2005.
- Weyl H. Matematicheskoe myshlenie [Mathematical thinking]. Moscow: Nauka, 1989.
- Kazaryan V. P. Vestnik Moskovskogo universiteta. Ser. 7. Filosofiya. 2012. No. 2. Pp. 33-47.
- Lolli G. Filosofiya matematiki: nasledie dvadtsatogo stoletiya [Philosophy of mathematics: legacy of the twentieth century]. N. Novgorod: izd-vo Nizhegorodskogo gosuniversiteta im. N. I. Lobachevskogo, 2012.
- Lyutikov P. V. Vestnik RGGU. Seriya Filosofiya. Sotsiologiya. 2010. No. 13(56). Pp. 259-262.
- Popper K. R. Ob''ektivnoe znanie. Evolyutsionnyi podkhod [Objective knowledge. Evolutionary approach]. Moscow: Editorial URSS, 2002.
- Rid Konstans. Hilbert. Moscow, 1977. URL: http://ega-math.narod.ru/Reid/p4.htm.
- Sultanova L. B. Liberal Arts in Russia. 2013. Vol. 2. No. 3. Pp. 237-251.
- Tselishchev V. V. Filosofiya matematiki [Philosophy of mathematics]. Novosibirsk: Nauka, 2002.