# The concept of truth of the mathematical theory in the context of contemporary mathematics substantiation

Liberal Arts in Russia. 2017. Vol. 6. No. 1. Pp. 40-47.

Get the full text (Russian) Email: michailova_mshrc@mail.ru#### Abstract

The concept of truth of the mathematical theory plays an important methodological role in philosophy of mathematics in the context of a link between ontological and gnoseological aspects of a problem of mathematics substantiation. In the article, the author analyzes how the features of mathematical knowledge are reflected in the understanding of concept of truth in the contemporary mathematics. The author claims that the concept of truth of mathematical offers and theorems is metamathematical concept; therefore, underestimation of distinction between mathematics and metamathematics can lead to philosophical misunderstanding. They consist primarily in the fact that theoretically possible level of rigor of contemporary mathematical theories has been virtually represented in the science. In order to resolve the fundamental philosophical and methodological difficulties of the problem of mathematics substantiation, the formal provability in logically consistent theory is necessary. However, contrary to the widespread belief, a rigid formalization of the proof is still not the synonymous with reliability and rigor of mathematical reasoning from the standpoint of the philosophy of contemporary mathematics substantiation.

#### Keywords

- • philosophy of mathematics
- • problem of truth in mathematics
- • consistency
- • substantiation of mathematics

#### References

- Hlebalin A. V. Sibirskij filosofskij zhurnal. 2016. Vol. 14. No. 2. Pp. 5-12.
- Janov Ju. I. Matematika, metamatematika i istina [Mathematics, metamathematics and the truth]. Moscow: KIAM. Preprint no 77, 2006.
- Jashin B. L. Matematika v kontekste filosofskih problem [Mathematics in the context of philosophical problems]. Moscow: MSPI, 2012. Pp. 49-55.
- Nikiforov A. L. Jepistemologija i filosofija nauki. 2008. Vol. XVI. No. 2. Pp. 50-65.
- Manin Ju. I. Matematika kak metafora. Jelektronnoe izdanie [Mathematics as metaphor. Electronic edition]. Moscow: MCCME, 2014. Pp. 93-105.
- Perminov V. Ja. Filosofija i osnovanija matematiki [Philosophy and foundations of mathematics]. Moscow: Progress-Tradition, 2001.
- Sultanova L. B. Nejavnoe znanie v razvitii matematiki: monografija [Implicit knowledge in the development of mathematics: a monograph]. Ufa: RIC BashGU, 2009.