# “The apology of mathematics” in diverse interactions of philosophical and mathematical studies

Liberal Arts in Russia. 2018. Vol. 7. No. 5. Pp. 335-345.

Get the full text (Russian) Email: erovenko@bsu.by#### Abstract

The category of interaction is one of the main philosophical categories; it indicates interconditionality of the considered research objects, directly or indirectly implying their productive communication as the final result of such interaction. The present article fills the gap in philosophical and mathematical studies. Despite a long story of mathematics formation, the number of works analyzing questions of philosophy and mathematics interaction from the point of view of mathematical knowledge development and justification is very small. Ascension of mathematical theories to high abstractions pulls together mathematics and philosophy; it became a condition of their diverse interaction, which includes philosophy of mathematical and the relevant research direction of a role of a mathematical component in philosophical and mathematical interaction. The extreme abstractness of philosophy and mathematical theories is their common feature. The main difference between mathematical and philosophical theories is observed in the research methods and applicability areas. However philosophical programs of mathematical justification are the examples of “rational philosophy”, methodologically as strict as mathematics, their distinctions are “seeming”.

#### Keywords

- • interaction of mathematics and philosophy
- • philosophy in mathematical studies
- • abstract unity

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