Yashin B.L. Sociocultural Aspects of Mathematical Knowledge and Ethnomathematics

Abstract: The subject of the research is the sociocultural (fundamentalist) approach to the philosophy of mathematics, in particular, ethnomathematics as the sphere of mathematical research. Particular attention is paid to the ideas of Oswald Spengler, the author of The Decline of the West, Neo-Kantian Hermann Cohen and Paul Natorp about the position and role of mathematics in the cognitive process as well as the relationship between mathematics and culture. The results of the research show that the human mind is able to offer many different ways to quantitative perception of the world, each of which arises from everyday practice, and that the paradigm adopted by contemporary mathematics is in fact only one of possibilities. The main research methods used by the author include generalization, logical and historical methods, as well as a comparative analysis. The novelty of the research is caused by the fact that it reveals the unity of ideas expressed in ethnomathematical researches that deal with the problems of occurrence and development of "experimental" mathematics as well as researches in the field of socio-cultural philosophy of mathematics. It is shown that these results support the idea of Spengler about the dependence of the forms of knowledge on human conditions of existence, about existence of not one but several mathematics, each of which is rooted in their own culture, as well as the ideas of the representatives of the Marburg Neo-Kantian School about mathematics being the "first principle" of thinking. The author of the article concludes that researches in the field of ethnomathematics, and in a broader context, as part of the socio-cultural approach to mathematical knowledge, are most effective when considering mathematics in terms of its historical development; that their results can serve as an additional argument in favor of mathematical empiricism in its confrontation with the mathematical apriorism. 

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