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SOCIAL-CULTURAL CONTEXTS OF MATHEMATICS

J. Mrozek

Abstract

The aim of this article is to show and critically analyse the explanation - different from traditional approaches - of the nature of mathematics with reference to the social-cultural factors. Speaking of traditional approaches, the author means the traditional approaches of philosophy of mathematics that came into being at the beginning of the 20th century, namely: logicism, intuitionism and formalism. The common feature of traditional approaches is to consider mathematics as a domain of objective knowledge, independent of a human being and having its own 'logic of development'. Such a vision of mathematics met with criticism whose main objections referred to: 1) the lack of match between the image of mathematics, proposed by the classical approaches of contemporary philosophy of mathematics, and the research practice of real mathematicians made of 'flesh and bones', 2) insufficient consideration of conclusions that result from the history of mathematics, in the reflection on the nature of mathematical knowledge. The consequence of a search for new, 'more adequate' explanations of the phenomenon of mathematics, that offer some hope to overcome one-sidedness of classical approaches, is an approach that takes into account the 'social dimension' of mathematics. This approach, which the author describes as 'socializing', in his opinion offers a description of the real development of mathematics that, apart from the logical relationships expressing the specificity of this domain, also accounts for external factors - of sociological, psychological and cultural nature. At the background of such an approach lie - as it seems - two, quite obvious, theses, namely that mathematical knowledge belongs to the cultural tradition of a given society and that the activity of mathematicians has a social character. The proponents of the sociological approach want to show the 'social context' of mathematics. For them, mathematics is a domain that is 'alive' and develops under the influence of many factors, also those from the social sphere, which have a real impact on its shape and content. In particular, this latter thesis - about the conditioning of the contents of mathematical theories by social factors - is an object of serious criticism by the proponents of the Classical approach. The author hopes to present the advantages as well as disadvantages of the social-cultural approach to the issue of the peculiarity of mathematical knowledge.

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DOI resolver: doi.org/10.5593/sgemsocial2015/b31/s11.090

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