Three Paradigms in the Philosophy of Mathematics

Shaposhnikov, V.A.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Web of Science, Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.

Автор: Shaposhnikov Vladislav A.
Журнал: Russian Studies in Philosophy
Том: 50
Номер: 4
Год издания: 2012
Издательство: M.E. Sharpe Inc.
Местоположение издательства: United States
Первая страница: 7
Последняя страница: 23
DOI: 10.2753/RSP1061-1967500401
Аннотация: The author analyzes the philosophy of mathematics through the prism of three historical paradigms - ontological, epistemological, and anthropological. Each of the paradigms creates its own unique image of mathematics determined by the questions that preoccupied philosophers of the respective historical periods. Within the ontological paradigm, mathematics is primarily considered as a special kind of existing reality; the epistemological model construes mathematics as a part of our knowledge, and thus inevitably shifts its interest to the question of how mathematical propositions interrelate with other components of our thought; and, finally, in the context of the anthropological paradigm, mathematics is interpreted as a particular activity of man. The author illustrates the differences between the paradigms by evoking their specific responses to the opposition between realism and nominalism, the problem of a priori, and the question of the applicability of mathematics. After surveying the main ideas of these three paradigms, the author argues in favour of the anthropological model as the most self-critical, flexible, and modest in its aspirations.
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