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Mathematical Knowledge and the Interplay of Practices$
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José Ferreirós

Print publication date: 2015

Print ISBN-13: 9780691167510

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691167510.001.0001

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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 26 September 2021

On Knowledge and Practices

On Knowledge and Practices

A Manifesto

(p.1) 1 On Knowledge and Practices
Mathematical Knowledge and the Interplay of Practices

José Ferreirós

Princeton University Press

This book proposes a novel analysis of mathematical knowledge from a practice-oriented standpoint and within the context of the philosophy of mathematics. The approach it is advocating is a cognitive, pragmatist, historical one. It emphasizes a view of mathematics as knowledge produced by human agents, on the basis of their biological and cognitive abilities, the latter being mediated by culture. It also gives importance to the practical roots of mathematics—that is, its roots in everyday practices, technical practices, mathematical practices themselves, and scientific practices. Finally, the approach stresses the importance of analyzing mathematics' historical development, and of accepting the presence of hypothetical elements in advanced mathematics. The book's main thesis is that several different levels of knowledge and practice are coexistent, and that their links and interplay are crucial to mathematical knowledge. This chapter offers some remarks that may help readers locate the book's arguments within a general scheme.

Keywords:   mathematical knowledge, practice, mathematics, agents, culture, technical practice, mathematical practice, scientific practice, advanced mathematics

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