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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: 22 September 2021

The Web of Practices

The Web of Practices

(p.17) 2 The Web of Practices
Mathematical Knowledge and the Interplay of Practices

José Ferreirós

Princeton University Press

This chapter is a general introduction to the current trend of studies of mathematical practice, with particular emphasis on historical and philosophical work. It offers a preliminary explanation of the notion of mathematical practice, first by considering the work of historians and philosophers on mathematical practices, from Archimedes and David Hilbert to Jens Høyrup, Penelope Maddy, Marcus Giaquinto, and Philip S. Kitcher. The chapter then characterizes the notion of mathematical practice by successively proposing several constraints. It argues that several different levels of practice and knowledge are coexistent and that their interrelationships are crucial to mathematical knowledge. It shows how the scheme of a web of interrelated practices—counting practices, measuring practices, technical practices, scientific practices—with their systematic links acting as constraint and guide, can be applied in the analysis of very different levels of mathematical activity.

Keywords:   mathematical practice, historians, philosophers, Philip S. Kitcher, mathematical knowledge, counting practice, measuring practices, technical practice, scientific practice, mathematical activity

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