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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: 18 September 2021

Agents and Frameworks

Agents and Frameworks

(p.44) 3 Agents and Frameworks
Mathematical Knowledge and the Interplay of Practices

José Ferreirós

Princeton University Press

This chapter introduces a “core scheme” for the analysis of mathematical practices that can be presented in a simplified way by means of a couple dubbed Framework–Agent. Mathematics in practice will typically depend on the performance of several Framework–Agent couples, intertwined in several possible ways. The chapter first considers two different kinds of frameworks, “theoretical” and “symbolic.” before discussing the role of exemplars in mathematical knowledge. It then explains how the links between different frameworks and practices are established concretely by an agent. It also examines the cognitive abilities involved in mastering counting practice, the importance of cognition in mathematics, and Philip S. Kitcher's concept of “metamathematics” in relation to agents. The chapter concludes by expounding on the notion of “systematic links.”

Keywords:   mathematical practice, Framework–Agent couples, agents, frameworks, mathematics, exemplars, counting practice, cognition, metamathematics, systematic links

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