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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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Agents and Frameworks

Agents and Frameworks

Chapter:
(p.44) 3 Agents and Frameworks
Source:
Mathematical Knowledge and the Interplay of Practices
Author(s):

José Ferreirós

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691167510.003.0003

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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