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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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Complementarity in Mathematics

Complementarity in Mathematics

(p.89) 4 Complementarity in Mathematics
Mathematical Knowledge and the Interplay of Practices

José Ferreirós

Princeton University Press

This chapter presents a thesis about what it regards as a crucial complementarity of elements in mathematical practice and in the configuration of mathematical knowledge: both conceptual and formalistic ingredients enter the game, both necessary, and neither reducible to the other. The approach advocates a rather natural way in which semantic considerations emerge from the interplay between agents and frameworks, in the context of mathematical knowledge and practices. As a result, the difficulties involved in postulating abstract semantic entities are avoided. The chapter first considers form and content in mathematics before discussing formal systems and intended models used in mathematics. It then explains the proposed approach, which emphasizes the coexistence of a multiplicity of practices and the centrality of their interplay, and concludes by taking a look at the case of complex numbers in order to illustrate the idea of the complementarity of symbols and thought.

Keywords:   complementarity, mathematical practice, mathematics, mathematical knowledge, agents, frameworks, semantic entities, practice, complex numbers, symbols

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