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The Philosophy of Mathematical Practice$
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Paolo Mancosu

Print publication date: 2008

Print ISBN-13: 9780199296453

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199296453.001.0001

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Diagram‐Based Geometric Practice

Diagram‐Based Geometric Practice

(p.65) 3 Diagram‐Based Geometric Practice
The Philosophy of Mathematical Practice

Kenneth Manders

Oxford University Press

This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based reasoning practice in Euclidean plane geometry, discussion focuses first on problems of diagram sensitivity, and then on the relationship between uniform treatment and geometrical generality. Here, one finds a balance between representationally enforced unresponsiveness (to differences among diagrams) and the intellectual agent's contribution to such unresponsiveness that is somewhat different from what one has come to expect in modern logic. Finally, challenges and opportunities for further work are indicated.

Keywords:   Euclid, generality, geometrical diagram, representational unresponsiveness, uniformity

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