Chapter

Diagram‐Based Geometric Practice

Kenneth Manders

in The Philosophy of Mathematical Practice

Published in print June 2008 | ISBN: 9780199296453
Published online February 2010 | e-ISBN: 9780191711961 | DOI: https://dx.doi.org/10.1093/acprof:oso/9780199296453.003.0004
 Diagram‐Based Geometric Practice

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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

Chapter.  5841 words. 

Subjects: Philosophy of Mathematics and Logic

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