Crossing Curves: A Limit to the Use of Diagrams in Proofs

Philosophia Mathematica 19 (3):281-307 (2011)
Abstract
This paper investigates the following question: when can one reliably infer the existence of an intersection point from a diagram presenting crossing curves or lines? Two cases are considered, one from Euclid's geometry and the other from basic real analysis. I argue for the acceptability of such an inference in the geometric case but against in the analytic case. Though this question is somewhat specific, the investigation is intended to contribute to the more general question of the extent and limits of reliable diagrammatic reasoning in mathematics
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DOI 10.1093/philmat/nkr023
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References found in this work BETA

Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.

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Citations of this work BETA

A Priori Concepts in Euclidean Proof.Peter Fisher Epstein - forthcoming - Proceedings of the Aristotelian Society.
Frege’s Philosophy of Geometry.Matthias Schirn - 2019 - Synthese 196 (3):929-971.

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