The Uses of Argument in Mathematics

Argumentation 19 (3):287-301 (2005)
Andrew Aberdein
Florida Institute of Technology
Stephen Toulmin once observed that ”it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying disagreement about the nature of the proof in question.
Keywords Euclid  mathematical argumentation  proof  rebuttal  Stephen Toulmin  undercutter
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DOI 10.1007/s10503-005-4417-8
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References found in this work BETA

The Uses of Argument.Stephen E. Toulmin - 1958 - Cambridge University Press.
Intentional Gaps in Mathematical Proofs.Don Fallis - 2003 - Synthese 134 (1-2):45 - 69.

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Mathematics and Argumentation.Andrew Aberdein - 2009 - Foundations of Science 14 (1-2):1-8.

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