Location

McMaster University

Document Type

Paper

Start Date

1-6-2005 9:00 AM

End Date

1-6-2005 5:00 PM

Abstract

Stephen Toulmin once observed that ‘it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ (Toulmin & al., 1979, 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.

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Jun 1st, 9:00 AM Jun 1st, 5:00 PM

The Uses of Argument in Mathematics

McMaster University

Stephen Toulmin once observed that ‘it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ (Toulmin & al., 1979, 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.