The dialectical tier of mathematical proof

In Frank Zenker (ed.), Argumentation: Cognition & Community. Proceedings of the 9th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18--21, 2011. OSSA (2011)

Andrew Aberdein
Florida Institute of Technology
Ralph Johnson argues that mathematical proofs lack a dialectical tier, and thereby do not qualify as arguments. This paper argues that, despite this disavowal, Johnson’s account provides a compelling model of mathematical proof. The illative core of mathematical arguments is held to strict standards of rigour. However, compliance with these standards is itself a matter of argument, and susceptible to challenge. Hence much actual mathematical practice takes place in the dialectical tier.
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Manifest Rationality.Ralph Johnson - 2000 - Lawrence Earlbaum Associates.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford University Press.
Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Cambridge University Press.
Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Studia Logica 81 (2):285-289.

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