Location

University of Windsor

Document Type

Paper

Keywords

argument, conclusive argument, dialectical tier, illative core, mathematical practice, mathematical reasoning, proof, Ralph Johnson

Start Date

18-5-2011 9:00 AM

End Date

21-5-2011 5:00 PM

Abstract

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 compel-ling 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 chal-lenge. Hence much actual mathematical practice takes place in the dialectical tier.

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Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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Philosophy Commons

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May 18th, 9:00 AM May 21st, 5:00 PM

The dialectical tier of mathematical proof

University of Windsor

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 compel-ling 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 chal-lenge. Hence much actual mathematical practice takes place in the dialectical tier.