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