Argumentation in Mathematical Practice

Andrew Aberdein () and Zoe Ashton
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Andrew Aberdein: School of Arts and Communication, Florida Institute of Technology
Zoe Ashton: Ohio State University, Department of Philosophy

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 2665-2687 from Springer

Abstract: Abstract Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of mathematical reasoning closely resemble patterns of reasoning in nonmathematical domains. Hence the tools developed to understand informal reasoning, collectively known as argumentation theory, are also applicable to much mathematical argumentation. This chapter investigates some of the details of that application. Consideration is given to the many contrasting meanings of the word “argument”; to some of the specific argumentation-theoretic tools that have been applied to mathematics, notably Toulmin layouts and argumentation schemes; to some of the different ways that argumentation is implicated in mathematical practices; and to the social aspects of mathematical argumentation.

Keywords: Argumentation schemes; Argumentation theory; Mathematical argumentation; Mathematical reasoning; Mathematical rhetoric; Problem choice; Toulmin layouts (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-40846-5_12

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