Argumentation in Mathematical Practice

TL;DR

This paper explores how argumentation theory, including Toulmin layouts and argumentation schemes, enhances understanding of mathematical reasoning beyond formal logic, emphasizing social and informal aspects.

Contribution

It demonstrates the applicability of argumentation theory tools to mathematical practice, highlighting the social and informal reasoning aspects often overlooked by formal logic.

Findings

Argumentation theory complements formal logic in analyzing mathematical reasoning.

Toulmin layouts and argumentation schemes are useful tools in understanding mathematical arguments.

Social and informal aspects are integral to mathematical argumentation.

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.