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Argumentation in Mathematical Practice

In: Handbook of the History and Philosophy of Mathematical Practice

Author

Listed:
  • Andrew Aberdein

    (School of Arts and Communication, Florida Institute of Technology)

  • Zoe Ashton

    (Ohio State University, Department of Philosophy)

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.

Suggested Citation

  • Andrew Aberdein & Zoe Ashton, 2024. "Argumentation in Mathematical Practice," Springer Books, in: Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, pages 2665-2687, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-40846-5_12
    DOI: 10.1007/978-3-031-40846-5_12
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