# The Argument of Mathematics

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Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 30)

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Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 30)

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations.

The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.

Argumentation theory Concept of Argumentation Formal proof verification Perelman’s system of argumentation Probability of Conjectures Toulmin’s layout of arguments Toulmin’s model of argumentation argumentation schemes informal logic mathematical diagrams mathematical fallacies mathematics education philosophy of mathematical practice visual reasoning in mathematics

- DOI https://doi.org/10.1007/978-94-007-6534-4
- Copyright Information Springer Science+Business Media Dordrecht 2013
- Publisher Name Springer, Dordrecht
- eBook Packages Humanities, Social Sciences and Law
- Print ISBN 978-94-007-6533-7
- Online ISBN 978-94-007-6534-4
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