Overview
- Investigates the relationship between argumentation theory and the philosophy of mathematical practice.
- Challenges the assumption that there is no role for informal logic in mathematics
- Offers large array of examples ranging from the history of mathematics to formal proof verification ?
- Includes supplementary material: sn.pub/extras
Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 30)
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Table of contents (18 chapters)
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Front Matter
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What are Mathematical Arguments?
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Front Matter
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Argumentation as a Methodology for Studying Mathematical Practice
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Front Matter
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Mathematics as a Testbed for Argumentation Theory
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Front Matter
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An Argumentational Turn in the Philosophy of Mathematics
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Front Matter
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Keywords
- 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
About this book
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.
Reviews
From the reviews:
“The Argument of Mathematics is an interesting and important resource for philosophers of mathematics who have not much considered alternative kinds of evidence. The points considered by many of the authors and the argumentative structures highlighted in many of the chapters are worth further reflection in works in the epistemology of mathematics. These considerations will play an increasingly important role in future philosophy of mathematics. This welcome volume is a good place to start.” (James Robert Brown and Kevin Kuhl, Notre Dame Philosophical Reviews, June, 2014)Editors and Affiliations
Bibliographic Information
Book Title: The Argument of Mathematics
Editors: Andrew Aberdein, Ian J Dove
Series Title: Logic, Epistemology, and the Unity of Science
DOI: https://doi.org/10.1007/978-94-007-6534-4
Publisher: Springer Dordrecht
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer Science+Business Media Dordrecht 2013
Hardcover ISBN: 978-94-007-6533-7Published: 11 July 2013
Softcover ISBN: 978-94-017-8194-7Published: 05 August 2015
eBook ISBN: 978-94-007-6534-4Published: 01 July 2013
Series ISSN: 2214-9775
Series E-ISSN: 2214-9783
Edition Number: 1
Number of Pages: X, 393
Topics: Logic, Mathematical Logic and Foundations, Mathematical Logic and Formal Languages