Logic, Epistemology, and the Unity of Science

The Argument of Mathematics

Editors: Aberdein, Andrew, Dove, Ian J. (Eds.)

  • 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 ​
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eBook $139.00
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Hardcover $179.00
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  • ISBN 978-94-007-6533-7
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Softcover $179.00
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  • ISBN 978-94-017-8194-7
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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)

Table of contents (18 chapters)

  • Introduction

    Aberdein, Andrew (et al.)

    Pages 1-8

  • Non-deductive Logic in Mathematics: The Probability of Conjectures

    Franklin, James

    Pages 11-29

  • Arguments, Proofs, and Dialogues

    Krabbe, Erik C. W.

    Pages 31-45

  • Argumentation in Mathematics

    Banegas, Jesús Alcolea

    Pages 47-60

  • Arguing Around Mathematical Proofs

    Dufour, Michel

    Pages 61-76

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-94-007-6534-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-94-007-6533-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-94-017-8194-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Argument of Mathematics
Editors
  • Andrew Aberdein
  • Ian J. Dove
Series Title
Logic, Epistemology, and the Unity of Science
Series Volume
30
Copyright
2013
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-007-6534-4
DOI
10.1007/978-94-007-6534-4
Hardcover ISBN
978-94-007-6533-7
Softcover ISBN
978-94-017-8194-7
Series ISSN
2214-9775
Edition Number
1
Number of Pages
X, 393
Topics