Logo - springer
Slogan - springer

Philosophy - Logic & Philosophy of Language | The Argument of Mathematics

The Argument of Mathematics

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

2013, X, 393 p. 74 illus.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-94-007-6534-4

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase

learn more about Springer eBooks

add to marked items


Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-94-007-6533-7

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

  • 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 ​

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.  ​

Content Level » Research

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

Related subjects » Logic & Philosophy of Language - Mathematics - Theoretical Computer Science

Table of contents 

Introduction.- Part I. What are Mathematical Arguments?.- Chapter 1. Non-Deductive Logic in Mathematics: The Probability of Conjectures; James Franklin.- Chapter 2. Arguments, Proofs, and Dialogues; Erik C. W. Krabbe.- Chapter 3. Argumentation in Mathematics; Jesús Alcolea Banegas.- Chapter 4. Arguing Around Mathematical Proofs; Michel Dufour.- Part II. Argumentation as a Methodology for Studying Mathematical Practice.- Chapter 5. An Argumentative Approach to Ideal Elements in Mathematics; Paola Cantù.- Chapter 6. How Persuaded Are You? A Typology of Responses; Matthew Inglis and Juan Pablo Mejía-Ramos.- Chapter 7. Revealing Structures of Argumentations in Classroom Proving Processes; Christine Knipping and David Reid.- Chapter 8. Checking Proofs; Jesse Alama and Reinhard Kahle.- Part III. Mathematics as a Testbed for Argumentation Theory.- Chapter 9. Dividing by Zero—and Other Mathematical Fallacies; Lawrence H. Powers.- Chapter 10. Strategic Maneuvering in Mathematical Proofs; Erik C. W. Krabbe.- Chapter. 11 Analogical Arguments in Mathematics; Paul Bartha.- Chapter 12. What Philosophy of Mathematical Practice Can Teach Argumentation Theory about Diagrams and Pictures; Brendan Larvor.- Part IV. An Argumentational Turn in the Philosophy of Mathematics.- Chapter 13. Mathematics as the Art of Abstraction; Richard L. Epstein.- Chapter 14. Towards a Theory of Mathematical Argument; Ian J. Dove.- Chapter 15. Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics; Alison Pease, Alan Smaill, Simon Colton and John Lee.- Chapter 16. Mathematical Arguments and Distributed Knowledge; Patrick Allo, Jean Paul Van Bendegem and Bart Van Kerkhove.- Chapter 17. The Parallel Structure of Mathematical Reasoning; Andrew Aberdein.- Index. ​

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Logic.