© 2013

The Argument of Mathematics

  • Andrew Aberdein
  • Ian J Dove

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

Table of contents

  1. Front Matter
    Pages i-x
  2. Andrew Aberdein, Ian J. Dove
    Pages 1-8
  3. What are Mathematical Arguments?

    1. Front Matter
      Pages 9-9
    2. Erik C. W. Krabbe
      Pages 31-45
    3. Jesús Alcolea Banegas
      Pages 47-60
    4. Michel Dufour
      Pages 61-76
  4. Argumentation as a Methodology for Studying Mathematical Practice

    1. Front Matter
      Pages 77-77
    2. Matthew Inglis, Juan Pablo Mejía-Ramos
      Pages 101-117
    3. Christine Knipping, David Reid
      Pages 119-146
    4. Jesse Alama, Reinhard Kahle
      Pages 147-170
  5. Mathematics as a Testbed for Argumentation Theory

  6. An Argumentational Turn in the Philosophy of Mathematics

    1. Front Matter
      Pages 255-255
    2. Richard L. Epstein
      Pages 257-289
    3. Ian J. Dove
      Pages 291-308

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.  ​


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

Editors and affiliations

  • Andrew Aberdein
    • 1
  • Ian J Dove
    • 2
  1. 1., Dept. Humanities & CommunicationFlorida Institute of TechnologyMelbourneUSA
  2. 2., Department of PhilosophyUniversity of NevadaLas VegasUSA

Bibliographic information


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)