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Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

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

Abstract

We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Lakatos, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, which uses work by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods.

Keywords

argumentation theory computational model Euler’s conjecture Lakatos philosophy of mathematics theory refinement. 

Notes

Acknowledgements

A prior version of this paper was published in Foundations of Science (2009), 14(1–2):111–135. We would like to thank our three reviewers who all gave comprehensive, constructive and thought-provoking reviews. One of the editors of this collection, Andrew Aberdein, made particularly helpful comments. This work was partly funded by EPSRC grant EP/F035594/1.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Alison Pease
    • 1
    • 2
  • Alan Smaill
    • 3
  • Simon Colton
    • 1
  • John Lee
    • 3
  1. 1.Department of ComputingImperial College LondonLondonUK
  2. 2.School of Electronic Engineering and Computer ScienceQueen Mary, University of LondonLondonUK
  3. 3.School of InformaticsUniversity of Edinburgh, Informatics ForumEdinburghUK

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