The informal logic of mathematical proof

In Reuben Hersh (ed.), 18 Unconventional Essays About the Nature of Mathematics. Springer Verlag. pp. 56-70 (2006)
  Copy   BIBTEX


Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of Stephen Toulmin [The uses of argument, Cambridge University Press, 1958] and the more recent studies of Douglas Walton, [e.g. The new dialectic: Conversational contexts of argument, University of Toronto Press, 1998]. The focus of both of these approaches has largely been restricted to natural language argumentation. However, Walton’s method in particular provides a fruitful analysis of mathematical proof. He offers a contextual account of argumentational strategies, distinguishing a variety of different types of dialogue in which arguments may occur. This analysis represents many different fallacious or otherwise illicit arguments as the deployment of strategies which are sometimes admissible in contexts in which they are inadmissible. I argue that mathematical proofs are deployed in a greater variety of types of dialogue than has commonly been assumed. I proceed to show that many of the important philosophical and pedagogical problems of mathematical proof arise from a failure to make explicit the type of dialogue in which the proof is introduced.



    Upload a copy of this work     Papers currently archived: 78,059

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Managing Informal Mathematical Knowledge: Techniques from Informal Logic.Andrew Aberdein - 2006 - Lecture Notes in Artificial Intelligence 4108:208--221.
Towards a theory of mathematical argument.Ian J. Dove - 2009 - Foundations of Science 14 (1-2):136-152.
Mathematical arguments in context.Jean Paul Van Bendegem & Bart Van Kerkhove - 2009 - Foundations of Science 14 (1-2):45-57.
How to think about informal proofs.Brendan Larvor - 2012 - Synthese 187 (2):715-730.


Added to PP

68 (#182,970)

6 months
5 (#169,874)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Andrew Aberdein
Florida Institute of Technology

References found in this work

Philosophical Investigations.Ludwig Josef Johann Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell.
Philosophical investigations.Ludwig Wittgenstein & G. E. M. Anscombe - 1953 - Revue Philosophique de la France Et de l'Etranger 161:124-124.
The Uses of Argument.Stephen E. Toulmin - 1958 - Philosophy 34 (130):244-245.
Fallacies.C. L. Hamblin - 1970 - Revue Philosophique de la France Et de l'Etranger 160:492-492.

View all 14 references / Add more references