In:Exploring Dialogue: Selected essays on argumentation by Erik C. W. Krabbe with contributions by Jan Albert van Laar
Edited by Erik C.W. Krabbe and Jan Albert van Laar
[Argumentation in Context 23] 2026
► pp. 326–343
Chapter 18Strategic maneuvering in mathematical proofs
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Article outline
- 1.Introduction
- 2.Proofs and arguments
- 3.Contexts of proof
- 4.Proofs in stages
- 4.1The confrontation stage
- 4.2The opening stage
- 4.3The argumentation stage
- 4.4The concluding stage
- 5.Conclusion
Acknowledgements Notes References
References (34)
Aristotle (1965
[1955]). On Sophistical
Refutations. Translated
by E. S. Forster. In: Aristotle, On
Sophistical Refutations, On Coming-To-Be and Passing-Away,
On the Cosmos. (E. S. Forster & D. J. Furley, Trans.) Cambridge, MA: Harvard University Press, & London: William Heinemann (The Loeb
Classical Library
400/442).
(1976
[1960]). Posterior Analytics,
Topica. Translated
by Hugh Tredennick (Posterior
Analytics) & E. S. Forster (Topica). Cambridge, MA: Harvard University Press, & London: William Heinemann (The Loeb
Classical Library
391).
Bell, Eric T. (1965
[1937]). Men of
Mathematics (Vol. 2). Harmondsworth: Penguin Books (Pelican Books
A 277).
Beth, Hermanus E. J. (1929). Inleiding in de niet-Euclidische meetkunde op
historischen grondslag [Introduction to non-Euclidean Geometry on a
Historical
Basis]. Groningen: Noordhoff.
Corcoran, John (1989). Argumentations
and Logic. Argumentation: An
International Journal on
Reasoning 3, 17–43.
Dove, Ian J. (2007). On
Mathematical Proofs and Arguments: Johnson and
Lakatos. In: Frans H. van Eemeren, J. Anthony Blair, Charles A. Willard & Bart Garssen (Eds.), Proceedings
of the Sixth Conference of the International Society for the
Study of
Argumentation (pp. 347–351). Amsterdam: Sic-Sat, International Center for the Study of Argumentation.
Edwards, Harold M. (1977). Fermat’s
Last Theorem: A Genetic Introduction to Algebraic Number
Theory. New York, etc.: Springer.
Euler, Leonard (1770). Vollständige
Anleitung zur Algebra. St. Petersburg: Kaiserliche Academie der Wissenschaften.
Frege, Gottlob (1879). Begriffsschrift,
eine der arithmetischen nachgebildete Formelsprache des
reinen
Denkens. Halle: Louis Nebert.
Goethe, Johann W. von (1949). Maximen
und
Reflexionen. In: Johann W. von Goethe, Die
Wahlverwandtschaften, Die Novellen, Die Maximen und
Reflexionen. Zürich: Artemis (Gedenkausgabe
der Werke, Briefe und Gespräche
9).
Johnson, Ralph H. (2000). Manifest
Rationality: A Pragmatic Theory of
Argument. Mahwah, NJ: Lawrence Erlbaum Associates.
Krabbe, Erik C. W. (1991). Quod erat demonstrandum: Wat
kan en mag een argumentatietheorie zeggen over
bewijzen? [QED: What can and may a theory of
argumentation say about
proofs?] In: M. M. H. Bax & W. Vuijk (Eds.), Thema’s
in de Taalbeheersing: Lezingen van het
VIOT-taalbeheersingscongres gehouden op 19, 20 en 21
december 1990 aan de Rijksuniversiteit
Groningen (pp. 8–16). Dordrecht: ICG.
(1997). Arguments,
Proofs, and
Dialogues. In: Michael Astroh, Dietfried Gerhardus & Gerhard Heinzmann (eds.), Dialogisches
Handeln: Eine Festschrift für Kuno
Lorenz (pp. 63–75). Heidelberg, Berlin & Oxford: Spektrum Akademischer Verlag. Translated and
revised version of Krabbe (1991).
(2004). Strategies
in Dialectic and
Rhetoric. In: Hans V. Hansen, Christopher W. Tindale, J. Anthony Blair, Ralph H. Johnson & Robert C. Pinto (Eds.), Argumentation
and its
Applications. (Proceedings of the
conference organized by the Ontario Society for the Study of
Argumentation, May 17–19,
2001, University of Windsor, CD-ROM.) Windsor, ON: Ontario Society for the Study of Argumentation.
Krabbe, Erik C. W., & Jan Albert van Laar (2007). About
Old and New Dialectic: Dialogues, Fallacies, and
Strategies. Informal Logic:
Reasoning and Argumentation in Theory and
Practice 27, 27–58.
Lakatos, Imre (1976). Proofs
and Refutations: The Logic of Mathematical
Discovery (edited
by John Worral & Elie G. Zahar). Cambridge: Cambridge University Press.
Plato (1997). Meno (translated
by G. M. A. Grube). In: Plato, Complete
Works, edited
by John M. Cooper & D. S. Hutchinson (pp.870–897). Indianapolis, IN & Cambridge, MA: Hackett.
Saccheri, G. Girolamo (1733). Euclides ab omni naevo
vindicatus [Euclid Freed from Every
Mole]. Milan: Paulus Antonius Montanus.
Tarski, Alfred (1956). The
Concept of Truth in Formalized
Languages. (J. H. Woodger, Trans.) In: Alfred Tarski, Logic,
Semantics, Metamathematics: Papers from 1923 to
1938 (pp. 152–278). Oxford: Clarendon.
(1983). The
Concept of Truth in Formalized
Languages. (J. H. Woodger, Trans.) In: Alfred Tarski, Logic,
Semantics, Metamathematics: Papers from 1923 to
1938 (2nd
ed., edited and introduced
by John Corcoran) (pp. 152–278). Indianapolis, IN: Hackett.
van Dalen, Dirk (2006). Weet u dat zeker? Over (on)zekerheden in de
wiskunde [Are
you sure? About (un)certainties in
mathematics]. Johann Bernoulli Lecture, Groningen, March 7th,
2006.
van Eemeren, Frans H., & Rob Grootendorst (1984). Speech
Acts in Argumentative Discussions: A Theoretical Model for
the Analysis of Discussions Directed Towards Solving
Conflicts of
Opinion. Dordrecht & Cinnaminson, NJ: Foris.
(1992). Argumentation,
Communication, and Fallacies: A Pragma-Dialectical
Perspective. Hillsdale NJ, etc.: Lawrence Erlbaum Associates.
(2004). A
Systematic Theory of Argumentation: The Pragma-Dialectical
Approach. Cambridge: Cambridge University Press.
van Eemeren, Frans H., & Peter Houtlosser (1999a). Delivering
the Goods in Critical
Discussion. In: Frans H. van Eemeren, Rob Grootendorst, J. Anthony Blair & Charles A. Willard (Eds.), Proceedings
of the Fourth International Conference of the International
Society for the Study of
Argumentation (pp. 163–167). Amsterdam: Sic-Sat.
(1999b). William
the Silent’s Argumentative
Discourse. In: Frans H. van Eemeren, Rob Grootendorst, J. Anthony Blair & Charles A. Willard (Eds.), Proceedings
of the Fourth International Conference of the International
Society for the Study of
Argumentation (pp. 168–171). Amsterdam: Sic-Sat.
(2002). Strategic
Manoeuvring in Argumentative Discourse: A Delicate
Balance. In: Frans H. van Eemeren & Peter Houtlosser (Eds.), Dialectic
and Rhetoric: The Warp and Woof of Argumentation
Analysis (pp. 131–159). Dordrecht: Kluwer (Argumentation
Library 6).
(2004). More
about Fallacies as Derailments of Strategic Maneuvering: The
Case of Tu
Quoque. In: Hans V. Hansen, Christopher W. Tindale, J. Anthony Blair, Ralph H. Johnson & Robert C. Pinto (Eds.), Argumentation
and its
Applications. (Proceedings of the
conference organized by the Ontario Society for the Study of
Argumentation, May 17–19,
2001, University of Windsor, CD-ROM.) Windsor, ON: OSSA.
(2005). Theoretical
construction and argumentative reality: An analytical model
of critical discussion and conventionalised types of
argumentative
activity. In: David Hitchcock (Ed.), The
Uses of Argument: Proceedings of a Conference at McMaster
University (pp. 75–84). Hamilton: Ontario Society for the Study of Argumentation.
Walton, Douglas N., & Erik C. W. Krabbe (1995). Commitment
in Dialogue: Basic Concepts of Interpersonal
Reasoning. Albany NY: State University of New York Press
Wikipedia (2007). Invalid
Proof. [URL] Accessed 10 October
2007.
