Perspectives On Mathematical Practices pp 135-151 | Cite as
The Informal Logic Of Mathematical Proof
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Abstract
Informal and formal logic are complementary methods of argument analysis. Informal logic provides a pragmatic treatment of features of argumentation which cannot be reduced to logical form. This paper shows how paying attention to aspects of mathematical argumentation captured by informal, but not formal, logic can offer a more nuanced understanding of mathematical proof and discovery.
Keywords
dialectic four colour theorem informal logic mathematical proof Stephen Toulmin Douglas WaltonPreview
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References
- [1]Jesús Alcolea Banegas, 1998, L’argumentació en matemátiques, in XIIé Congrés Valenciá de Filosofia (E. Casaban i Moya, editor), Valenciá, pp. 135–147.Google Scholar
- [2]Kenneth Appel & Wolfgang Haken, 1978, The four colour problem, reprinted 2002 in The philosophy of mathematics: An anthology (D. Jacquette, editor), Blackwell, Oxford, pp. 193–208.Google Scholar
- [3]J. Borwein, P. Borwein, R. Girgensohn & S. Parnes, 1995, Experimental mathematics: A discussion, CECM preprint no. 95:032, \underline {http://www.cecm.sfu.ca/preprints/1995pp.html}.Google Scholar
- [4]Wayne Brockriede & Douglas Ehninger, 1960, Toulmin on argument: An interpretation and application. Quarterly journal of speech, 46, pp. 44–53.CrossRefGoogle Scholar
- [5]Winston Churchill, 1937, Great contemporaries, Thornton Butterworth, LondonGoogle Scholar
- [6]Frans van Eemeren & Rob Grootendorst, 1992, Argumentation, communication and fallacies, Lawrence Erlbaum Associates, Hillsdale, N.J..Google Scholar
- [7]Frans van Eemeren, Rob Grootendorst & Tjark Kruiger, 1987, Handbook of argumentation theory: A critical survey of classical backgrounds and modern studies, Foris, DordrechtGoogle Scholar
- [8]Charles Hamblin, 1970, Fallacies, Methuen, LondonGoogle Scholar
- [9]Paul Hoffman, 1998, The man who loved only numbers, Fourth Estate, LondonGoogle Scholar
- [10]Arthur Jaffe & Frank Quinn, 1993, “Theoretical mathematics”: Toward a cultural synthesis of mathematics and theoretical physics, Bulletin of the American Mathematical Society, 29, pp. 1–13CrossRefGoogle Scholar
- [11]Alfred Kempe, 1879, On the geographical problem of the four colours, American journal of mathematics, 2, pp. 193–200CrossRefGoogle Scholar
- [12]Donald MacKenzie, 1999, Slaying the Kraken: The sociohistory of a mathematical proof, Social studies of science, 29, pp. 7–60CrossRefGoogle Scholar
- [13]Susan Newman & Catherine Marshall, 1992, Pushing Toulmin too far: Learning from an argument representation scheme, Xerox PARC technical report no. SSL-92-45, \underline {http://www.csdl.tamu.edu/∼ marshall/toulmin.pdf}Google Scholar
- [14]Yehuda Rav, 1999, Why do we prove theorems?, Philosophia Mathematica, 7, pp. 5–41CrossRefGoogle Scholar
- [15]Gian-Carlo Rota, 1997, The phenomenology of mathematical proof, Synthese, 111, pp. 183–196CrossRefGoogle Scholar
- [16]Edward Swart, 1980, The philosophical implications of the four-color problem, The American mathematical monthly, 87, pp. 697–707CrossRefGoogle Scholar
- [17]William Thurston, 1994, On proof and progress in mathematics, Bulletin of the American Mathematical Society, 30, pp. 161–171CrossRefGoogle Scholar
- [18]Stephen Toulmin, 1958, The uses of argument, Cambridge University Press, CambridgeGoogle Scholar
- [19]Stephen Toulmin, Richard Rieke & Allan Janik, 1979, An introduction to reasoning, Macmillan, LondonGoogle Scholar
- [20]Thomas Tymoczko, 1979, The four-color problem and its philosophical significance, Journal of philosophy, 76, pp. 57–83CrossRefGoogle Scholar
- [21]Douglas Walton, 1997, How can logic best be applied to arguments? Logic journal of the IGPL, 5, pp. 603–614CrossRefGoogle Scholar
- [22]Douglas Walton, 1998, The new dialectic: Conversational contexts of argument, Toronto University Press, TorontoGoogle Scholar
- [23]Douglas Walton & Erik Krabbe, 1995, Commitment in dialogue: Basic concepts of interpersonal reasoning, SUNY Press, Albany, N.YGoogle Scholar
- [24]Charles Willard, 1976, On the utility s and criticism of arguments, Communication monographs, 43, pp. 308–319CrossRefGoogle Scholar
- [25]Robin Wilson, 2002, Four colours suffice: How the map problem was solved, Allen Lane, LondonGoogle Scholar
- [26]Ludwig Wittgenstein, 1953, Philosophical Investigations, Blackwell, OxfordGoogle Scholar
- [27]Doron, Zeilberger, 1993, Theorems for a price: Tomorrow's semi-rigorous mathematical culture, Notices of the American Mathematical Society, 40, pp. 978--981.Google Scholar
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