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Arguments and Proofs About Arguments and Proofs

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Educational Research: Proofs, Arguments, and Other Reasonings

Part of the book series: Educational Research ((EDRE,volume 4))

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Abstract

Both rhetoric and mathematics are ancient, elaborate and still active fields of study that cover a time span of more than two millennia. That much, they undisputedly have in common. However, in the domain of mathematics one will search in vain for traces, positive or negative, of rhetoric, and in the domain of rhetoric, although the relation between mathematics and rhetoric is often discussed, the standard claim is to deny that they are intimately related or intertwined. Moreover, things have hardly changed over two millennia. Let us present two examples, which I freely admit, present a slight bias. The first example is taken from what is commonly referred to as ‘old rhetoric’ and the second, from ‘new rhetoric’.

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References

  • Birkhoff, G. D. (1961). Mathematics of aesthetics. In J. R. Newman (Ed.), The world of mathematics (Vol. IV, pp. 2185–2195). London: George Allen and Unwin.

    Google Scholar 

  • Carroll, L. (1895). What the tortoise said to Achilles. Mind, 4, 278–280.

    Article  Google Scholar 

  • François, K., & Van Bendegem, J. P. (Eds.). (2007). Philosophical dimensions in mathematics education. New York: Springer. (Mathematics Education Library 42)

    Google Scholar 

  • Grattan-Guinness, I. (2000). The search for mathematical roots, 1870–1940. Logics, set theories and the foundations of mathematics from Cantor through Russell to Gödel. Princeton: Princeton University Press.

    Google Scholar 

  • Heinz, B. (2000). Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin. New York: Springer.

    Google Scholar 

  • Kuhn, T. (1962, postscript 1969). The structure of scientific revolutions. Chicago: University of Chicago Press.

    Google Scholar 

  • Mathias, A. R. D. (2002). A term of length 4.523.659.424.929. Synthese, 133(1–2), 75–86.

    Article  Google Scholar 

  • Menger, K. (1956). Why Johnny hates math. The Mathematics Teacher, 49, 578–584.

    Google Scholar 

  • Netz, R. (1999). The shaping of deduction in Greek mathematics. A study in cognitive history. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Perelman, C., & Olbrechts-Tyteca, L. (1970). Traité de l’argumentation. La nouvelle rhétorique. Brussels: Éditions de l’ULB.

    Google Scholar 

  • Rahman, S., Gabbay, D., Symons J., & Van Bendegem, J. P. (Eds.). (2004). Logic, epistemology and the unity of science (LEUS) (Vol. 1). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Schmitz, W. H. (1990). De Hollandse Significa. Een reconstructie van de geschiedenis van 1892 tot 1926 [The Dutch Significs. A reconstruction of its history from 1892 to 1926]. Assen: Van Gorcum.

    Google Scholar 

  • Van Bendegem, J. P. (2003). Draaien in cirkels of de relativiteit van funderingen (Turning round in circles or the relativity of foundations). In J. Stuy, J. Van Bellingen, & M. Vandenbossche (Eds.), De precisie van het lezen. Liber Amicorum Maurice Weyembergh (pp. 137–148). Brussels: VUBPRESS.

    Google Scholar 

  • Van Bendegem, J. P.(2004). Why do so many search so desperately for a universal language (and fortunately fail to find it)? In F. Brisard, S. D’Hondt, & T. Mortelmans (Eds.), Language and revolution/Language and time. Antwerp Papers in Linguistics, 106 (pp. 93–113). Antwerp: University of Antwerp, Department of Linguistics.

    Google Scholar 

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Correspondence to Jean Paul Van Bendegem .

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Van Bendegem, J.P., Coessens, K. (2009). Arguments and Proofs About Arguments and Proofs. In: Smeyers, P., Depaepe, M. (eds) Educational Research: Proofs, Arguments, and Other Reasonings. Educational Research, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3249-2_9

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