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How and Why Mathematics is Unique as a Social Practice

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Perspectives On Mathematical Practices

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 5))

Abstract

Difficulties are raised for views that explain consensus in mathematics using only sociological pressure. Mathematical proof is sociologically very peculiar, when compared to other socially constrained practices. A preliminary analysis of the factors that have been at work historically in the “benign fixation of mathematical practice” are then exhumed: dispositions, implicit applications, an implicit logic, all play a role.

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References

  • Anderson, Stephen R. 1988. Morphological change. In Linguistics: the Cambridge survey, Vol.I: Linguistic theory: foundations. Cambridge: Cambridge University Press, 324-362.

    Google Scholar 

  • Azzouni, Jody 1994. Metaphysical myths, mathematical practice: the ontology and epistemology of the exact sciences. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Azzouni, 2000a. Applying mathematics: an attempt to design a philosophical problem, The Monist 83(2):209-227.

    Article  Google Scholar 

  • Azzouni, 2000b. Knowledge and reference in empirical science. London: Routledge.

    Book  Google Scholar 

  • Azzouni, 2004a. Deflating existential commitment: a case for nominalism. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Azzouni, 2004b. Proof and ontology in Euclidean mathematics. , In New Trends in the History and Philosophy of Mathematics, eds. Tinne Hoff Kjeldsen, Stig Andur Pedersen, Lise Mariane Sonne-Hansen (pp. 117-33). Denmark: University Press of Southern Denmark. .

    Google Scholar 

  • Azzouni, 2004c. The derivation-indicator view of mathematical practice, Philosophia Mathematica 12(3): 81-105.

    Article  Google Scholar 

  • Bloor, David 1983. Wittgenstein: a social theory of knowledge. New York: Columbia University Press.

    Google Scholar 

  • Brown, James Robert 1999. Philosophy of mathematics: an introduction to the world of proofs and pictures. London: Routledge.

    Google Scholar 

  • Descartes, René 1931a. Rules for the direction of the mind. The philosophical works of Descartes, trans. by Elizabeth S. Haldane and G.R.T.Ross (pp. 1-77), Cambridge: Cambridge University Press.

    Google Scholar 

  • Descartes, René 1931b. Meditations on first philosophy. In The philosophical works of Descartes, trans. by Elizabeth S. Haldane and G.R.T.Ross (pp. 131-99). Cambridge: Cambridge University Press.

    Google Scholar 

  • Dudley, Underwood 1987. A Budget of trisections. New York: Springer-Verlag.

    Book  Google Scholar 

  • Evans, Gareth 1973. The causal theory of names. In Collected papers, 1-24. Oxford: Oxford University Press (1985).

    Google Scholar 

  • Hersh, Ruben 1997. What is mathematics, really? Oxford: Oxford University Press.

    Google Scholar 

  • Jesseph, Douglas M. 1999. Squaring the circle: the war between Hobbes and Wallis. Chicago: University of Chicago Press.

    Google Scholar 

  • Kline, Morris 1980. Mathematics: the loss of certainty. Oxford: Oxford University Press.

    Google Scholar 

  • Kripke, Saul A. 1982. Wittgenstein on rules and private language. Cambridge, Massachusetts: Harvard University Press.

    Google Scholar 

  • Orwell, George 1949. 1984. New York: Harcourt, Brace and Company, Inc.

    Google Scholar 

  • Putnam, Hilary 1975. The meaning of ‘meaning’. In Mind, language and reality: philosophical papers (Vol. 2, pp. 139-52). Cambridge: Cambridge University Press.

    Google Scholar 

  • Resnik, Michael D. 1997. Mathematics as a science of patterns. Oxford: Oxford University Press.

    Google Scholar 

  • Westfall, Richard S. 1980. Never at rest: a biography of Isaac Newton. Cambridge: Cambridge University Press.

    Google Scholar 

  • Wittgenstein, Ludwig 1953. Philosophical investigations. Trans. G.E.M. Anscombe. New York: The Macmillan Company.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Tufts University, MA, USA

    Jody Azzouni

Authors
  1. Jody Azzouni
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Editor information

Editors and Affiliations

  1. Vrije Universiteit Brussel, Belgium

    Bart van Kerkhove  & Jean Paul van Bendegem  & 

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Azzouni, J. (2007). How and Why Mathematics is Unique as a Social Practice. In: van Kerkhove, B., van Bendegem, J.P. (eds) Perspectives On Mathematical Practices. Logic, Epistemology, and the Unity of Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5034-8_1

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