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Crisis and Return of Intuition in Hans Hahn’s Philosophy of Mathematics

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The Foundational Debate

Part of the book series: Vienna Circle Institute Yearbook [1995] ((VCIY,volume 3))

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Abstract

In the long history of 2000 years of interaction between philosophy and mathematics three major problem areas have been dealt with, following the three classic disciplines logic, metaphysics (as general ontology) and epistemology:

  • the problem of truth of mathematical statements

  • the problem of existence of mathematical objects and

  • the problem of how to recognize mathematical objects.

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Notes

  1. Philip J. Davis and Reuben Hersh, ErfahrungMathematik. Basel, Boston, Stuttgart: Birkhäuser 1986, p. 337.

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  4. Hans Hahn, Empirismus, Logik, Mathematik. With an introduction by Karl Menger, ed. by Brian McGuinness. Frankfurt a.M.: Suhrkamp 1988, p. 9.

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  5. Hans Hahn, op.cit. p. 21.

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  6. Hans Hahn, op.cit. p. 27.

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  7. Hans Hahn, “Die Krise der Anschauung”. In: Krise und Neuaufbau in den exakten Wissenschaften. Leipzig und Wien: Franz Deuticke 1933, pp. 41–64. (Engl.) The Crisis in Intuition. In: J.R. Newman (Ed.), The World of Mathematics, New York: Simon and Schuster, pp. 1956–1976.

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  8. Hans Hahn, Die Krise der Anschauung,op.cit., p. 44.

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  10. Emile Sorel, Méthodes et problèmes de théorie des fonctions,Paris 1922.

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Authors
  1. Erhard Oeser
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Editors and Affiliations

  1. University of Vienna, Austria

    Werner Depauli-Schimanovich  & Eckehart Köhler  & 

  2. Institut ‘Wiener Kreis’, Vienna, Austria

    Friedrich Stadler

  3. University of Vienna, Austria

    Friedrich Stadler

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© 1995 Springer Science+Business Media Dordrecht

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Oeser, E. (1995). Crisis and Return of Intuition in Hans Hahn’s Philosophy of Mathematics. In: Depauli-Schimanovich, W., Köhler, E., Stadler, F. (eds) The Foundational Debate. Vienna Circle Institute Yearbook [1995], vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3327-4_19

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  • DOI: https://doi.org/10.1007/978-94-017-3327-4_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4617-8

  • Online ISBN: 978-94-017-3327-4

  • eBook Packages: Springer Book Archive

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