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Hypothetical Extensions of Constructive 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

What are the most striking features of modern (classical) mathematics? It works! It’s fun! It’s beautiful! It’s useful! It’s profitable! It’s respected! Then, why does it need “foundation”?

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Notes

  1. Solomon Feferman, “Constructive theories of functions and classes”, in: Maurice Boffa, Dirk van Dalen, Kenneth McAloon (Eds.), Logic Colloquium ‘78, Amsterdam: North-Holland 1979, pp. 159–224.

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  2. Michael J. Beeson, Foundations of constructive mathematics, Berlin: Springer 1985.

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  3. Anne S. Troelstra and Dirk van Dalen, Constructivism in mathematics, volumes I and II, Amsterdam: North-Holland 1988.

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  4. Peter H. Krauss, “A constructive interpretation of classical mathematics”, in: Mathematische Schriften Kassel, Preprint No. 5, 1992.

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  5. Clifford Spector, “Provably recursive functionals of analysis: A consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics”, in: J. C. E. Dekker (Ed.), Recursive function theory, Proceedings of Symposia in Pure Mathematics V, Providence: American Mathematical Society 1962, pp. 1–27.

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  6. Peter H. Krauss, “A constructive interpretation of classical mathematics”, op. cit.

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  7. Anne S. Troelstra and Dirk van Dalen, Constructivism in mathematics, op. cit.,p.193 pp. 212–214, p. 223, p. 228.

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Authors
  1. Peter H. Krauss
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Editor information

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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Krauss, P.H. (1995). Hypothetical Extensions of Constructive 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_12

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  • DOI: https://doi.org/10.1007/978-94-017-3327-4_12

  • 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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