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Validity and quantification in intuitionism

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Abstract

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the “most natural” reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.

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References

  1. M.Dummett, Elements of Intuitionism, Oxford University Press, Oxford 1977.

    Google Scholar 

  2. A.Heyting, Intuitionism: an Introduction, North Holland, Amsterdam, 1971.

    Google Scholar 

  3. H.Putnam, Philosophy of Logic, George Allen and Unwin Ltd., London, 1972.

    Google Scholar 

  4. H. C. M.deSwart, ‘An intuitionistically plausible interpretation of intuitionistic logic’, Journal of Symbolic Logic 42 (1977), 564–578.

    Google Scholar 

  5. H. C. M.deSwart, ‘Elements of intuitionistic analysis: Rolle's theorem and complete totally bounded, metric spaces’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 22 (1976), 289–298.

    Google Scholar 

  6. H. C. M.deSwart, ‘Elements of intuitionistic analysis: The Stone-Weierstrass Theorem and Ascoli's Theorem’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 22 (1976), 501–508.

    Google Scholar 

  7. A. S.Troelstra, Principles of Intuitionism, Springer Verlag, Berlin, 1969.

    Google Scholar 

  8. W.Veldman, ‘An intuitionistic completeness theorem for intuitionistic predicate logic’, Journal of Symbolic Logic 41 (1976), 159–166.

    Google Scholar 

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Authors and Affiliations

  1. Katholieke Hogeschool, Tilburg, The Netherlands

    H. C. M. de Swart & C. J. Posy

  2. The University of Pittsburgh, Pittsburgh, USA

    H. C. M. de Swart & C. J. Posy

Authors
  1. H. C. M. de Swart
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  2. C. J. Posy
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Additional information

This paper was partly written while the first author, H. C. M. de Swart, was a Visiting Fellow at Princeton University for the academic year 1976–1977. This opportunity was given to him by the Niels Stensen Stichting in Amsterdam, the department of philosophy of the Catholic University in Nijmegen and by Princeton University. He is happy to express his appreciation for that opportunity.

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de Swart, H.C.M., Posy, C.J. Validity and quantification in intuitionism. J Philos Logic 10, 117–126 (1981). https://doi.org/10.1007/BF00253915

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  • DOI: https://doi.org/10.1007/BF00253915

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