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Constructions, proofs and the meaning of logical constants

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Bibliography

  • Beeson, M., A Theory of Constructions and Proofs, Preprint No. 134, Dept. of Mathematics, Univ. of Utrecht (1979).

  • Beeson, M., Problematic Principles in Constructive Mathematics, Preprint No. 185, Dept. of Mathematics, Univ. of Utrecht (1981).

  • Beeson, M., ‘Formalizing Constructive Mathematics: Why and how?’, in Richman, E. (ed.), Constructive Mathematics, Lecture Notes in Mathematics, Vol. 873, pp. 146–190, Springer, Berlin (1981a).

    Google Scholar 

  • Bell, D. Frege's Theory of Judgement, Clarendon Press, Oxford (1979).

    Google Scholar 

  • Brouwer, L. E. J., ‘Mathematik, Wissenschaft, Sprache’, Monatshefte f. Mathematik und Physik 36 (1929), 153–164.

    Article  Google Scholar 

  • Brouwer, L. E. J., ‘Consciousness, Philosophy and Mathematics’, in Proc. Xth Intern. Congress Philosophy, pp. 1235–1249, North-Holland, Amsterdam (1948).

    Google Scholar 

  • Brouwer, L. E. J., Brouwer's Cambridge Lectures on Intuitionism, v. Dalen (ed.), C.U.P., Cambridge (1981).

    Google Scholar 

  • de Bruijn, N. G., ‘A Survey of the Project AUTOMATH’, in Seldin and Hindley (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pp. 579–606, Academic Press, London (1980).

    Google Scholar 

  • van Dalen, D., ‘Lectures on Intuitionism’, in Mathias, A. D. and Rogers, H. (eds.), Cambridge Summer School in Mathematical Logic, pp. 1–94, Lecture Notes in Mathematics 337, Springer, Berlin (1973).

    Google Scholar 

  • van Dalen, D., ‘Interpreting Intuitionistic Logic’, in Baayer, v. Dulst and Oosterhoof (eds.), Proc. Bicentenical Congress Wiskundig Genootschap, Vol. I, pp. 133–148. Mathematical Centre Tracts 100, Mathematisch Centrum, Amsterdam (1979).

    Google Scholar 

  • Dummett, M., ‘The Philosophical Singnificance of Gödel's Theorem’, in TE, pp. 186–201 (1963). Also published in Ratio V (1963), 140–155.

  • Dummett, M., ‘The Reality of the Past’, in TE, pp. 358–374 (1969).

  • Dummett, M., Frege, Duckworth. London (1973).

    Google Scholar 

  • Dummett, M., ‘The Justification of Deduction’, in TE, pp. 290–318 (1973a). Also published in Proc. British Academy, Vol. LIX, 1975, pp. 201–232.

  • Dummett, M., ‘What is a Theory of Meaning? (II)’, in Evans and McDowell (eds.), Truth and Meaning, Clarendon Press, Oxford (1976).

    Google Scholar 

  • Dummett, M., Elements of Intuitionism, Clarendon Press, Oxford (1977).

    Google Scholar 

  • Dummett, M., ‘Comments on Professor Prawitz's Paper’, in von Wright (ed.), Logic and Philosophy, pp. 11–18, Nijhoff, The Hague (1980).

    Google Scholar 

  • TE, Truth and Other Enigmas, Duckworth, London (1978).

  • Feferman, S., ‘Constructive Theories of Functions and Classes’, in Boffa v. Dalen and McAloon (eds.), Logic Colloquim '78, pp. 159–224, North-Holland, Amsterdam (1979).

    Google Scholar 

  • Frege, G., ‘Der Gedanke’, Beiträge zur Philosophie des Deutschen Idealismus 1 (1918), 588–77.

    Google Scholar 

  • Goodman, N., ‘A Theory of Constructions Equivalent to Arithmetic’, in Kino, Myhill and Vesley (eds.), Intuitionism and Proof Theory, pp. 101–120, North-Holland, Amsterdam (1970).

    Google Scholar 

  • Heyting, A., ‘Sur la logique intuitioniste’, Acad. Royale de Belgique, Bulletin de la classe de Sciences (5), 16 (1930), 957–963.

    Google Scholar 

  • Heyting, A., ‘Die intuitionistische Grundlegung der Mathematik’, Erkenntnis 2 (1931), 106–115.

    Google Scholar 

  • Heyting, A., Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, Springer. Berlin (1934).

    Google Scholar 

  • Heyting, A., ‘Intuitionism in Mathematics’, in R. Klibansky (ed.), Philosophy in the Mid-century: A Survey, pp. 101–115, La nuova editrice, Firenze (1958).

    Google Scholar 

  • Heyting, A., ‘Blick von den intuitionitischen Warte’, Dialectica 12, (1958a) 332–345.

    Google Scholar 

  • Heyting, A., ‘On truth in mathematics’, in Verslag van de plechtige viering van het hondervijftigjarig bestaan der Koninklijke Nederlanse Akademie van Wetenschappen met de teksten der bij die gelegenheid gehouden redevoeringen en voordrachten, pp. 227–279, North-Holland, Amsterdam (1958b).

    Google Scholar 

  • Heyting, A., ‘Remarques sur le constructivisme’, Logique et Analyse 3 (1960), 177–182.

    Google Scholar 

  • Heyting, A., ‘Intuitionism in Mathematics’, in R. Klibansky (ed.), Contemporary Philosophy. A survey I Logic and Foundations of Mathematics, pp. 316–323, La Nuova Italia editrice, Firenze (1968).

    Google Scholar 

  • Heyting, A., ‘Intuitionistic Views on the Nature of Mathematics’, Synthese 27 (1974), 79–91.

    Google Scholar 

  • Howard, W. A., ‘The Formulae-as-types Notion of Construction’, in Seldin and Hindley (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pp. 479–490, Academic Press, London (1980).

    Google Scholar 

  • Kleene, S. C., ‘On the Interpretation of Intuitionistic Number Theory’, Journal of Symbolic Logic 10 (1945), 109–124.

    Google Scholar 

  • Kolmogoroff, A., ‘Zur Deutung der Intuitionistischen Logik’, Math. Zeitschr. 35 (1932), 58–65.

    Google Scholar 

  • Kreisel, G., ‘Essay-review of Wittgenstein (1956)’ British J. Philosophy of Science, Vol. XI (1958), 135–158.

    Google Scholar 

  • Kreisel, G., ‘Set-theoretical Problems Suggested by the Notion of Potential Totality’, in Infinitistic Methods, pp. 103–140, Pergamon Press, Oxford (1961).

    Google Scholar 

  • Kreisel, G., ‘Foundations of Intuitionistic Logic’, in Nagel, Suppes and Tarski (eds.), Logic, Methodology and Philosophy of Science, pp. 198–210. Stanford Univ. Press, Stanford (1962).

    Google Scholar 

  • Kreisel, G., ‘Mathematical Logic’, in Saaty (ed.) Lectures on Modern Mathematics, III, pp. 95–195, Wiley, New York (1965).

    Google Scholar 

  • Kreisel, G., ‘Perspectives in the Philosophy of Pure Mathematics’, in Suppes, Henkin, Joja and Moisil (eds.), Logic, Methodology and Philosophy of Science IV, pp. 255–278, North-Holland, Amsterdam (1973).

    Google Scholar 

  • Läuchli, H., ‘An Abstract Notion of Realizability for which Intuitionistic Predicate Calculus is Complete’, in Myhill, Kino and Vesley (eds.) Intuitionism and Proof Theory, pp. 227–234, North-Holland, Amsterdam (1970).

    Google Scholar 

  • Martin-Löf, P., An Intuitionistic Theory of Types; Predicative Part’, in Rose and Shepherdson (eds.), Logic Colloquim '73, pp. 73–118, North-Holland, Amsterdam (1975).

    Google Scholar 

  • Martin-Löf, P., ‘About Models for Intuitionistic Type-theories and the Notion of Definitional Equality’, in Kanger (ed.), Proc. 3rd Scand. Logic Symp., pp. 81–109. North-Holland, Amsterdam (1975a).

    Google Scholar 

  • Martin-Löf, P., Constructive Mathematics and Computer Programming, Report No. 11, Dept. of Mathematics, Univ. of Stockholm (1979). Forthcoming in the Proceedings of the VIth Conference for Logic, Methodology and Philosophy of Science.

  • Myhill, J., ‘Notes Towards and Axiomatization of Intuitionistic Analysis’, Logique et Analyse 35 (1967), 280–297.

    Google Scholar 

  • Myhill, J., ‘The Formalization of Intuitionism’, in R. Klibansky (ed.), Contemporary Philosophy I; Logic and Foundations of Mathematics, pp. 324–341, La Nuova Italia Editrice, Firenze (1968).

    Google Scholar 

  • Scott, D. S., ‘Constructive Validity’, in Symposium on Automatic Demonstration, Lecture Notes in Mathematics 125, pp. 237–275, Springer, Berlin (1970).

    Google Scholar 

  • Troelstra, A. S. Principles of Intuitionism, Lecture Notes in Mathematics 95, Springer, Berlin (1969).

    Google Scholar 

  • Troelstra, A. S., ‘Aspects of Constructive Mathematics’, in Barwise, J. (ed.), Handbook of Mathematical Logic, pp. 973–1052, North-Holland, Amsterdam (1977).

    Google Scholar 

  • Troelstra, A. S., ‘Arend Heyting and his Contribution to Intuitionism’, Niew Archief voor Wiskunde (3), XXIX (1981), 1–23.

    Google Scholar 

  • Wittgenstein, L., Remarks on the Foundations of Mathematics, Blackwell, Oxford (1956).

    Google Scholar 

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Authors and Affiliations

  1. Central Interfaculty of Philosophy, University of Nijmegen, Postbus 9108, 6500 HK, Nijmegen, The Netherlands

    Göran Sundholm

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  1. Göran Sundholm
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The research reported herein was supported by a Fellowship by Examination at Magdalen College, Oxford. It was begun when I was a Visiting Lecture at Utrecht, Spring 1980, as a reaction to Beeson's 1979, and I am grateful to him, van Dalen and Visser for almost daily opposition. The paper has been presented at Stockholm, Manchester, Oxford, Münster and Oberwohlfach and I have benefitted from comments by participants in those seminars and Peter Aczel in particular. Professors Kreisel and Martin-Löf, as well as the Editor offered detailed and constructive comments on a preliminary version.

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Sundholm, G. Constructions, proofs and the meaning of logical constants. J Philos Logic 12, 151–172 (1983). https://doi.org/10.1007/BF00247187

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