Intuitionism and the Anti-Justification of Bivalence

  • Peter Pagin
Part of the Synthese Library book series (SYLI, volume 341)


Dag Prawitz has argued [12] that it is possible intuitionistically to prove the validity of ’ A → there is a proof of ⌌A⌍’ by induction over formula complexity, provided we observe an object language/meta-language distinction. In the present paper I mainly argue that if the object language with its axioms and rules can be represented as a formal system, then the proof fails. I also argue that if this restriction is lifted, at each level of the language hierarchy, then the proof can go through, but at the expense of virtually reducing the concept of a proof to that of truth in a non-constructive sense.


Formal System Object Language Equivalence Principle Intuitionistic Logic Logical Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dummett, M., 1976, ‘What is a theory of meaning? (II)’, in G. Evans and J. McDowell (eds.), Truth and Meaning, Oxford University Press, Oxford. Reprinted in Dummett 1998, 34–93. Page references to the reprint.Google Scholar
  2. 2.
    Dummett, M., 1980, ‘The philosophical significance of Gödel’s theorem’, in Truth and Other Enigmas, 186–201. Duckworth, London, 2nd edn., Originally published in Ratio V, 1963, 140–155.Google Scholar
  3. 3.
    Dummett, M., 1982, ‘Realism’, Synthese 52:55–112.CrossRefMathSciNetGoogle Scholar
  4. 4.
    Dummett, M., 1991, The Logical Basis of Metaphysics, Harvard University Press, Cambridge, Mass.Google Scholar
  5. 5.
    Dummett, M., 1998, The Seas of Language, Clarendon Press, Oxford.Google Scholar
  6. 6.
    Kreisel, G., 1962, ‘Foundations of intuitionistic logic’, in E. Nagel ed., Logic, Methodology and Philosophy of Science I, North-Holland, Amsterdam.Google Scholar
  7. 7.
    Martin-Löf, P., 1984, Intuitionistic Type Theory, Bibliopolis, Napoli.zbMATHGoogle Scholar
  8. 8.
    Nelson, D., 1947, ‘Recursive functions and intuitionistic number theory’, Transactions of the American Mathematical Society 61:307–368.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Pagin, P., 1998, ‘Bivalence: meaning theory vs metaphysics’, Theoria LXIV:157–186.Google Scholar
  10. 10.
    Prawitz, D., 1980, ‘Intuitionistic logic: a philosophical challenge’, in G. H. von Wright ed., Logic and Philosophy, Martinus Nijhoff Publishers, The Hague.Google Scholar
  11. 11.
    Prawitz, D., 1994, ‘Meaning theory and anti-realism’, in B. McGuinnes and G. Oliveri (eds.), The Philosophy of Michael Dummett, Kluwer, Dordrecht, 79–89.Google Scholar
  12. 12.
    Prawitz, D., 1998, ‘Comments on Peter Pagin’s paper’, Theoria LXIV.Google Scholar
  13. 13.
    Tennant, N., 1996, ‘The law of excluded middle is synthetic a priori, if valid’, Philosophical Topics 24:205–229.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Peter Pagin
    • 1
  1. 1.Department of PhilosophyStockheelm UniversityStockheelmSweden

Personalised recommendations