, Volume 13, Issue 2, pp 135–145 | Cite as

Never say never

  • Timothy Williamson


I. An argument is presented for the conclusion that the hypothesis that no one will ever decide a given proposition is intuitionistically inconsistent. II. A distinction between sentences and statements blocks a similar argument for the stronger conclusion that the hypothesis that I have not yet decided a given proposition is intuitionistically inconsistent, but does not block the original argument. III. A distinction between empirical and mathematical negation might block the original argument, and empirical negation might be modelled on Nelson's strong negation, but only on intuitionistically unacceptable assumptions. IV. Intuitionists may have to accept the original argument, and therefore be committed to a dubious view of time on which there cannot be merely inductive evidence for statements about the infinite future.


Intuitionistic Logic Original Argument Strong Negation Fair Coin Kripke Semantic 
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  1. Brouwer, L. E. J.: 1975,Collected Works I: Philosophy and Mathematics, in Heyting, A. (Ed.), Amsterdam: North-Holland.Google Scholar
  2. Dalen, D. van: 1986, ‘Intuitionistic Logic’, in Gabbay, D. and Guenthner, F. (Eds.),Handbook of Philosophical Logic III: Alternatives to Classical Logic, Dordrecht, Reidel.Google Scholar
  3. Dudman, V.: 1992, ‘Probability and Assertion’,Analysis 52, 204–211.CrossRefGoogle Scholar
  4. Dummett, M. A. E.: 1969, ‘The Reality of the Past’,Proceedings of the Aristotelian Society 69, 239–258; in Dummett (1978).Google Scholar
  5. Dummett, M. A. E.: 1973,Frege: Philosophy of Language, London, Duckworth.Google Scholar
  6. Dummett, M. A. E.: 1975, ‘The Philosophical Basis of Intuitionistic Logic,’ in Rose, H. E. and Shepherdson, J. C. (Eds.),Logic Colloquium '73, Amsterdam: North-Holland, and Dummett (1978).Google Scholar
  7. Dummett, M. A. E.: 1977,Elements of Intuitionism, Oxford, Clarendon Press.Google Scholar
  8. Dummett, M. A. E.: 1978,Truth and Other Enigmas, London, Duckworth.Google Scholar
  9. Dummett, M. A. E.: 1993,The Seas of Language, Oxford, Clarendon Press.Google Scholar
  10. Edgington, D.: 1985, ‘The Paradox of Knowability,’Mind 94, 557–568.CrossRefGoogle Scholar
  11. Ewald, W. B.: 1986, ‘Intuitionistic Tense and Modal Logic’,Journal of Symbolic Logic 51, 166–179.CrossRefGoogle Scholar
  12. Fitch, F. B.: 1963, ‘A Logical Analysis of Some Value Concepts,’,Journal of Symbolic Logic 28, 135–142.CrossRefGoogle Scholar
  13. Hart, W. D.: 1979, ‘The Epistemology of Abstract Objects: Access and Inference’,Proceedings of the Aristotelian Society 53 (suppl): 152–165.Google Scholar
  14. Kreisel, G. and Troelstra, A. S.: 1970, ‘Formal Systems for Some Branches of Intuitionistic Analysis’,Annals of Mathematical Logic 1, 229–387.CrossRefGoogle Scholar
  15. Melia, J.: 1991, ‘Anti-Realism Untouched’,Mind 100, 341–342.CrossRefGoogle Scholar
  16. Miglioli, P., Moscato, U., Ornaghi, M. and Usberti, G.: 1989, ‘A Constructivism Based on Classical Truth’,Notre Dame Journal of Formal Logic 30, 67–90.CrossRefGoogle Scholar
  17. Nelson, D.: 1949, ‘Constructible Falsity’,Journal of Symbolic Logic 14, 16–26.CrossRefGoogle Scholar
  18. Percival, P.: 1990, ‘Fitch and Intuitionistic Knowability’,Analysis 50, 182–187.CrossRefGoogle Scholar
  19. Percival, P.: 1991, ‘Knowability, Actuality and the Metaphysics of Context-Dependence’,Australasian Journal of Philosophy 69, 82–97.CrossRefGoogle Scholar
  20. Prawitz, D.: 1977, ‘Meaning and Proofs: On the Conflict between Classical and Intuitionistic Logic’,Theoria 43, 2–40.CrossRefGoogle Scholar
  21. Rabinowicz, W.: 1985, ‘Intuitionistic Truth’,Journal of Philosophical Logic 14, 191–228.CrossRefGoogle Scholar
  22. Rabinowicz, W. and Segerberg, K.: 1994, ‘Actual Truth, Possible Knowledge’,Topoi 13, 101–115.CrossRefGoogle Scholar
  23. Rasiowa, H.: 1974,An Algebraic Approach to Non-Classical Logics, Amsterdam, North-Holland.Google Scholar
  24. Slote, M. A.: 1979, ‘Assertion and Belief’, in Dancy, J. (Ed.),Papers on Language and Logic, Keele, Keele University Library.Google Scholar
  25. Thomason, R. H.: 1969, ‘A Semantical Study of Constructible Falsity,’Zeitschrift für mathematische Logik und Grundlagen der Mathematik 15, 247–257.CrossRefGoogle Scholar
  26. Unger, P.: 1975,Ignorance, Oxford, Oxford University Press.Google Scholar
  27. Williamson, T.: 1982, ‘Intuitionism disproved?’,Analysis 42, 203–207.CrossRefGoogle Scholar
  28. Williamson, T.: 1987, ‘On the Paradox of Knowability’,Mind 96, 256–261.CrossRefGoogle Scholar
  29. Williamson, T.: 1988, ‘Knowability and Constructivism’,Philosophical Quarterly 38, 422–432.CrossRefGoogle Scholar
  30. Williamson, T.: 1992, ‘On Intuitionistic Modal Epistemic Logic’,Journal of Philosophical Logic 21, 63–89.Google Scholar
  31. Wright, C. J. G.: 1987,Realism, Meaning and Truth, Oxford, Blackwell.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Timothy Williamson
    • 1
  1. 1.University CollegeOxfordU.K.

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