282
Views
23
CrossRef citations to date
0
Altmetric
Original Articles

Conceptions of truth in intuitionism

Pages 131-145 | Received 27 May 2003, Published online: 20 Feb 2007

References

References

  • Beeson M 1985 Foundations of Constructive Mathematics Berlin and Heidelberg: Springer-Verlag
  • Bishop E 1970 Mathematics as a numerical language in A. Kino et al, eds, Intuitionism and Proof Theory, Amsterdam: North-Holland pp. 53–71
  • Bridges D 1997 Constructive mathematics Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/mathematics-constructive/
  • Brouwer LEJ 1908 The unreliability of logical principles in Brouwer 1975 pp. 107–111
  • Brouwer LEJ 1912 Intuitionism and formalism Bulletin of the American Mathematical Society 20 81 96 Reprinted in Brouwer 1975, pp. 123–138
  • Brouwer LEJ 1933 Willen, Weten, Spreken Euclides 9 177 193 English translation in van Stigt 1990, appendix 5
  • Brouwer LEJ 1948 Consciousness, philosophy and mathematics Proceedings of the 10th International Congress of Philosophy, Amsterdam 1948, III pp. 1235–1249 Reprinted in Brouwer 1975, pp. 489–494
  • Brouwer LEJ 1951 Note for a Lecture’ [BMS 47] in van Stigt 1990, appendix 8
  • Brouwer LEJ 1951/52 Changes in the relation between classical logic and mathematics (handwritten manuscript for a lecture [BMS 59], in van Stigt 1990, appendix 9
  • Brouwer LEJ 1952 Historical background, principles and methods of intuitionism South African Journal of Science 49 139 146 Reprinted in Brouwer 1975, pp. 508–515
  • Brouwer LEJ 1955 The effect of intuitionism on classical algebra of logic Proceedings of the Royal Irish Academy Sect A 57 113 116 Reprinted in Brouwer 1975, pp. 551–554
  • Brouwer LEJ 1975 Collected Works I A. Heyting, ed, Amsterdam: North-Holland
  • Dummett M 1959 Truth reprinted (with Postscript) in Dummett 1978 pp. 1–24
  • Dummett M 1963 Realism in Dummett 1978 pp. 145–165
  • Dummett M 1973 Frege: Philosophy of Language London: Duckworth
  • Dummett M 1975a The philosophical basis for intuitionistic logic reprinted in Dummett 1978 pp. 215–247
  • Dummett M 1975b Justification of deduction reprinted in Dummett 1978 pp. 290–318
  • Dummett M 1977 Elements of Intuitionism Oxford: Oxford University Press
  • Dummett M 1978 Truth and Other Enigmas London: Duckworth
  • Dummett M 1982 Realism reprinted in M. Dummett, The Seas of Language, Oxford: Oxford University Press, 1993 pp. 230–279
  • Dummett M 1987 Reply to Dag Prawitz in B. Taylor, ed Michael Dummett—Contributions to Philosophy, Dordrecht: Martinus Nijhoff Publishers pp. 281–286
  • Dummett M 1993 Wittgenstein on necessity: some reflection in M. Dummett, The Seas of Language, Oxford: Oxford University Press pp. 446–461
  • Dummett M 1994a Reply to Prawitz in B. McGuinness and G. Oliveri, eds, 1994 pp. 292–298
  • Dummett M 1994b Reply to Sundholm in B. McGuinness and G. Oliveri, eds, 1994 pp. 318–328
  • Dummett , M . 1998 . Truth from the constructive standpoint . Theoria , 64 : 122 – 138 .
  • Dummett , M . 2003 . Truth and the past . Journal of Philosophy , 100 : 5 – 53 .
  • Franchella , M . 1994 . Heyting's contribution to the change in research into the foundations of mathematics . History and Philosophy of Logic , 15 : 149 – 172 .
  • George , A . 1993 . How not to refute realism . Journal of Philosophy , 90 : 53 – 72 .
  • Heyting A 1930 Sur la logique intuitionniste Académie Royale de Belgique, Bulletin 16 957 963
  • Heyting , A . 1931 . Die intuitionistische Grundlegung der Mathematik . Erkenntnis , 2 : 106 – 115 .
  • Heyting , A . 1956a . La conception intuitionniste de la logique . La études philosophiques , 11 : 226 – 233 .
  • Heyting A 1956b Intuitionism: An Introduction Amsterdam: North-Holland
  • Heyting A 1958a On truth in mathematics Verlag van de plechtige viering van het honderdvijftigjarig bestaan der Koninklijke Nederlandse Akademie van Wetenschappen met de teksten der bij die gelegenheit gehouden redevoeringen en voorgedrachte, Amsterdam: North-Holland, 1958 pp. 277–279
  • Heyting A 1958b Intuitionism in mathematics in R. Klibansky, ed., Philosophy in the mid-century. A survey, Firenze: La Nuova Italia pp. 101–115
  • Heyting A 1959 Some remarks on intuitionism in Constructivity in Mathematics, Amsterdam: North-Holland pp. 69–71
  • Heyting , A . 1974 . Intuitionistic views on the nature of mathematics . Synthese , 27 : 79 – 91 .
  • Martin-Löf P 1995 Verificationism then and now Vienna Circle Institute Yearbook 3, Dordrecht: Kluwer pp. 187–196
  • McGuinness B Oliveri G (eds) 1994 The Philosophy of Michael Dummett Dordrecht: Kluwer
  • Moore AW 1998 Antirealism in the philosophy of mathematics in E. Craig, ed., Routledge Encyclopedia of Philosophy, London and New York: Routledge
  • Pagin P 1998 Intuitionistic logic and antirealism in E. Craig, ed., Routledge Encyclopedia of Philosophy, London and New York: Routledge
  • Parsons C 1983 Mathematics in Philosophy: Selected Essays Ithaca: Cornell University Press
  • Parsons C 1986 Intuition in constructive mathematics in Jeremy Butterfield, ed. Language, Mind, and Logic, Cambridge: Cambridge University Press pp. 211–229
  • Parsons C 1997 What can we do “in principle”? in M. L. Dalla Chiara et al., eds, Logic and Scientific Method, Volume One of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995, Dordrecht: Kluwer pp. 335–354
  • Prawitz D 1980 Intuitionistic logic: a philosophical challenge in G. H. von Wright, ed., Logic and Philosophy, The Hague: Martinus Nijhoff Publishers pp. 1–10
  • Prawitz D 1987 Dummett on a theory of meaning and its impact on logic in B. Taylor, ed. Michael Dummett—Contributions to Philosophy, Dordrecht: Martinus Nijhoff Publishers pp. 117–165
  • Prawitz D 1994 Meaning theory and anti-realism in B. McGuinness and G. Oliveri, eds, 1994 79 89
  • Prawitz D 1998a Truth and objectivity from a verificationist point of view in H. G. Dales and G. Oliveri, eds Truth in Mathematics, Oxford: Clarendon Press pp. 41–51
  • Prawitz , D . 1998b . Comments on Michael Dummett's paper “Truth from the constructive standpoint” . Theoria , 64 : 283 – 292 .
  • Sellars W 1963 Phenomenalism in W. Sellars Science, Perception, and Reality, London: Routledge & Kegan Paul 60 105
  • Sundholm , G . 1983 . Constructions, proofs and the meaning of logical constants . Journal of Philosophical Logic , 12 : 151 – 172 .
  • Troelstra AS 1969 Principles of Intuitionism Lecture Notes in Mathematics 95, Berlin: Springer
  • Van Stigt W 1990 Brouwer's Intuitionism Amsterdam: North-Holland

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.