Proofs instead of Meaning Explanations: Understanding Classical vs Intuitionistic Mathematics from the Outside

  • Chapter
Deduction, Computation, Experiment
  • 691 Accesses

Abstract

The conflict between classical and intuitionistic mathematics - henceforth, the C- I conflict — has been discussed at length and in depth by a number of famous scholars. Why an outside perspective? Is such a perspective interesting, or even possible?

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (France)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 85.59
Price includes VAT (France)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 105.49
Price includes VAT (France)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. S. Berardi and S. Valentini: Krivine’s intuitionistic proof of classical completeness (for countable languages). Annals of Pure and Applied Logic 129 (2004) pp 93–106

    Article  Google Scholar 

  2. E. Bishop: Foundations of Constructive Analysis (McGraw-Hill, New York 1967)

    Google Scholar 

  3. D. S. Bridges: Constructive truth in practice. In: Truth in Mathematics, ed by H. G. Dales and G. Oliveri (Clarendon Press, Oxford 1998) pp 53–69

    Google Scholar 

  4. M. Dummett: The philosophical basis of intuitionistic logic. Reprinted in: Truth and other Enigmas (BLA, London 1978) pp 215–247

    Google Scholar 

  5. M. Dummett: Elements of Intuitionism (Oxford University Press, Oxford 1977) (Revised and reprinted in 2000)

    Google Scholar 

  6. M. Dummett: The Logical Basis of Metaphysics (Harvard University Press, Harvard 1991)

    Google Scholar 

  7. G. Hellman: Never say “Never”! On the communication problem between intuitionism and classicism. Philosophical Topics 17 (1989) pp 47–67

    Google Scholar 

  8. J.-L. Krivine: Une preuve formelle et intuitionistique du Theoreme de Completude de la Logique Classique. Bulletin of Symbolic Logic 2 (1996) pp 405–21

    Article  Google Scholar 

  9. J. Lipton: Kripke semantics for dependent type theory and realizability interpretations. In: Constructivity in Computer Science, LNCS 613 (Springer, Berlin 1992) pp 22–32

    Chapter  Google Scholar 

  10. J. MacFarlane: Making sense of relative truth. Proceedings of the Aristotelian Society 105 (2005) pp 321–39

    Article  Google Scholar 

  11. P. Martin-Löf: Notes on Constructive Mathematics (Almquist & Wiksell, Stockholm 1970)

    Google Scholar 

  12. P. Martin-Löf: Intuitionistic Type Theory (Notes by G. Sambin) (Bibliopolis, Napoli 1984)

    Google Scholar 

  13. D. C. McCarty: Undecidability and intuitionistic incompleteness. Journal of Philosophical Logic 25 (1996) pp 559–565

    Article  Google Scholar 

  14. D. Prawitz: Meaning and proofs: on the conflict between classical and intuitionistic logic. Theoria 43 (1977) pp 2–40

    Article  Google Scholar 

  15. F. Richman: Intuitionism as generalization. Philosophia Mathematica 5 (1990) pp 124–128

    Google Scholar 

  16. G. Sambin: Some points in formal topology. Theoretical Computer Science 305 (2003) pp 347–408

    Article  Google Scholar 

  17. A. Troelstra and D. van Dalen: Constructivism in Mathematics; An Introduction. Vols. I–II (North-Holland, Amsterdam 1988)

    Google Scholar 

  18. D. Westerstahl: Perspectives on the dispute between intuitionistic and classical mathematics. In: Ursus Philosophicus, Philosophical Communications, web series no. 32, Gothenburg University (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Italia

About this chapter

Cite this chapter

Westerstahl, D. (2008). Proofs instead of Meaning Explanations: Understanding Classical vs Intuitionistic Mathematics from the Outside. In: Lupacchini, R., Corsi, G. (eds) Deduction, Computation, Experiment. Springer, Milano. https://doi.org/10.1007/978-88-470-0784-0_10

Download citation

Publish with us

Policies and ethics

Navigation