Skip to main content
Log in

Another Paradox In Naive Set-Theory

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Burali-Forti, C., ‘A question on transfinite numbers’, Rendiconti del Circolo matematico di Palermo 11:154–164, 1897. Reprinted in [9].

    Google Scholar 

  2. Cantor, G., ‘Letter to Dedekind’. Reprinted in [9].

  3. Coquand, T., ‘An analysis of Girard's paradox’, First Logic in computer science symposium, Boston, July 1986.

  4. Frege, G., ‘Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought’. Reprinted in [9].

  5. Martin-Löf, P., ‘An intuitionistic theory of types’, 1972.

  6. Martin-Löf, P., ‘Twenty-five years of constructive type theory’(Venice, 1995), Oxford Logic Guides, 36, 127–172, Oxford Univ. Press, New York, 1998.

    Google Scholar 

  7. Russell, B., ‘Letter to Frege’. Reprinted in [9].

  8. Troelstra, A.S., and D. van Dalen, Constructivism in mathematics. Vol. II. An introduction, Studies in Logic andthe Foundations of Mathematics, 123. North-Holland Publishing Co., Amsterdam, 1988.

    Google Scholar 

  9. van Heijenoort, J. (ed.), From Frege to Gödel, A source book in Mathematical Logic, Harvard University Press, 1967.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Loïc Colson.

Additional information

Presented by Robert Goldblatt

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colson, L. Another Paradox In Naive Set-Theory. Stud Logica 85, 33–39 (2007). https://doi.org/10.1007/s11225-007-9025-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-007-9025-1

Keywords

Navigation