Skip to main content
Log in

On interpreting Gödel's Second Theorem

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Summary

In this paper I have considered various attempts to attribute significance to G2.25 Two of these attempts (Beth-Cohen and the position maintaining that G2 shows the failure of Hilbert's Program), I have argued, are literally false. Two others (BCR and Resnik's Interpretation), I have argued, are groundless.

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.

Similar content being viewed by others

Bibliography

  1. BethEvert W., The Foundations of Mathematics, 2nd ed. rev., North-Holland Publishing Co., Amsterdam, 1968.

    Google Scholar 

  2. CohenPaul J., Set Theory and the Continuum Hypothesis, W. A. Benjamin, Inc., Reading, Mass., 1966.

    Google Scholar 

  3. CohenPaul J., ‘Comments on the Foundations of Set Theory’, In Axiomatic Set Theory, edited by DanaScott, Proceedings of Symposia in Pure Mathematics, Vol. 13, pt. 1, The American Mathematical Society, New York, 1971.

    Google Scholar 

  4. Detlefsen, Michael, ‘The Importance of Gödel's Second Incompleteness Theorem for the Foundations of Mathematics’. Doctoral Thesis, The Johns Hopkins University, 1976.

  5. GrzegorczykAndrzej, An Outline of Mathematical Logic, D. Reidel Publishing Co., Boston, 1974.

    Google Scholar 

  6. MostowskiAndrzej, ‘On Models of Axiomatic Systems’. Fundamenta Mathematicae 39 (1952), 133–147.

    CAS  PubMed  Google Scholar 

  7. NagelE. and NewmanJ. R., Gödel's Proof, New York University Press, New York, 1958.

    Google Scholar 

  8. ResnikMichael D., ‘The Philosophical Significance of Consistency Proofs’. Journal of Philosophical Logic 3 (1974), 133–147.

    Google Scholar 

  9. RosserJ. B., ‘Gödel Theorems for Non-Constructive Logics’, Journal of Symbolic Logic 2 (1937), 129–137.

    Google Scholar 

  10. WangHao, Logic, Computers, and Sets, Chelsea Publishing Co., New York, 1970.

    Google Scholar 

  11. WangHao, From Mathematics to Philosophy, Humanities Press, New York, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

I would like to thank Dale Gottlieb, Stephen Barker, Tim McCarthy, Philip Kitcher, Michael Resnik and Richmond Thomason for extensive and helpful discussion of this work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Detlefsen, M. On interpreting Gödel's Second Theorem. J Philos Logic 8, 297–313 (1979). https://doi.org/10.1007/BF00258433

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00258433

Navigation