Limits in the Revision Theory

More Than Just Definite Verdicts


We present a new proposal for what to do at limits in the revision theory. The usual criterion for a limit stage is that it should agree with any definite verdicts that have been brought about before that stage. We suggest that one should not only consider definite verdicts that have been brought about but also more general properties; in fact any closed property can be considered. This more general framework is required if we move to considering revision theories for concepts that are concerned with real numbers, but also has consequences for more traditional revision theories such as the revision theory of truth.


  1. 1.

    Belnap, ND. (1982). Gupta’s rule of revision theory of truth. Journal of Philosophical Logic, 11(1), 103–116.

    Article  Google Scholar 

  2. 2.

    Campbell-Moore, C. (2016). Self-referential probability. PhD thesis, Ludwig-Maximilians-Universität München.

  3. 3.

    Campbell-Moore, C, Horsten, L, Leitgeb, H. Probability for the revision theory of truth, to appear in this volume.

  4. 4.

    Chapuis, A. (1996). Alternative revision theories of truth. Journal of Philosophical Logic, 25(4), 399–423.

    Article  Google Scholar 

  5. 5.

    Gupta, A. (1982). Truth and paradox. Journal of Philosophical Logic, 11(1), 1–60.

    Article  Google Scholar 

  6. 6.

    Gupta, A, & Belnap, ND. (1993). The revision theory of truth. Cambridge: MIT Press.

    Google Scholar 

  7. 7.

    Halbach, V. (2011). Axiomatic theories of truth. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  8. 8.

    Herzberger, HG. (1982). Notes on naive semantics. Journal of Philosophical Logic, 11(1), 61–102.

    Article  Google Scholar 

  9. 9.

    Leitgeb, H. (2008). On the probabilistic convention T. The Review of Symbolic Logic, 1(02), 218–224.

    Article  Google Scholar 

  10. 10.

    Leitgeb, H. (2012). From type-free truth to type-free probability. In G. Restall, & G. Russel (Eds.) New waves in philosophical Logic edited by Restall and Russell (pp. 84–94). New York: Palgrave Macmillan.

  11. 11.

    McGee, V. (1985). How truthlike can a predicate be? A negative result. Journal of Philosophical Logic, 14(4), 399–410.

    Article  Google Scholar 

  12. 12.

    Willard, S. (1970). General topology. New York: Courier Corporation.

    Google Scholar 

Download references


I would like to thank Hannes Leitgeb, Johannes Stern, Seamus Bradley and Leon Horsten and for their helpful discussions and comments on versions of this paper. I am also very grateful to the organisers and participants at a number of conferences, including: Predicate Approaches to Modality, Munich; 45th meeting of the Society for Exact Philosophy, Caltech, Pasadena; Bristol-Leuven conference, Bristol; Logic Seminar, Cambridge; Bristol-München Conference on Truth and Rationality, Bristol.

Author information



Corresponding author

Correspondence to Catrin Campbell-Moore.

Additional information

This work was done partly while at the Munich Center for Mathematical Philosophy, funded by the Alexander von Humboldt Foundation, and partly while at Corpus Christi College, Cambridge, funded by the college.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Campbell-Moore, C. Limits in the Revision Theory. J Philos Logic 48, 11–35 (2019).

Download citation


  • Revision theory
  • Self-reference
  • Circular definitions
  • Taking limits
  • Probability