Journal of Philosophical Logic

, Volume 48, Issue 1, pp 87–112 | Cite as

Probability for the Revision Theory of Truth

  • Catrin Campbell-Moore
  • Leon HorstenEmail author
  • Hannes Leitgeb
Open Access


We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfinite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable properties of the resulting probability function. One such property is Leitgeb’s Probabilistic Convention T, which says that the probability of φ equals the probability that φ is true.


Liar paradox Semantic paradox Revision theory of truth Probabilistic convention T 



We would like to thank Philip Welch and Johannes Stern for helpful discussions on this topic, as well as anonymous referees for this journal for their helpful suggestions. Catrin Campbell-Moore would also like to thank Corpus Christi College, Cambridge, where she was based as a Stipendiary Research Fellow while this paper was being written.


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© The Author(s) 2018

Open AccessThis 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.

Authors and Affiliations

  • Catrin Campbell-Moore
    • 1
  • Leon Horsten
    • 1
    Email author
  • Hannes Leitgeb
    • 2
  1. 1.Department of PhilosophyUniversity of BristolBristolUK
  2. 2.Munich Center for Mathematical PhilosophyLudwig Maximilians Universität MünchenMünchenGermany

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