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.
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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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Campbell-Moore, C., Horsten, L. & Leitgeb, H. Probability for the Revision Theory of Truth. J Philos Logic 48, 87–112 (2019). https://doi.org/10.1007/s10992-018-9475-0
- Liar paradox
- Semantic paradox
- Revision theory of truth
- Probabilistic convention T