Probability for the Revision Theory of Truth

Journal of Philosophical Logic:1-26 (forthcoming)
Authors
Catrin Campbell-Moore
Bristol University
Leon Horsten
Bristol University
Hannes Leitgeb
Ludwig Maximilians Universität, München
Abstract
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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DOI 10.1007/s10992-018-9475-0
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