Probability for the Revision Theory of Truth
- 256 Downloads
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.
KeywordsLiar 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.
- 3.Benci, V., Horsten, L., Wenmackers, S. (2018). Infinitesimal probabilities. The British Journal for the Philosophy of Science, 69(2).Google Scholar
- 4.Brickhill, H., & Horsten, L. (2018). Triangulating non-Archimedean probability. The Review of Symbolic Logic, 1–28. https://doi.org/10.1017/S1755020318000060.
- 5.Campbell-Moore, C. (2018). Limits in the revision theory: more than just definite verdicts. Journal of Philosophical Logic, this edition.Google Scholar
- 6.Gupta, A., & Belnap, N.D. (1993). The revision theory of truth. Cambridge: MIT Press.Google Scholar
- 10.Leitgeb, H. (2012). From type-free truth to type-free probability. In Restall, G., & Russel, G. (Eds.) New Waves in philosophical logic (pp. 84–94). Palgrave Macmillan.Google Scholar
- 11.Lewis, D. (1980). A subjectivist’s guide to objective chance. In Jeffrey, R. (Ed.) Studies in inductive logic and probability, (Vol. 2 pp. 263–293). Berkeley and Los Angeles: University of California Press.Google Scholar
- 13.Roeper, P., & Leblanc, H. (1999). Probability theory and probability logic. University of Toronto Press.Google Scholar
- 15.Williams, J.R.G. (2014). Probability and non-classical logic. In Hitchcock, C., & Hájek, A. (Eds.) Oxford Handbook of Probability and Philosophy (pp. 248–276). Oxford University Press.Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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.