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.
Highlights
The revision theory of truth is an influential way to account for a type-free truth predicate
The sentence T 0 = 0, for example, settles down on being true, whereas the liar sentence will have its truth value continuing to switch throughout the revision sequence
In this paper we construct such probability functions that measure how often a sentence is true in a revision sequence of hypotheses
Summary
The revision theory of truth is an influential way to account for a type-free truth predicate. In this paper we construct such probability functions that measure how often a sentence is true in a revision sequence of hypotheses This idea was pioneered in Leitgeb [9], where the finite stages of the revision theory of truth are used to define probabilities for sentences that may include a type-free truth predicate. We explore ways that Leitgeb’s construction can be extended to determine probability values dependent on the transfinite stages of the revision sequence, answering a question in Leitgeb [10]. Our proposal extends his by assigning probabilities at a transfinite ordinal stage, measuring how often the sentence is true in the revision sequence up to that ordinal.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.