The Revision Theory of Truth

Abstract

In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological contexts. The latter include, for instance, contexts that generate Liar Paradox. Their central claim is that truth is a circular concept. In support of this claim they provide a widely applicable theory (the "revision theory") of circular concepts. Under the revision theory, when truth is seen as circular both its ordinary features and its pathological features fall into a simple understandable pattern. The Revision Theory of Truth is unique in placing truth in the context of a general theory of definitions. This theory makes sense of arbitrary systems of mutually interdependent concepts, of which circular concepts, such as truth, are but a special case. Bradford Books imprint

Probability for the Revision Theory of Truth

“…In the revision theory of truth (Gupta and Belnap [6]), one constructs revision sequences, which are sequences of interpretations of a truth predicate. These can be used to determine appropriate interpretations of T, or at least facts about how appropriate interpretations will treat different sentences.…”

“…5 Thus we have also probabilistic reasons for extending Leitgeb's construction into the transfinite. 6…”

NOTES ONω-INCONSISTENT THEORIES OF TRUTH IN SECOND-ORDER LANGUAGES

“…The revision theory of truth is an attempt to show how a classical language may contain its own truth predicate by describing and explaining the behavior of this predicate in ordinary as well as in problematic cases such as those posed by semantic paradoxes. It was originally introduced by Gupta (1982) and Herzberger (1982) and fully developed by Gupta & Belnap (1993), the locus classicus on the topic. The revision theory is said to be a semantic truth theory.…”

“…What about unstable sentences? Gupta & Belnap (1993) consider all possible ways of adding some unstable sentences to the extension of T at each limit stage λ. 9 Let A be any sentence of L 2 T and λ any subset of ω:…”

“…However, for readability purposes we will frequently identify expressions with their codes. 9 Previously, some alternatives have been explored in the literature by Belnap (1982), Gupta (1982) and Herzberger (1982), for which Gupta & Belnap (1993) notion seems to be an improvement. Later, Yaqūb (1993) and Chapuis (1996) worked on several refinements.…”