Abstract

DITTRICH, Jonathan. A Nontransitive Theory of Truth Over pA. Anal. filos. [online]. 2021, vol.41, n.2, pp.273-283. ISSN 1851-9636.  http://dx.doi.org/10.36446/af.2021.456.

David Ripley has argued extensively for a nontransitive theory of truth by dropping the rule of Cut in a sequent calculus setting in order to get around triviality caused by paradoxes such as the Liar. However, comparing his theory with a wide range of classical approaches in the literature is problematic because formulating it over an arithmetical background theory such as Peano Arithmetic is non-trivial as Cut is not eliminable in Peano Arithmetic. Here we make a step towards closing this gap by providing a suitable restriction of the Cut rule, which allows for a nontransitive theory of truth over Peano Arithmetic that is proof-theoretically as strong as the strongest known classical theory of truth.

Keywords : Cut; Paradox; Liar; Truth.