Abstract
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.
| Item Type: | Journal article |
|---|---|
| Faculties: | Philosophy, Philosophy of Science and Religious Science |
| Subjects: | 100 Philosophy and Psychology > 100 Philosophy |
| ISSN: | 0326-1301 |
| Language: | English |
| Item ID: | 97753 |
| Date Deposited: | 05. Jun 2023, 15:26 |
| Last Modified: | 05. Jun 2023, 15:26 |
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