A Nontransitive Theory of Truth over PA
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 probl...
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| Format: | Article |
| Language: | English |
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Sociedad Argentina de Análisis Filosófico (SADAF)
2021-11-01
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| Series: | Análisis Filosófico |
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| Online Access: | http://analisisfilosofico.org/index.php/af/article/view/456 |
| Summary: | 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. |
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| ISSN: | 0326-1301 1851-9636 |