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 |
| Subjects: | |
| Online Access: | http://analisisfilosofico.org/index.php/af/article/view/456 |
| _version_ | 1797766874916716544 |
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| author | Jonathan Dittrich |
| author_facet | Jonathan Dittrich |
| author_sort | Jonathan Dittrich |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T20:31:36Z |
| format | Article |
| id | doaj.art-b3eba9aa49fc410bb7e7336e8f3e9952 |
| institution | Directory Open Access Journal |
| issn | 0326-1301 1851-9636 |
| language | English |
| last_indexed | 2024-03-12T20:31:36Z |
| publishDate | 2021-11-01 |
| publisher | Sociedad Argentina de Análisis Filosófico (SADAF) |
| record_format | Article |
| series | Análisis Filosófico |
| spelling | doaj.art-b3eba9aa49fc410bb7e7336e8f3e99522023-08-02T00:00:42ZengSociedad Argentina de Análisis Filosófico (SADAF)Análisis Filosófico0326-13011851-96362021-11-01412273283https://doi.org/10.36446/af.2021.456A Nontransitive Theory of Truth over PAJonathan Dittrich0Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität, Munich, GermanyDavid 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.http://analisisfilosofico.org/index.php/af/article/view/456cutparadoxliartruth |
| spellingShingle | Jonathan Dittrich A Nontransitive Theory of Truth over PA Análisis Filosófico cut paradox liar truth |
| title | A Nontransitive Theory of Truth over PA |
| title_full | A Nontransitive Theory of Truth over PA |
| title_fullStr | A Nontransitive Theory of Truth over PA |
| title_full_unstemmed | A Nontransitive Theory of Truth over PA |
| title_short | A Nontransitive Theory of Truth over PA |
| title_sort | nontransitive theory of truth over pa |
| topic | cut paradox liar truth |
| url | http://analisisfilosofico.org/index.php/af/article/view/456 |
| work_keys_str_mv | AT jonathandittrich anontransitivetheoryoftruthoverpa AT jonathandittrich nontransitivetheoryoftruthoverpa |