The Yablo Paradox and Circularity
In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that...
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| Format: | Article |
| Language: | English |
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Sociedad Argentina de Análisis Filosófico (SADAF)
2012-05-01
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| Series: | Análisis Filosófico |
| Subjects: | |
| Online Access: | https://analisisfilosofico.org/index.php/af/article/view/104 |
| _version_ | 1797744323602677760 |
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| author | Eduardo A. Barrio |
| author_facet | Eduardo A. Barrio |
| author_sort | Eduardo A. Barrio |
| collection | DOAJ |
| description | In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. |
| first_indexed | 2024-03-12T15:09:05Z |
| format | Article |
| id | doaj.art-43f9c373be5a4450a111a610b22a8d9a |
| institution | Directory Open Access Journal |
| issn | 0326-1301 1851-9636 |
| language | English |
| last_indexed | 2024-03-12T15:09:05Z |
| publishDate | 2012-05-01 |
| publisher | Sociedad Argentina de Análisis Filosófico (SADAF) |
| record_format | Article |
| series | Análisis Filosófico |
| spelling | doaj.art-43f9c373be5a4450a111a610b22a8d9a2023-08-12T00:07:09ZengSociedad Argentina de Análisis Filosófico (SADAF)Análisis Filosófico0326-13011851-96362012-05-01321720https://doi.org/10.36446/af.2012.104The Yablo Paradox and CircularityEduardo A. Barrio0Universidad de Buenos Aires / CONICET - G[af]In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume.https://analisisfilosofico.org/index.php/af/article/view/104yablo paradoxtruthcircularityfinitism |
| spellingShingle | Eduardo A. Barrio The Yablo Paradox and Circularity Análisis Filosófico yablo paradox truth circularity finitism |
| title | The Yablo Paradox and Circularity |
| title_full | The Yablo Paradox and Circularity |
| title_fullStr | The Yablo Paradox and Circularity |
| title_full_unstemmed | The Yablo Paradox and Circularity |
| title_short | The Yablo Paradox and Circularity |
| title_sort | yablo paradox and circularity |
| topic | yablo paradox truth circularity finitism |
| url | https://analisisfilosofico.org/index.php/af/article/view/104 |
| work_keys_str_mv | AT eduardoabarrio theyabloparadoxandcircularity AT eduardoabarrio yabloparadoxandcircularity |