Models & Proofs: LFIs Without a Canonical Interpretations
In different papers, Carnielli, W. & Rodrigues, A. (2012), Carnielli, W. Coniglio, M. & Rodrigues, A. (2017) and Rodrigues & Carnielli, (2016) present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of...
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Universidade Federal de Santa Catarina
2018-08-01
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| Series: | Principia: An International Journal of Epistemology |
| Online Access: | https://periodicos.ufsc.br/index.php/principia/article/view/58635 |
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| author | Eduardo Alejandro Barrio |
| author_facet | Eduardo Alejandro Barrio |
| author_sort | Eduardo Alejandro Barrio |
| collection | DOAJ |
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In different papers, Carnielli, W. & Rodrigues, A. (2012), Carnielli, W. Coniglio, M. & Rodrigues, A. (2017) and Rodrigues & Carnielli, (2016) present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of Evidence) and the second—that is a conservative extension of BLE—is named LETJ (the Logic of Evidence and Truth). Roughly, BLE and LETJ are two non-classical (paraconsistent and paracomplete) logics in which the Laws of Explosion (EXP) and Excluded Middle (PEM) are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency (an LFI). This means that there is an operator that, roughly speaking, identifies a formula as having classical behavior. Both systems are motivated by the idea that there are different conditions for accepting or rejecting a sentence of our natural language. So, there are some special introduction and elimination rules in the theory that are capturing different conditions of use. Rodrigues & Carnielli’s paper has an interesting and challenging idea. According to them, BLE and LETJ are incompatible with dialetheia. It seems to show that these paraconsistent logics cannot be interpreted using truth-conditions that allow true contradictions. In short, BLE and LETJ talk about conflicting evidence avoiding to talk about gluts. I am going to argue against this point of view. Basically, I will firstly offer a new interpretation of BLE and LETJ that is compatible with dialetheia. The background of my position is to reject the one canonical interpretation thesis: the idea according to which a logical system has one standard interpretation. Then, I will secondly show that there is no logical basis to fix that Rodrigues & Carnielli’s interpretation is the canonical way to establish the content of logical notions of BLE and LETJ . Furthermore, the system LETJ captures inside classical logic. Then, I am also going to use this technical result to offer some further doubts about the one canonical interpretation thesis.
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| format | Article |
| id | doaj-art-2218a1febf294c559abe1bbf9b10b2e9 |
| institution | Kabale University |
| issn | 1808-1711 |
| language | English |
| publishDate | 2018-08-01 |
| publisher | Universidade Federal de Santa Catarina |
| record_format | Article |
| series | Principia: An International Journal of Epistemology |
| spelling | doaj-art-2218a1febf294c559abe1bbf9b10b2e92025-08-20T03:42:13ZengUniversidade Federal de Santa CatarinaPrincipia: An International Journal of Epistemology1808-17112018-08-0122110.5007/1808-1711.2018v22n1p8729441Models & Proofs: LFIs Without a Canonical InterpretationsEduardo Alejandro Barrio0IIF-Conicet - UBA - BA-Logic In different papers, Carnielli, W. & Rodrigues, A. (2012), Carnielli, W. Coniglio, M. & Rodrigues, A. (2017) and Rodrigues & Carnielli, (2016) present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of Evidence) and the second—that is a conservative extension of BLE—is named LETJ (the Logic of Evidence and Truth). Roughly, BLE and LETJ are two non-classical (paraconsistent and paracomplete) logics in which the Laws of Explosion (EXP) and Excluded Middle (PEM) are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency (an LFI). This means that there is an operator that, roughly speaking, identifies a formula as having classical behavior. Both systems are motivated by the idea that there are different conditions for accepting or rejecting a sentence of our natural language. So, there are some special introduction and elimination rules in the theory that are capturing different conditions of use. Rodrigues & Carnielli’s paper has an interesting and challenging idea. According to them, BLE and LETJ are incompatible with dialetheia. It seems to show that these paraconsistent logics cannot be interpreted using truth-conditions that allow true contradictions. In short, BLE and LETJ talk about conflicting evidence avoiding to talk about gluts. I am going to argue against this point of view. Basically, I will firstly offer a new interpretation of BLE and LETJ that is compatible with dialetheia. The background of my position is to reject the one canonical interpretation thesis: the idea according to which a logical system has one standard interpretation. Then, I will secondly show that there is no logical basis to fix that Rodrigues & Carnielli’s interpretation is the canonical way to establish the content of logical notions of BLE and LETJ . Furthermore, the system LETJ captures inside classical logic. Then, I am also going to use this technical result to offer some further doubts about the one canonical interpretation thesis. https://periodicos.ufsc.br/index.php/principia/article/view/58635 |
| spellingShingle | Eduardo Alejandro Barrio Models & Proofs: LFIs Without a Canonical Interpretations Principia: An International Journal of Epistemology |
| title | Models & Proofs: LFIs Without a Canonical Interpretations |
| title_full | Models & Proofs: LFIs Without a Canonical Interpretations |
| title_fullStr | Models & Proofs: LFIs Without a Canonical Interpretations |
| title_full_unstemmed | Models & Proofs: LFIs Without a Canonical Interpretations |
| title_short | Models & Proofs: LFIs Without a Canonical Interpretations |
| title_sort | models proofs lfis without a canonical interpretations |
| url | https://periodicos.ufsc.br/index.php/principia/article/view/58635 |
| work_keys_str_mv | AT eduardoalejandrobarrio modelsproofslfiswithoutacanonicalinterpretations |