Paraconsistency and its Philosophical Interpretations

Barrio, Eduardo Alejandro; Ré, Bruno Da

doi:10.26686/ajl.v15i2.4860

Cited by 25 publications

(18 citation statements)

References 16 publications

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“…One could adopt the epistemic approach in some cases, and dialetheism in others, depending on the circumstances. This is not the position advanced by Carnielli and Rodrigues, though, and this should be clear by now (see also Barrio and da Re 2018 for this reading of the proposal by Carnielli and Rodrigues). They clearly see their approach as dispensing dialetheism, to say the least (as the previous quote makes clear).…”

Section: The Epistemic Approachmentioning

confidence: 78%

“…Besides the mentioned sources of the epistemic approach, we also find it explicitly in Rodrigues et al (2020) p. 11 the claim that evidence is "well-suited to a non-dialetheist reading of paraconsistency" (we take it that "reading" and "interpreting" do the same work here). Along with Carnielli and Rodrigues, Barrio and da Re (2018) also advance the claim that systems of logic must be interpreted in a philosophical way, although they also do not explicitly define what that would mean. A good indication, however, appears in Barrio and da Re (2018) p. 159, where we find a distinction between pure logic, applied logic, and philosophical interpretations of logic.…”

Section: Disentangling Two Proposalsmentioning

confidence: 99%

“…Under these conditions, not every proposition follows from a contradiction. This restriction on explosion characterizes paraconsistent logics (see da Costa et al (2007), Barrio and da Re (2018), advance further discussion). Dialetheism, then, is closely related to paraconsistency.…”

Section: Introductionmentioning

confidence: 99%

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The evidence approach to paraconsistency versus the paraconsistent approach to evidence

Arenhart

2020

Synthese

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In this paper, we analyze the epistemic approach to paraconsistency. This approach is advanced as an alternative to dialetheism on what concerns interpreting paraconsistency and contradictions; instead of having to accept that there are true contradictions (as dialetheists argue), it is suggested that we may understand such situations as involving only conflicting evidence, which restricts contradictions to a notion of evidence weaker than truth. In this paper, we first distinguish two conflicting programs entangled in the proposal: (1) interpreting paraconsistency in general through the notion of evidence, and (2) modeling reasoning with evidence by using paraconsistent logic. The first part of the program, we argue, does not succeed, on the grounds that it does not lead to a uniform proposal to the understanding of paraconsistency, and fails to engage with dialetheism in a legitimate dispute about interpretation of paraconsistency. Also, when seen through the lights of the second kind of approach, a 'logic as modeling' approach, weaknesses of dealing with evidence through paraconsistency come to light, basically because evidence does not seem to suggest the need of a paraconsistent treatment. As a result, one can neither approach paraconsistency in general through evidence, nor approach evidence with the use of paraconsistent logics.

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Section: The Epistemic Approachmentioning

confidence: 78%

Section: Disentangling Two Proposalsmentioning

confidence: 99%

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The evidence approach to paraconsistency versus the paraconsistent approach to evidence

Arenhart

2020

Synthese

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“…Cerca del final de la sección 2 dije que Cartwright, al introducir el concepto de MN, no está postulando entidades extrañas en la empresa científica, sino que ofrece una manera nueva de mirar lo que ya hay en ella. El concepto de MN-L debe entenderse de la misma forma: los elementos son los mismos, y en alguna medida puede decirse que la MN-L se corresponde, más o menos directamente, con lo que algunos autores han llamado la interpretación filosófica de un sistema lógico (véase, por ejemplo, Barrio y Da Ré (2018)). En este mismo sentido, me atrevería a decir que lo que distingue entre un sistema lógico puramente formal y una teoría lógica con contenido científico (i. e. interpretación filosófica) es precisamente la existencia de la MN-L 17 .…”

Section: La Dignidad De La Lógica Clásicaunclassified

Esbozo de una concepción particularista de las Leyes Lógicas

Lisboa¹,

Agustín²

2021

Culturas Científicas

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El Anti-Excepcionalismo Lógico afirma que la Lógica es como cualquier otra ciencia. Si esta afirmación es cierta, entonces ella no sólo es revisable, sino que además todo lo que se puede decir sobre las ciencias aplica, mutatis mutandis, para la misma. El propósito de este artículo es explorar esta consecuencia del Anti-Excepcionalismo Lógico, acercando a la Filosofía de la Lógica el marco teórico de las Máquinas Nomológicas de Nancy Cartwright. De acuerdo con esta visión, lo que hay de verdadero en las teorías científicas no está en el mundo sino en sus modelos: sistemas altamente controlados, estables, artificiales y específicos, dentro de los cuales se manifiestan regularidades sistematizables y enseñables. Mi afirmación es que lo mismo puede decirse de la Lógica: ella no captura las Leyes del Pensamiento o de la Razón, porque el pensamiento y la razón no están gobernados necesariamente por leyes. Sobre lo que sí puede decirse que versan las Leyes de la Lógica son metafísicas posibles: historias acerca de qué son las proposiciones, el pensamiento, la verdad y la validez. A fin de ilustrar y defender esta tesis, presento un ejemplo de Máquina Nomológica de la Lógica Clásica, basada en una lectura original del Tractatus de Wittgenstein, e investigo algunas de sus consecuencias. Mi conclusión es que esta imagen de la Lógica impacta en el problema de la revisión de la Lógica Clásica, en la medida en que muestra que dicha revisión no necesariamente responde a un proceso racional de adecuación de la teoría a los hechos porque los “hechos” relevantes no son anteriores a la teoría misma, sino que están moldeados y conducidos por ella. Palabras clave: Anti-Excepcionalismo Lógico, Abductivismo, Máquinas Nomológicas, Revisión Lógica, Filosofía de la Lógica.

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“…But, some logicians have also rejected this point of view: for example, Omori 2016. 7 For a discussion of this point, see: Barrio & Da Ré(2018). 8 Thanks Dave Ripley for this suggestion.…”

Section: Notesmentioning

confidence: 99%

Models & Proofs: LFIs Without a Canonical Interpretations

Barrio¹

2018

Principia

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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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Paraconsistency and its Philosophical Interpretations

Cited by 25 publications

References 16 publications

The evidence approach to paraconsistency versus the paraconsistent approach to evidence

The evidence approach to paraconsistency versus the paraconsistent approach to evidence

Esbozo de una concepción particularista de las Leyes Lógicas

Models & Proofs: LFIs Without a Canonical Interpretations

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