Eduardo Alejandro Barrio
Universidad de Buenos Aires (UBA)
In different papers, Carnielli, W. & Rodrigues, A., Carnielli, W. Coniglio, M. & Rodrigues, A. and Rodrigues & Carnielli, present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE and the second—that is a conservative extension of BLE—is named LETJ. Roughly, BLE and LETJ are two non-classical logics in which the Laws of Explosion and Excluded Middle are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic of Formal Inconsistency. 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.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.5007/1808-1711.2018v22n1p87
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,714
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

On the Plurality of Worlds.David Lewis - 1986 - Wiley-Blackwell.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.

View all 29 references / Add more references

Citations of this work BETA

Paraconsistency and its Philosophical Interpretations.Eduardo Barrio & Bruno Da Re - 2018 - Australasian Journal of Logic 15 (2):151-170.
Paraconsistencia pura.Bruno Da Ré - 2019 - Revista de Humanidades de Valparaíso 13:90-101.

Add more citations

Similar books and articles

Problemas para a Explicação Matemática.Eduardo Castro - 2017 - Revista Portuguesa de Filosofia 73 (3-4):1437-1462.
Proof and Canonical Proof.Bernhard Weiss - 1997 - Synthese 113 (2):265-284.
Heyting-Valued Interpretations for Constructive Set Theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1-3):164-188.
Generalising Canonical Extension to the Categorical Setting.Dion Coumans - 2012 - Annals of Pure and Applied Logic 163 (12):1940-1961.
What Is Gibbs’s Canonical Distribution?Kevin Davey - 2009 - Philosophy of Science 76 (5):970-983.
Quasi-Modal Equivalence of Canonical Structures.Robert Goldblatt - 2001 - Journal of Symbolic Logic 66 (2):497-508.
Action Emulation Between Canonical Models.Floor Sietsma & Jan van Eijck - 2013 - Journal of Philosophical Logic 42 (6):905-925.
Graded Modalities, II (Canonical Models).Francesco Caro - 1988 - Studia Logica 47 (1):1 - 10.


Added to PP index

Total views
16 ( #651,532 of 2,462,719 )

Recent downloads (6 months)
1 ( #449,387 of 2,462,719 )

How can I increase my downloads?


My notes