In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, from Consistency to Inconsistency. Springer Verlag (2018)

Authors
Damian Szmuc
Universidad de Buenos Aires (UBA)
Federico Pailos
Universidad de Buenos Aires (UBA)
Eduardo Alejandro Barrio
Universidad de Buenos Aires (UBA)
Abstract
Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively.
Keywords logic  substructural logic  paraconsistent logic  paraconsistency  cut  non-transitive
Categories (categorize this paper)
Buy the book Find it on Amazon.com
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
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

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.
Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.

View all 20 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.
Models & Proofs: LFIs Without a Canonical Interpretations.Eduardo Alejandro Barrio - 2018 - Principia: An International Journal of Epistemology 22 (1):87-112.

View all 10 citations / Add more citations

Similar books and articles

Paraconsistency Everywhere.Greg Restall - 2002 - Notre Dame Journal of Formal Logic 43 (3):147-156.
Paraconsistent Logic.David Ripley - 2015 - Journal of Philosophical Logic 44 (6):771-780.
Meeting Hintikka's Challenge to Paraconsistentism.Walter Carnielli - 2009 - Principia: An International Journal of Epistemology 13 (3):283-297.
Paraconsistent Dynamics.Patrick Girard & Koji Tanaka - 2016 - Synthese 193 (1):1-14.
Kantian and Non-Kantian Logics.L. Z. Puga, N. N. C. A. Da Costa & W. Carnielli - 1988 - Logique Et Analyse 31 (121/122):3-9.
Omnibus Review. [REVIEW]F. G. Asenjo - 1991 - Journal of Symbolic Logic 56 (4):1503-1504.
[Omnibus Review].F. G. Asenjo - 1991 - Journal of Symbolic Logic 56 (4):1503-1504.
New Directions in Paraconsistent Logic.Jean-Yves Beziau (ed.) - 2015 - New Delhi, India: Springer, India.

Analytics

Added to PP index
2019-01-28

Total views
286 ( #31,321 of 2,439,695 )

Recent downloads (6 months)
42 ( #17,348 of 2,439,695 )

How can I increase my downloads?

Downloads

My notes