Philosophy of Paraconsistency
& Associated Logics
Stanford Encyclopedia of Philosophy:
Dialetheism by Graham Priest (last revision Oct 3, 2008)
Paraconsistent Logic by Graham Priest & Koji Tanaka (last revision Mar 20, 2009)
Inconsistent Mathematics by Chris Mortensen (last revision Jul 31, 2008)
Many-Valued Logic by Siegfried Gottwald (last revision Nov 17, 2004)
Relevance Logic by Edwin Mares (last revision Jan 2, 2006)
Substructural Logics by Greg Restall (last revision Jan 16, 2008)
Internet Encyclopedia of Philosophy:
Wikipedia, the free encyclopedia:
Newton da Costa
Principle of explosion
the philosophy of paraconsistency
CLE e-Prints of the Centre for Logic (CLE/UNICAMP) - Editors
Universal Logic: Logics as Structures (Jean-Yves Béziau)
Geometry.Net - Mathematical_Logic: Paraconsistent Logics
Inconsistent images (Mortensen)
Paraconsistent Newsletters (check here for news: conferences, publications, links). Link defunct; to subscribe email Jean-Yves Béziau.
Conferences & Journals
The First World Congress on Paraconsistency, Wednesday 30 July Saturday 2 August 1997
II World Congress on Paraconsistency - May 08-12, 2000
WCP 3 - III world congress on paraconsistency, 28-31 July 2003
5th World Congress on Paraconsistency, 13-17 February 2014, Kolkata, India (& earlier conferences)
First World Congress and School on Universal Logic
Second World Congress and School on Universal Logic, Xi'An, China, August 16-22, 2007
Logic4Peace, online conference, 22-23 April 2022.
Sorites. Digital Journal of Analytical Philosophy. Editor: Lorenzo Peña.
Journal, no. 2 (1999)
Special Issue on Paraconsistent Logic and Paraconsistency
The future of paraconsistent logic
Reviews, The Bulletin of Symbolic Logic Volume 9, Number 3, Sept. 2003.
Graham Priest's web site
Lorenzo Peña's Home Page
From here, click on 'jybhomepage', then on whichever page you want to view, e.g. papers.
João Marcos de Almeida
Arnon Avron - Online Available Papers
Articles of Particular Interest
Beall, J.C. A Priestly Recipe for Explosive Curry, Logical Studies Journal, no. 7, 2001.
Benado, M.E. Orellana; Bobenrieth, Andrés; Verdugo, Carlos. Metaphilosophical Pluralism and Paraconsistency: From Orientative to Multi-level Pluralism.
ABSTRACT: In a famous passage, Kant claimed that controversy and the lack of agreement in metaphysicshere understood as philosophy as a wholewas a scandal. Attempting to motivate his critique of pure reason, a project aimed at both ending the scandal and setting philosophy on the secure path of science, Kant endorsed the view that for as long as disagreement reigned sovereign in philosophy, there would be little to be learned from it as a science. The success of philosophy begins when controversy ends and culminates when the discipline itself as it has been known disappears. On the other hand, particularly in the second half of the twentieth century, many have despaired of the very possibility of philosophy constituting the search for truth, that is to say, a cognitive human activity, and constituting thus a source of knowledge. This paper seeks to sketch a research program that is motivated by an intuition that opposes both of these views.
Béziau, Jean-Yves. Adventures in the Paraconsistent Jungle, CLE e-Prints, Vol. 4(1), 2004 (Section Logic).
Béziau, Jean-Yves. From Paraconsistent Logic to Universal Logic, Sorites, Issue #12, May 2001.
Béziau, Jean-Yves. The Future of Paraconsistent Logic, in Logical Studies Journal, no. 2 (1999).
Béziau, Jean-Yves; Sarenac, Darko. Possible Worlds: A Fashionable Nonsense?. 2001.
Béziau, Jean-Yves. S5 is a Paraconsistent Logic and so is First-Order Classical Logic, in Logical Studies Journal, no. 9, 2002.
Bremer, Manuel. "The Logic of Truth in Paraconsistent Internal Realism," Studia Philosophica Estonica, vol. 1, no.1, 2008, pp. 76-83. Special Issue "Truth" (Part I), edited by Daniel Cohnitz.
Bremer, Manuel. "Why and How to Be a Dialetheist," Studia Philosophica Estonica, vol. 1, no.2, 2008, pp. 208-227. Special Issue "Truth" (Part II), edited by Daniel Cohnitz.
Brunner, Andreas B.M.; Carnielli, Walter A. Anti-Intuitionism and Paraconsistency, CLE e-Prints, Vol. 3 (1), 2003.
ABSTRACT: This paper aims to help to elucidate some questions on the duality between the intuitionistic and the paraconsistent paradigms of thought, proposing some new classes of anti-intuitionistic propositional logics and investigating their relationships with the original intuitionistic logics. It is shown here that anti-intuitionistic logics are paraconsistent, and in particular we develop a rst anti-intuitionistic hierarchy starting with Johansson's dual calculus and ending up with Goedel's three-valued dual calculus, showing that no calculus of this hierarchy allows the introduction of an internal implication symbol. Comparing these anti-intuitionistic logics with well-known paraconsistent calculi, we prove that they do not coincide with any of these. On the other hand, by dualizing the hierarchy of the paracomplete (or maximal weakly intuitionistic) many-valued logics [logical symbols] we show that the anti-intuitionistic hierarchy [logical symbols] obtained from [logical symbols] does coincide with the hierarchy of the many-valued paraconsistent logics [logical symbols] . Fundamental properties of our method are investigated, and we also discuss some questions on the duality between the intuitionistic and the paraconsistent paradigms, including the problem of self-duality. We argue that questions of duality quite naturally require refutative systems (which we call elenctic systems) as well as the usual demonstrative systems (which we call deictic systems), and multiple-conclusion logics are used as an appropriate environment to deal with them.
Carnielli, Walter; Coniglio, Marcelo E.; Marcos, João. "Logics of Formal Inconsistency," CLE e-Prints, Vol. 5 (1), 2005.
da Costa, Newton C. A.; Krause, Décio. Complementarity and Paraconsistency.
ABSTRACT: Bohrs Principle of Complementarity is controversial and there has been much dispute over its precise meaning. Here, without trying to provide a detailed exegesis of Bohrs ideas, we take a very plausible interpretation of what may be understood by a theory which encompasses complementarity in a definite sense, which we term C-theories. The underlying logic of such theories is a kind of logic which has been termed paraclassical, obtained from classical logic by a suitable modification of the notion of deduction. Roughly speaking, C-theories are non-trivial theories which may have physically incompatible theorems (and, in particular, contradictory theorems). So, their underlying logic is a kind of paraconsistent logic.
da Costa, Newton C. A.; Krause, Décio. The Logic of Complementarity. August 30, 2003.
ABSTRACT: This paper is the sequel of a previous one where we have introduced a paraconsistent logic termed paraclassical logic to deal with complementary propositions . Here, we enlarge upon the discussion by considering certain meaning principles, which sanction either some restrictions of classical procedures or the utilization of certain classical incompatible schemes in the domain of the physical theories. Here, the term classical refers to classical physics. Some general comments on the logical basis of a scientific theory are also put in between the text, motivated by the discussion of complementarity.
da Costa, Newton C. A.; Krause, Décio. Remarks on the Applications of Paraconsistent Logic to Physics.
ABSTRACT: In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P. -D. F´evriers logic of complementarity as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed paraclassical logic.
da Costa, Newton C. A.; Krause, Décio; Bueno, Otávio. Paraconsistent Logics and Paraconsistency: Technical and Philosophical Developments. CLE e-Prints, Vol. 4 (3), 2004. May, 19th 2004.
da Costa, Newton C. A.; Krause, Décio; Bueno, Otávio. Paraconsistent Logics and Paraconsistency. October13, 2005. Also in Handbook of the Philosophy of Science, vol. 5.
Decker, Hendrik. A Case for Paraconsistent Logic as a Foundation of Future Information Systems.
ABSTRACT: Logic links philosophy with computer science and is the acknowledged foundation of information systems. Since the large scale proliferation of the internet and the world wide web, however, a rush of new technologies is avalanching, in many cases without much consideration of a solid foundation that would be up to par with the rigor of the traditional logic fundament. Philosophy may help to question established foundations, especially in times of technological breakthroughs that seem to override such foundations. In particular, the intolerance associated with the consistency requirements of classical logic begs question of its legitimacy, in the face of ubiquitous inconsistency in virtually all information systems of sizable extent. Based on that, we propose to overcome classical logic foundations by adopting paraconsistency as a foundational concept for future information systems engineering (ISE).
Faust, Don. Conflict without Contradiction: Noncontradiction as a Scientific Modus Operandi. Presented at the Twentieth World Congress of Philosophy, Boston, Massachusetts, August 10-15, 1998.
ABSTRACT: We explicate the view that our ignorance of the nature of the real world R, more so than a lack of ingenuity or sufficient time to have deduced the truth from what is so far known, accounts for the inadequacies of our theories of truth and systems of logic. Because of these inadequacies, advocacy of substantial correctness of such theories and systems is certainly not right and should be replaced with a perspective of Explorationism which is the broadest possible investigation of potential theories and systems along with the realization that all such theories and systems are partial and tentative. For example, the position of classical logic is clearly untenable from the perspective of explorationism. Due to ignorance regarding R and, consequently, the partial and evidential nature of our knowledge about R, an explorationist foundational logical framework should contain machinery which goes beyond that of classical logic in the direction of allowing for the handling of confirmatory and refutatory evidential knowledge. Such a foundational framework (which I call Evidence Logic) is described and analysed in terms of its ability to tolerate substantial evidential conflict while not allowing contraditions.
Field, Hartry. Review of Graham Priest, Doubt Truth to Be a Liar (2006), Notre Dame Philosophical Reviews, 2006.03.18.
Flynt, Henry. Is Mathematics a Scientific Discipline? 1996.
Gratz, David; White, V. Alan. Review of Graham Priest, Logic: A Very Short Introduction, Essays in Philosophy, vol. 5, no. 1, January 2004.
Marcos de Almeida, João. Thesis: Possible-Translations Semantics (in Portuguese).
Marcos, João. "Wittgenstein & Paraconsistência," CLE e-Prints, vol. 1(7), 2001.
Peña, Lorenzo. "Alboran Is and Is Not Dry: Katalin Havas on Logic and Dialectic," Logique et Analyse, issue #131-132 (1990), pp. 331-338.
Peña, Lorenzo. Dialectics, from Handbook of Metaphysics and Ontology, 1991.
Peña, Lorenzo. Graham Priest's «Dialetheism»Is It Althogether True? [Review of Graham Priest, In Contradiction], Sorites, Issue #07, November 1996, pp. 28-56.
Peña, Lorenzo. «Partial Truth, Fringes and Motion: Three Applications of a Contradictorial Logic», Studies in Soviet Thought, vol 37 (1990), pp. 83-122.
Rahman, Shahid; Van Bendegem, Jean Paul. The Dialogical Dynamics of Adaptive Paraconsistency.
ABSTRACT: The dialogical approach to paraconsistency as developed by Rahman and Carnielli (), Rahman and Roetti () and Rahman (,  and ) suggests a way of studying the dynamic process of arguing with inconsistencies. In his paper on Paraconsistency and Dialogue Logic () Van Bendegem suggests that an adaptive version of paraconsistency is the natural way of capturing the inherent dynamics of dialogues. The aim of this paper is to develop a formulation of dialogical paraconsistent logic in the spirit of an adaptive approach and which explores the possibility of eliminating inconsistencies by means of logical preference strategies.
Rauser, Randal. "Is the Trinity a True Contradiction?" Quodlibet Journal, Volume 4 Number 4, November 2002. (groan!)
Restall, Greg. Paraconsistency Everywhere. May 9, 2002.
Tanaka, Koji. Three Schools of Paraconsistency. The Australasian Journal of Logic, vol. 1, July 1, 2003.
ABSTRACT: A logic is said to be paraconsistent if it does not allow everything to follow from contradictory premises. There are several approaches to paraconsistency. This paper is concerned with several philosophical positions on paraconsistency. In particular, it concerns three schools of paraconsistency: Australian, Belgian and Brazilian. The Belgian and Brazilian schools have raised some objections to the dialetheism of the Australian school. I argue that the Australian school of paraconsistency need not be closed down on the basis of the Belgian and Brazilian schools objections. In the appendix of the paper, I also argue that the Brazilian schools view of logic is not coherent.
Tuziak, Roman. Popper and Paraconsistency. Karl Popper 2002 Centenary Congress, Vienna, 3-7 July 2002.
ABSTRACT: Paraconsistent logic was introduced in order to provide the framework for inconsistent but nontrivial theories. It was initiated by J. Lukasiewicz (1910) in Poland and, independently, by N. A. Vasilev (1911-13) in Russia, but only in 1948 the first paraconsistent formal system was designed. Since then thousands of papers have been published in this field. Paraconsistency became one of the fastest growing branches of logic, due to its fruitful applications to computer science, information theory, and artificial intelligence. K. R. Popper touched on the problem in his paper What is Dialectic? (1940). Although only mentioned, his basic idea of the possibility of a formal system of such a logic was fresh and original. Another attempt of exploring the logic of contradiction, this time as a dual to intuitionistic logic, was made by Popper in his paper On the Theory of Deduction I and II (1948). The same idea was formalized by N. D. Goodman (1981) and developed by D. Miller (1993) under a label Logic for Falsificationists. Popper`s contribution to the subject of paraconsistent logic has not been properly recognized so far. Since Lukasiewicz`s and Vasilev`s works were still not translated into any West European languages in the 1940s, he should be undoubtedly regarded as an independent forerunner of paraconsistency. On the other hand, it seems tempting to adapt some of Popper`s other ideas for the theory of paraconsistent logic (the way it was done with Vasilev`s very general concepts) and, especially, for the theory of artificial intelligence.
Ursic, Marko. Paraconsistency and Dialectics as Coincidentia Oppositorum in the Philosophy of Nicholas of Cusa.
Woods, John. "Dialectical Considerations on the Logic of Contradiction: Part I," Logic Journal of IGPL 2005 13(2): 231-260. See abstract.
Woods, John. Dogmatism and Dialethism: Reflections on Remarks of Sorenson and Armour-Garb.
Woods, John. Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences, excerpt from chapter 1, pp. 1-20.
Zelený, Jindřich. Paraconsistency and Dialectical Consistency [corrected from original, which appeared in From the Logical Point of View (Prague), Vol. 1, 1994, pp. 35 51].
Recent Publications of Technical or Philosophical Interest Online
Analyti, A.; Antoniou, G.; Damásio, C. V.; Wagner, G. "Negation and Negative Information in the W3C Resource Description Framework", Annals of Mathematics, Computing & Teleinformatics, vol 1, no 2, 2004, pp 25-34.
Batens, Diderik; Meheus, Joke; Provijn, Dagmar. "An Adaptive Characterization of Signed Systems for Paraconsistent Reasoning", Pre-print, January 11, 2006.
Béziau, Jean-Yves. "The Paraconsistent Logic Z: A Possible Solution to Jaskowski's Problem", Logic and Logical Philosophy, Vol.15 (2006): 99-111.
McGinnis, Casey. Paraconsistency and Deontic Logic: Formal Systems for Reasoning with Normative Conflicts. PhD Thesis, University of Minnesota, 2006.
Marcos, João. "Modality and Paraconsistency," in In M. Bilkova and L. Behounek, editors, The Logica Yearbook 2004 (Prague: Filosofia, 2005), pp. 213-222.
Marcos, João. "Nearly every normal modal logic is paranormal," Logique et Analyse, 48:279-300, 2005. Preprint.
Priest, Graham. "60% Proof: Lakatos, Proof, and Paraconsistency," Pre-print. January 30, 2006.
Priest, Graham. Beyond
true and false, Aeon Magazine, 5 May 2014.
Buddhist philosophy is full of contradictions. Now modern logic is learning why that might be a good thing.
Shapiro, Stewart. "Lakatos and Logic: Comments of Graham Priest's "60% proof: Lakatos, proof and paraconsistency"", Pre-print, 2006.
Sorites, no. 17, October 2006.
Latest Paraconsistent Newsletter, Fall 2006.
Guides to Philosophical Logic
Bibliography on Adaptive Logics: Applications
Bibliography on Fuzziness and the Sorites Paradox, updated: Nov. 23 1994
Computational Linguistics Offprint Library, Bibliography (1999)
DoCIS: Documents in Computing and Information Science
Pathways to Philosophical Logic and the Philosophy of Logic
EpistemeLinks.com: Logic and Philosophy of Logic
Foundations of Mathematics
Musgrave, Alan. Against Paraconsistentism, in New Approaches to Scientific Realism, edited by Wenceslao J. Gonzalez (Berlin: Walter de Gruyter, 2020), pp. 133-144.
Conze, Edward. The Principle of Contradiction: On the Theory of Dialectical Materialism (1932), translated by Holger R. Heine, foreword by Graham Priest, introduction by Holger R. Heine, review by Herbert Marcuse. Lanham, MD: Lexington Books (Rowman & Littlefield), 2016.
Łukasiewic, Jan. The Principle of Contradiction in Aristotle: A Critical Study, translated with an introduction and commentaty by Holger R. Heine, foreword by Graham Priest. Honolulu: Topos Productions, 2021.
Weber, Zach. Paradoxes and Inconsistent Mathematics. Cambridge, UK: Cambridge University Press, 2021.
This Paradoxical Life (Paraconsistent logics find structure in our inconsistent world)| by Zach Weber, Aeon Essays, 11 Jan 2022.
(7/27/2005, rev. 8/2/2005, 8/14/2005, 3/23/2006, 10/5/2006, 1/24/07, 2/8/07, 1/7/09, 3/31/09, 6/17/14, 6/21/18, 2/17/ 19, 8/6/20, 1/11/22, 7/21/22, 1/14/23, 5/21/23, 7/30/23, 9/16/23, 11/24/23)
Graham Priest's Inclosure Schema
Paraconsistent Logic, and Philosophy, Or, Logic and Reality
by R. Dumain
Priest vs Erwin Marquit on Contradiction
by R. Dumain
is the Relationship Between Logic and Reality?”
by R. Dumain
Adornos True Thoughts & the Logic of Aphorisms
by R. Dumain
Paraconsistency in the provinces
Logic and thought
by Susan Haack
Dialectics of Metamathematics" (Excerpts)
by Peter Vardy
Foundations of Non-Fregean Logic"
by Boguslaw Wolniewicz
Logic of Marx: (Contents)
by Jindřich Zelený
(Logic), Frye & Levi (Logic), Wood (Knowledge) reviewed
by Herbert Marcuse
in A Dictionary of Marxist Thought
Roy Edgley · Roy Bhaskar · Robert M. Young
Note on the Poznan School
Wittgenstein and Dialectic: An Annotated Bibliography
Reflexivity & Situatedness Study Guide
Paradox, & Reductio ad Absurdum:
Selected Online Sources
Indian Logic & Argumentation: Selected Bibliography
History of Chinese Logic, Argumentation, & Rhetoric to 1950: Essential Bibliography
Argumentation & Controversies: Selected Bibliography
Susan Haack — An Introductory Guide
Category Theory — History & Philosophy: An Introductory Bibliography
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