**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:*

Dialetheism

Graham Priest

Newton da Costa

Paraconsistent logic

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)

**Newsletters**

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

Sorites. Digital Journal of Analytical Philosophy. Editor: Lorenzo Peña.

Logical Studies
Journal, no. 2 (1999)

Special Issue on Paraconsistent Logic and Paraconsistency

The future of paraconsistent logic

Jean-Yves Béziau

Reviews,
*The Bulletin of Symbolic Logic* Volume 9, Number 3, Sept. 2003.

**People**

Graham Priest's web site

Jean-Yves Béziau

From here, click on 'jybhomepage', then on whichever page you want to view,
e.g. papers.

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 metaphysics—here understood as philosophy as a whole—was 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: Bohr’s Principle of Complementarity is controversial and there has been much dispute over its precise meaning. Here, without trying to provide a detailed exegesis of Bohr’s 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’ [17]. 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´evrier’s ’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 ([1]), Rahman and Roetti ([2]) and Rahman ([3], [4] and [5]) suggests a way of studying the dynamic process of arguing with inconsistencies. In his paper on Paraconsistency and Dialogue Logic ([6]) 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 school’s 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

Musgrave, Alan. “Against Paraconsistentism,” in
*New Approaches to Scientific Realism*, edited by Wenceslao J. Gonzalez (Berlin: Walter de Gruyter, 2020), p. 133-144.

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)

Graham Priest's Inclosure Schema

Graham Priest,
Paraconsistent Logic, and Philosophy, Or, Logic and Reality

by R. Dumain

Graham Priest vs Erwin Marquit on Contradiction by R. Dumain

“What is the Relationship Between Logic and Reality?” by R. Dumain

Paraconsistency in the provinces

"On the Dialectics of Metamathematics" (Excerpts) by Peter Vardy

"Wittgensteinian Foundations of Non-Fregean Logic" by Boguslaw Wolniewicz

*The
Logic of Marx*: (Contents) by Jindřich Zelený

Ushenko (Logic), Frye & Levi (Logic), Wood (Knowledge) reviewed by Herbert Marcuse

Dialectics
in *A Dictionary of Marxist Thought**
*Roy Edgley · Roy Bhaskar · Robert M. Young

Wittgenstein and Dialectic: An Annotated Bibliography

Reflexivity & Situatedness Study Guide

Irony,
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

Home Page | Site
Map | What's New | Coming Attractions | Book
News

Bibliography | Mini-Bibliographies | Study
Guides | Special Sections

My Writings | Other Authors' Texts | Philosophical
Quotations

Blogs | Images
& Sounds | External Links

**CONTACT** Ralph Dumain

Uploaded 27 July 2005

Last update 11 January 2022

Previous update 21 December 2020

©2005-2022 Ralph Dumain