Philosophy of Paraconsistency
& Associated Logics

General resources on the web

Stanford Encyclopedia of Philosophy:

Dialetheism
Paraconsistent Logic
Inconsistent Mathematics
Many-Valued Logic

Lorenzo Peña's Home Page

http://www.cle.unicamp.br/e-prints/ [CLE e-Prints of the Centre for Logic (CLE/UNICAMP) - Editors]

Newsletters

http://luna.unine.ch/alexandre.costa/pnews.html. Paraconsistent Newsletters (check here for news: conferences, publications, links)

Conferences & Journals

http://logica.rug.ac.be/centrum/events/WCP97. The First World Congress on Paraconsistency, Wednesday 30 July – Saturday 2 August 1997

http://logica.cle.unicamp.br/wcp/wcp2000.htm [II World Congress on Paraconsistency - May 08-12, 2000]

http://www.cle.unicamp.br/wcp3/ [WCP 3 - III world congress on paraconsistency], 28-31 July 2003

http://www.logic.ru/LogStud/02/LS2.html. Logical Studies Journal, no. 2
Special Issue on Paraconsistent Logic and Paraconsistency

http://www.logic.ru/Russian/LogStud/02/LS_2_e_Beziau.pdf. The future of paraconsistent logic
Jean-Yves Béziau

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

Articles of particular interest

Beall, J.C. http://www.logic.ru/LogStud/07/No7-06.html. 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. http://www.cle.unicamp.br/e-prints/vol_4,n_1,2004.html: 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. http://www.logic.ru/Russian/LogStud/02/LS_2_e_Beziau.pdf. The Future of Paraconsistent Logic, in http://www.logic.ru/LogStud/02/LS2.html. Logical Studies Journal, no. 2 (1999)

Béziau, Jean-Yves; Sarenac, Darko. Possible Worlds: A Fashionable Nonsense?. 2001.

Béziau, Jean-Yves. http://www.logic.ru/LogStud/09/No9-01.html. Is a Paraconsistent Logic and so is First-Order Classical Logic, in http://www.logic.ru/LogStud/09/LS9.html. Logical Studies Journal, no. 9, 2002.

Carnielli, Walter; Coniglio, Marcelo E.; Marcos, João. "http://www.cle.unicamp.br/e-prints/vol_5,n_1,2005.html: 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; Bueno, Otávio. Paraconsistent Logics and Paraconsistency. July 5, 2005.

Decker, Hendrik. http://kybele.estcet.urjc.es/PHISE05/papers/sesionI/Decker.pdf. 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.

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.

Restall, Greg. Paraconsistency Everywhere. May 9, 2002.

Tanaka, Koji. http://www.philosophy.unimelb.edu.au/ajl/2003/2003_3.pdf. 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. http://www.univie.ac.at/karlpopper2002/abstracts/ContributedPapers/Tuziak.pdf [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, Jindrich. Paraconsistency and Dialectical Consistency [corrected from original, which appeared in http://nb.vse.cz/kfil/elogos/logpoint/94-1/ZELN.htm (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. http://logica.rug.ac.be/dirk/signed_d10.pdf. 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.

Bibliography on Adaptive Logics: Applications

Bibliography on Fuzziness and the Sorites Paradox, updated: Nov. 23 1994

Pathways to Philosophical Logic and the Philosophy of Logic

http://www.epistemelinks.com/Main/Topics.aspx?TopiCode=Logi">EpistemeLinks.com: Logic and Philosophy of Logic

Factasia Logic

Foundations of Mathematics