Überconsistent Logics And Dialetheism
Main Article Content
Abstract
An überconsistent logic is one where the set of logical truths is inconsistent. Examples of such logics have been known for a long time. However, it has recently been recognized that this is an important new class of logics. Dialetheism is the view that some contradictions are true. Since logical truths are true, it might be thought that these logics provide an important new argument for dialetheism. However, matters are not that straightforward. This paper is an initial discussion of the matter. The first part of the paper provides the background on paraconsistency and dialetheism required for the discussion. The second half is a discussion of three überconsistent logics and their bearing on dialetheism. The first is the logic LP with a logical constant for the value both true and false; the second is Second-Order LP; the third is a certain kind of connexive logic.
Downloads
Article Details
PLUMX Metrics
References
Carroll, Lewis, 1894, “A Logical Paradox”, Mind, vol. 3, no. 11, pp. 436–438.
Cooper, William, 1968, “The Propositional Logic of Ordinary Discourse, Inquiry, vol. 11, pp. 295–320.
Hazen, Allen, and Jeffry Pelletier, 2018, “Second-Order Logic of Paradox”, Notre Dame Journal of Formal Logic, vol. 59, no. 4, pp. 547–558.
McCall, Storrs, 2012, “A History of Connexivity”, in Dov Gabbay, Jeffry Pelletier, and John Woods (eds.), Handbook of the History of Logic, vol. 11, North Holland, Amsterdam, pp. 415–449.
Orilia, Francesco, and Michele Paoletti, 2020, “Properties”, Stanford Encyclopedia of Philosophy, in Edward N. Zalta (ed.), available at: https://plato.stanford.edu/entries/properties/.
Priest, Graham, 202+, “Interpretations of the Third Value”, to appear.
Priest, Graham, 2024, “Substructural Solutions to the Semantic Paradoxes: a Dialetheic Perspective”, in Mattia Petrolo and Giorgio Venturi (eds.), Paradoxes Between Truth and Proof, Springer, Berlin, pp. 165–192.
Priest, Graham, 2008, Introduction to Non-Classical Logic, Cambridge University Press, Cambridge.
Priest, Graham, 2006, Doubt Truth to be a Liar, Oxford University Press, Oxford.
Priest, Graham, 2002, “Paraconsistent Logic”, in Dov Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd edn, vol. 6, pp. 287–393, Kluwer Academic Publishers, Dordrecht.
Priest, Graham, 2000, “Motivations for Paraconsistency: the Slippery Slope from Classical Logic to Dialetheism”, in Diderik Batens, Chris Mortensen, Graham Priest, and Jean-Paul Van Bendegem (eds.), Frontiers of Paraconsistent Logic, Research Studies Press, London.
Priest, Graham, 1999, “Negation as Cancellation, and Connexivism”, Topoi, vol. 18, pp. 141–148.
Priest, Graham, 1987, In Contradiction, Martinus Nijhoff, Dordrecht; 2nd edn, 2006, Oxford University Press, Oxford.
Priest, Graham, and Richard Routley, 1983, On Paraconsistency, Department of Philosophy, RSSS, ANU, Canberra. This appeared as the introductory chapters of Graham Priest, Richard Routley, and Jean Norman, 1989.
Priest, Graham, Richard Routley, and J. Norman, 1989, Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, Munich.
Priest, Graham, Koji Tanaka, and Zach Weber, 2022, “Paraconsistent Logic”, Stanford Encyclopedia of Philosophy, in Edward N. Zalta (ed.), available at: https://plato.stanford.edu/entries/logic-paraconsistent/.
Quine, Willard, 1970, Philosophy of Logic, Prentice Hall, Englewood Cliffs, NJ.
Wansing, Heinrich, 2005, “Connexive Modal Logic”, in R. Schmidt, et al. (eds.), Advances in Modal Logic, vol. 5, King’s College Publications, London, pp. 367–383.
Wansing, Heinrich, 2023, “Connexive Logic”, Stanford Encyclopedia of Philosophy, in Edward N. Zalta (ed.), available at:
https://plato.stanford.edu/entries/logic-connexive/.
Wansing, Heinrich, 202+, “Beyond Paraconsistency. A Plea for a Radical Breach with the Aristotelian Orthodoxy in Logic”, to appear.
Weiss, Yale, 2022, “Semantics for Pure Theories of Connexive Implication”, Review of Symbolic Logic, vol. 15, pp. 591–606.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Crítica, Revista Hispanoamericana de Filosofía by Universidad Nacional Autónoma de México is licensed under a Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional License.
Creado a partir de la obra en http://critica.filosoficas.unam.mx/index.php/critica.