Trivial Dialetheism and the Logic of Paradox

Jean-Yves Beziau

doi:10.12775/LLP.2015.022

Authors

Jean-Yves Beziau University of Brazil, Rio de Janeiro

DOI:

https://doi.org/10.12775/LLP.2015.022

Keywords

Dialetheia, Paraconsistent Logic, Many-Valued Logic, Truth

Abstract

In this paper we explain that the paraconsistent logic LP (Logic of Paradox) promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.

Author Biography

Jean-Yves Beziau, University of Brazil, Rio de Janeiro

Brazilian Research Council, CNPq

References

Becker Arenhart, J.R., “Liberating paraconsistency from contradiction”, Logica Universalis, 9, 4 (2015): 523–544. DOI: 10.1007/s11787-015-0131-y

Beziau, J.-Y., “Idempotent full paraconsistent negations are not algebraizable”, Notre Dame Journal of Formal Logic, 39, 1 (1998): 135–139. DOI: 10.1305/ndjfl/1039293025

Beziau, J.-Y., “S5 is a paraconsistent logic and so is first-order classical logic”, Logical Investigations, 9 (2002): 301–309.

Beziau, J.-Y., “The paraconsistent logic Z. A possible solution to Jaśkowski’s problem”, Logic and Logical Philosophy, 15 (2006): 99–111. DOI: 10.12775/LLP.2006.006

Beziau, J.-Y., “Bivalent semantics for De Morgan logic (the uselessness of four-valuedness)”, pages 391–402 in W.A. Carnielli, M.E. Coniglio, and I.M.L. D’Ottaviano (eds.), The many sides of logic, College Publication, London, 2009.

Beziau, J.-Y., “History of truth-values”, pages 233–305 in D.M. Gabbay, F.J. Pelletier, and J. Woods (eds.), Handbook of the History of Logic, Vol. 11 “Logic: A history of its central concepts”, Elsevier, Amsterdam, 2012.

Beziau, J.-Y., “Round squares are no contradictions (Tutorial on Negation, Contradiction and Opposition)”, in J.-Y. Beziau , M. Chakraborty, S. Dutta (eds.), New Directions in Paraconsistent Logic, Springer, New Delhi, 2016.

Beziau, J.-Y., W.A. Carnielli, and D.M. Gabbay (eds.), Handbook of Paraconsistency (Studies in Logic), College Publication, London, 2007.

Kleene, S., “On a notation for ordinal numbers”, Journal of Symbolic Logic, 3 (1938): 150–155. DOI: 10.2307/2267778

Klement, K., “Propositional logic”, Internet Encyclopedia of Philosophy, 2015. http://www.iep.utm.edu/prop-log/

Łukasiewicz, J., “O logice trójwartościowej”, Ruch Filozoficzny, 5 (1920): 170–171.

Priest, G., “The logic of paradox”, Journal of Philosophical Logic, 8, 1 (1979): 219–241. DOI: 10.1007/BF00258428

Priest, G., and F. Berto, “Dialetheism”, Stanford Encyclopedia of Philosophy, 2013. http://plato.stanford.edu/entries/dialetheism/

Pogorzelski, W.A., Notions and theorems of elementary formal logic, Warsaw University, Białystok Branch, Białystok, 1994.

Sette, A.M., On the propositional calculus P1, “Notas e comunicacões de matemática”, Vol. 17, Recife, 1971.

Wittgenstein, L., “Logisch-philosophische Abhandlung”, Annalen der Naturphilosophie, 14 (1921), 185–262. Translated as Tractatus Logico-Philosophicus, Kegan Paul, London, 1922.