In Defence of Dialetheism: A Reply to Beziau and Tkaczyk
DOI:
https://doi.org/10.12775/LLP.2017.030Keywords
dialetheism, paraconsistent logics, logic of paradox, self-referential paradoxesAbstract
In recent editions of this journal, Jean-Yves Beziau [8] and Marcin Tkaczyk [41] have criticised a prominent dialetheic logic and common arguments for dialetheism, respectively. While Beziau argues that Priest’s logic LP commits the dialetheist to trivialism, the thesis that all propositions are true, Tkaczyk maintains that the arguments traditionally proposed for dialetheism are faulty and ultimately that dialetheism should be rejected as self-refuting. This paper shows that both are mistaken in their contentions. Beziau’s argument conflates truth-in-an-interpretation with truth simpliciter and Tkaczyk misconstrues the substance of dialetheic arguments. In the process of identifying these weaknesses of both arguments, the paper clarifies elements of both dialetheic logics and dialetheism which these discussions demonstrate are still misunderstood within the literature.References
Anderson, A.R., and N.D. Belnap, Jr., Entailment: The Logic of Relevance and Necessity, Vol. 1, Princeton, NJ: Princeton University Press, 1975.
Armour-Garb, B., “Diagnosing dialetheism”, pages 113–125 in Priest, G., Jc. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Clarendon Press, 2004.
Asenjo, F.G., “A calculus of antinomies”, Notre Dame Journal of Formal Logic 7 (1966): 103–5. DOI: 10.1305/ndjfl/1093958482
Batens, D., “Paraconsistency and its relation to worldviews” Foundations of Science 3 (1999): 259–283. DOI: 10.1023/A:1009678125533
Beall, Jc., Spandrels of Truth, Oxford: Clarendon Press, 2009.
Beall, Jc., “Why Priest’s reassurance is not reassuring”, Analysis 72 (2012): 517–525. DOI: 10.1093/analys/ans069
Beall, Jc., and G. Restall, Logical Pluralism, Oxford: Oxford University Press, 2006.
Beziau, J.-Y., “Trivial dialetheism and the Logic of Paradox”, Logic and Logical Philosophy 25 (2016): 51–56. DOI: 10.12775/LLP.2015.022
Brown, B., “Yes, Virginia, there really are paraconsistent logics”, Journal of Philosophical Logic 28 (1999): 489–500. DOI: 10.1023/A:1004390309035
Brown, B., “Simple natural deduction for weakly aggregative paraconsistent logics”, pages 137–148 in D. Batens et al. (eds.), Frontiers of Paraconsistent Logic, Exeter: Research Studies Press, 2000.
da Costa, N.C.A., “On the theory of inconsistent formal systems”, Notre Dame Journal of Formal Logic, 15 (1974): 497–510. DOI: 10.1305/ndjfl/1093891487
Dunn, J.M., “Intuitive semantics for first-degree entailments and ‘coupled trees’”, Philosophical Studies 29 (1976): 149–68. DOI: 10.1007/BF00373152
Field, H., Saving Truth from Paradox, Oxford: Oxford University Press, 2008.
Harman, G., Change in View: Principles of Reasoning, Cambridge, MA: MIT Press, 1986.
Howson, C., “More about the liar”, Erkenntnis 17 (1982): 263–265. DOI: 10.1007/BF00170153
Hugly, P., and C. Sayward, “Is English inconsistent?”, Erkenntnis 15 (1980): 343–347. DOI: 10.1007/BF02070843
Jaśkowski, S., “Propositional calculus for contradictory deductive systems”, Studia Logica 24 (1969): 143–57. DOI: 10.1007/BF02134311. The second English version: “A propositional calculus for inconsistent deductive system”, Logic and Logical Philosophy 7 (1999): 35–56. DOI: 10.12775/LLP.1999.003. Originally published as: “Rachunek zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensis, Sect. A, vol. I, no. 5 (1948): 57–77.
Jaśkowski, S., “On the discussive conjunction in the propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy 7 (1999): 57–59. DOI: 10.12775/LLP.1999.004. Originally published as: “O koniunkcji dyskusyjnej w rachunku zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensis, Sect. A, vol. I, no. 8 (1949): 171–172.
Jennings, R. E., and P.K. Scotch, “The preservation of coherence” Studia Logica 43 (1984): 89–106. DOI: 10.1007/BF00935743
Kabay, P.D., “A defense of trivialism” (PhD thesis), University of Melbourne, Australia, 2008.
Kleene, S.C., Introduction to Metamathematics, Amsterdam, Netherlands: North-Holland, 1971.
Lewis, D.K., “Logic for equivocators”, Noûs 16 (1982): 431–441. DOI: 10.2307/2216219
Littmann, G., and K. Simmons, “A critique of dialetheism”, pages 314–335 in Priest, G., Jc. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Clarendon Press, 2004.
Marcos, J., “Logics of formal inconsistency” (PhD thesis), Universidade Técnica De Lisboa, Portugal (2005).
Mares, E.D., “Semantic dialetheism”, pages 264–275 in Priest, G., Jc. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Clarendon Press, 2004.
Martin, B., “Dialetheism and the impossibility of the world”, Australasian Journal of Philosophy 93 (2015): 61–75. DOI: 10.1080/00048402.2014.956768
Meheus, J. (ed.), Inconsistency in Science, Dordrecht, Netherlands: Kluwer, 2002.
Parsons, T., “True contradictions”, Canadian Journal of Philosophy 20 (1990): 335–354. DOI: 10.1080/00455091.1990.10716495
Priest, G., “Logic of Paradox”, Journal of Philosophical Logic 8 (1979): 219–241. DOI: 10.1007/BF00258428
Priest, G., Beyond the Limits of Thought, Cambridge: Cambridge University Press, 1995.
Priest, G., “Everett’s trilogy”, Mind 105 (1996): 631–47. DOI: 10.1093/mind/105.420.631
Priest, G., “What is so bad about contradictions?”, pages 23–38 in Priest, G., Jc. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Clarendon Press, 2004.
Priest, G., Doubt Truth to be a Liar, Oxford: Clarendon Press, 2006.
Priest, G., In Contradiction: A Study of the Transconsistent (2 nd ed.), Oxford: Clarendon Press, 2006.
Priest, G., and F. Berto “Dialetheism”, in E.N. Zalto (ed.), The Stanford Encyclopedia of Philosophy, 2013, Summer. http://plato.stanford.edu/archives/sum2013/entries/dialetheism/
Priest, G., and R. Routley, “Systems of paraconsistent logic”, pages 151–186 in G. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, München, Germany: Philosophia Verlag, 1989.
Ray, G., “Tarski and the metalinguistic liar”, Philosophical Studies 115 (2003): 55–80. DOI: 10.1023/A:1024908230635
Shapiro, S., “Simple truth, contradiction, and consistency”, pages 336–354 in Priest, G., Jc. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Clarendon Press, 2004.
Tarski, A., “The semantic conception of truth and the foundations of semantics”, Philosophy and Phenomenological Research, 4 (1944): 341–375. DOI: 10.2307/2102968
Tarski, A., “On the concept of truth in formalized languages” (translated by J. H. Woodger), pages 152–278 Logic, Semantics, and Metamathematics, J. Corcorn (ed.), Indianapolis, IN: Hackett Publishing, 1983. Originally published in 1933.
Tennant, N., “An anti-realist critique of dialetheism”, pages 355–384 in Priest, G., Jc. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Clarendon Press, 2004.
Tkaczyk, M., “The case of dialetheism”, Logic and Logical Philosophy 25 (2016): 203–24. DOI: 10.12775/LLP.2016.012
Zalta, E.N., “In defense of the law of non-contradiction”, pages 418–436 in Priest, G., Jc. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford: Clarendon Press, 2004.
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 1
Number of citations: 5
