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Logic and Logical Philosophy

The Liar Paradox: Between Evidence and Truth
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The Liar Paradox: Between Evidence and Truth

Authors

  • Jonas Becker Arenhart Federal University of Santa Catarina https://orcid.org/0000-0001-8570-7336
  • Ederson S. Melo Federal University of Maranhão https://orcid.org/0000-0003-1706-1128

DOI:

https://doi.org/10.12775/LLP.2022.005

Keywords

paraconsistency, Liar paradox, epistemic approach, evidence, truth

Abstract

Systems of paraconsistent logics violate the law of explosion: from contradictory premises not every formula follows. One of the philosophical options for interpreting the contradictions allowed as premises in these cases was put forward recently by Carnielli and Rodrigues, with their epistemic approach to paraconsistent logics. In a nutshell, the plan consists in interpreting the contradictions in epistemic terms, as indicating the presence of non-conclusive evidence for both a proposition and its negation. Truth, in this approach, is consistent and is dealt with by classical logic. In this paper we discuss the fate of the Liar paradox in this picture. While this is a paradox about truth, it cannot be accommodated by the classical part of the approach, due to trivialization problems. On the other hand, the paraconsistent part does not seem fit as well, due to the fact that its intended reading is in terms of non-conclusive evidence, not truth. We discuss the difficulties involved in each case and argue that none of the options seems to accommodate the paradox in a satisfactory manner.

References

Arenhart, J. R. B., 2021, “The evidence approach to paraconsistency versus the paraconsistent approach to evidence”, Synthese 198: 11537–11559. DOI: https://doi.org/10.1007/s11229-020-02813-x

Arenhart, J. R. B., and E. S. Melo, 2018, “Dialetheists’ Lies about the Liar”, Principia: an International Journal of Epistemology 22 (1): 59–85. DOI: https://doi.org/10.5007/1808-1711.2018v22n1p59

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Barrio, E., and B. da Ré, 2018, “Paraconsistency and its philosophical interpretations”, Australasian Journal of Logic 15 (2): 151–170. DOI: https://oi.org/10.26686/ajl.v15i2.4860

Barrio, E., F. Pailos, and D. Szmuc, 2018, “What is a paraconsistent logic?”, pages 89–108 in W. Carnielli and J. Malinowski (eds.), Contradictions, From Consistency to Inconsistency, Springer. DOI: https://doi.org/10.1007/978-3-319-98797-2_5

Beall, JC, 2009, Spandrels of Truth, Oxford, Oxford Un. Press. DOI: https://doi.org/10.1093/acprof:oso/9780199268733.001.0001

Beall, JC, M. Glanzberg, and D. Ripley, 2020, “Liar Paradox”, in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2020 Edition). https://plato.stanford.edu/archives/fall2020/entries/liar-paradox/

Carnielli, W., M. Coniglio, and A. Rodrigues, 2018, “On formal aspects of the epistemic approach to paraconsistency”, pages 49–74 in M. Freund, M. Fernández, and M. Ruffino (eds.), Logic and Philosophy of Logic. Recent Trends in Latin America and Spain, London: College.

Carnielli, W., and A. Rodrigues, 2015, “On the philosophy and mathematics of the logics of formal inconsistency”, pages 57–88, in J.-Y. Béziau, M. Chakraborty, and S. Dutta (eds.), New Directions in Paraconsistent Logic, New Delhi: Springer. DOI: https://doi.org/10.1007/978-81-322-2719-9_3

Carnielli, W., and A. Rodrigues, 2019, “An epistemic approach to paraconsistency: A logic of evidence and truth”, Synthese 196: 3789–3813. DOI: https://doi.org/10.1007/s11229-017-1621-7

Carnielli, W., and A. Rodrigues, 2021, “On epistemic and ontological interpretations of intuitionistic and paraconsistent”, Logic Journal of the IGPL 29 (4): 569–584. DOI: https://doi.org/10.1093/jigpal/jzz041

Mares, E., 2004, “Semantic dialetheism”, pages 264–275, in G. Priest, JC Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction. New Philosophical Essays, Clarendon Press: Oxford. DOI: https://doi.org/10.1093/acprof:oso/9780199265176.003.0017

Priest, G., 2006a, In Contradiction: A Study of the Transconsistent, 2nd edition, Oxford, Oxford Un. Press. DOI: https://doi.org/10.1093/acprof:oso9780199263301.001.0001

Priest, G., 2006b, Doubt Truth to be a Liar, Oxford, Oxford Un. Press. DOI: https://doi.org/10.1093/0199263280.003.0005

Priest, G., 2019, “Some comments and replies”, pages 575–675, in C. Baskent, T. Ferguson (eds.) Graham Priest on dialetheism and paraconsistency, Springer. DOI: https://doi.org/10.1007/978-3-030-25365-3_27

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Williamson, T., 2017, “Semantic paradoxes and abductive methodology”, in B. Armour-Garb (ed.), Reflections on the Liar, Oxford: Oxford Un. Press. DOI: https://doi.org/10.1093/oso/9780199896042.003.0013

Logic and Logical Philosophy

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Published

2022-02-05

How to Cite

1.
BECKER ARENHART, Jonas and SAFRA MELO, Ederson. The Liar Paradox: Between Evidence and Truth. Logic and Logical Philosophy. Online. 5 February 2022. Vol. 31, no. 2, pp. 289-311. [Accessed 1 July 2025]. DOI 10.12775/LLP.2022.005.
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Vol. 31 No. 2 (2022): June

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Copyright (c) 2022 Jonas Becker Arenhart, Ederson S. Melo

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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