The Liar Paradox: Between Evidence and Truth
DOI:
https://doi.org/10.12775/LLP.2022.005Keywords
paraconsistency, Liar paradox, epistemic approach, evidence, truthAbstract
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
Barrio, E., 2018, “Models & proofs: LFIs without a canonical interpretation”, Principia: an International Journal of Epistemology 22 (1): 87–112. DOI: https://doi.org/10.5007/1808-1711.2018v22n1p87
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
Priest, G., F. Berto, and Z. Weber, 2018, “Dialetheism”, in E. N. Zalta (ed.) The Stanford Encyclopedia of Philosophy (Fall 2018 Edition). https://plato.stanford.edu/archives/fall2018/entries/dialetheism/
Scharp, K., and S. Shapiro, 2017, “Revising inconsistent concepts”, in B. Armour-Garb (ed.), Reflections on the Liar, Oxford: Oxford Un. Press. DOI: https://doi.org/10.1093/oso/9780199896042.003.0010
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
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Jonas Becker Arenhart, Ederson S. Melo
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Stats
Number of views and downloads: 1844
Number of citations: 0
