Paraconsistent Paradoxes
the price of consistency
DOI :
https://doi.org/10.51359/2357-9986.2025.263787Mots-clés :
paraconsistent logics, liar paradox, logics of formal inconsistency, dialetheismRésumé
Logics of Formal Inconsistency (LFIs) are usually considered a philosophically neutral logic with respect to paraconsistency, in the sense that they provide a good basis to think in terms of dialetheias, i.e. true contradictions, or in terms of conflicting information, a notion weaker than truth. In this article, I will show how this claim of neutrality fails in the face of the Liar Paradox: in classical logic, the sentence A: “A is false.” implies a contradiction. By adopting a paraconsistent logic, we avoid that contradictions lead to triviality. LFIs, however, add a consistency operator that recovers classical logic to propositions to which it applies. In this context, the Liar Paradox arises once again by a type of Liar’s Revenge: now, we can construct the sentence B: “B is only false.”, and that gives us triviality once again. With this result, we conclude that LFIs are not suitable logics to deal with semantic paradoxes
Références
ARENHART, J. B.; MELO, E. S. The Liar Paradox: between evidence and truth. Logic and Logical Philosophy, Nicolaus Copernicus University, v. 31, n. 2, p. 289–311, 2022.
BARRIO, E. A. Models & proofs: LFIs without a canonical interpretations. Principia: an international journal of epistemology, v. 22, n. 1, p. 87–112, 2018.
BARRIO, E. A.; PAILOS, F. M.; SZMUC, D. E. A paraconsistent route to semantic closure. Logic Journal of the IGPL, Oxford University Press, v. 25, n. 4, p. 387–407, 2017.
CARNIELLI, W.; CONIGLIO, M. E.; MARCOS, J. Logics of Formal Inconsistency. In: Handbook of Philosophical Logic. Edição: D.M. Gabbay e F. Guenthner. Dordrecht: Springer Netherlands, 2007. P. 1–93.
CARNIELLI, W.; MARCOS, J.; DE AMO, S. Formal inconsistency and evolutionary data-bases. Logic and logical philosophy, n. 8, p. 115–152, 2000.
CARNIELLI, W.; RODRIGUES, A. Towards a philosophical understanding of the logics of formal inconsistency. Manuscrito, SciELO Brasil, v. 38, n. 2, p. 155–184, 2015.
CARNIELLI, W.; RODRIGUES, A. A logic for evidence and truth. CLE e-Prints, v. 15, n. 5, p. 1–13, 2015.
CARNIELLI, W.; RODRIGUES, A. An epistemic approach to paraconsistency: a logic of evidence and truth. Synthese, Springer, v. 196, n. 9, p. 3789–3813, 2019.
CARNIELLI, W.; RODRIGUES, A. On epistemic and ontological interpretations of intuitionistic and paraconsistent paradigms. Logic Journal of the IGPL, Oxford University Press, v. 29, n. 4, p. 569–584, 2021.
CARNIELLI, W. A.; CONIGLIO, M. E. Paraconsistent Logic: Consistency, Contradiction and Negation. Berlin: Springer, 2016. v. 40.
D’OTTAVIANO, I. M. The completeness and compactness of a three-valued first-order logic. Revista Colombiana de Matematicas, Universidad Nacional de Colombia, v. 19, n. 1-2, p. 77–94, 1985.
GOODSHIP, L. On Dialethism. Australasian Journal of Philosophy, Taylor & Francis, v. 74, n. 1, p. 153–161, 1996.
MARCOS, J. Logics of formal inconsistency. Brazil: Fundação Biblioteca Nacional, 2005.
PRIEST, G. In Contradiction. USA: Oxford University Press, 2006.
PRIEST, G. The Logic of Paradox. Journal of Philosophical logic, Springer, p. 219–241, 1979.
RODRIGUES, A.; CARNIELLI, W. On Barrio, Lo Guercio, and Szmuc on logics of evidence and truth. Logic and Logical Philosophy, v. 31, n. 2, p. 313–338, 2022.
ROSENBLATT, L. Expressing consistency consistently. Thought: A Journal of Philosophy, Wiley Online Library, v. 10, n. 1, p. 33–41, 2021.
SMULLYAN, R. M. Diagonalization and self-reference. USA: Oxford University Press, 1994.
TAJER, D. LFIs and methods of classical recapture. Logic Journal of the IGPL, Oxford University Press, v. 28, n. 5, p. 807–816, 2020.
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© Rafael Ongaratto 2025
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