Sí hay negación lógica
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Abstract
In this paper we discuss Jc Beall’s thesis that there is no logical negation. We asses the soundness of Beall’s argument and we put forward two reasons to negate the truth of one of its premises: that negation has to be whether exclusive or exhaustive. The first reason involves an alternative presentation of the rules for negation in sequent systems different to that presupposed by Beall. The second reason establishes that negation need not be neither exclusive nor exhaustive.
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Nicolás Francisco, R. A., & Estrada González, L. (2020). Sí hay negación lógica. Crítica. Revista Hispanoamericana De Filosofía, 52(155), 55–72. https://doi.org/10.22201/iifs.18704905e.2020.1194
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References
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Restall, G., 2013, “Assertion, Denial and Non-Classical Theories”, en K. Tanaka y col (eds.), Paraconsistency: Logic and Applications. Logic, Epistemology, and the Unity of Science, Springer, Dordrecht.
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Shapiro, L., 2016b, “The Very Idea of a Substructural Approach to Paradox”, Synthese. (doi: 10.1007/s11229-016-1230-x).
Suszko, R., 1975, “Remarks on Lukasiewicz’s Three-Valued Logic”, Bulletin of the Section of Logic, vol. 4, no. 3, pp. 87–90.
Teijeiro, P., 2020), “Not a Knot”, Thought: A Journal of Philosophy, vol. 9, no. 1, pp. 14–24.
Weber, Z., 2010, “A Paraconsistent Model of Vagueness”, Mind, vol. 119, no. 476, pp. 1025–1045.
Weber, Z. y col., 2014, “Tolerating Gluts”, Mind, vol. 123, no. 491, pp. 813–828.
Barrio, E., F. Pailós y D. Szmuc, 2018, “A Recovery Operator for Nontransitive Approaches”, Review of Symbolic Logic, vol. 13, no. 1, pp. 80–104.
Beall, Jc., 2018, “The Simple Argument for Subclassical Logic”, Philosophical
Issues, vol. 28, no. 1, pp. 30–54.
Beall, Jc., 2017, “There Is No Logical Negation: True, False, Both and Neither”,
Australasian Journal of Logic, vol. 14, no. 1, pp. 1–29.
Beall, Jc., 2009, Spandrels of Truth, Oxford University Press, Oxford.
Beall, Jc y G. Restall, 2006, Logical Pluralism, Oxford University Press, Oxford.
Berto, F., 2015, “A Modality Called ‘Negation’ ”, Mind, vol. 124, no. 495, pp. 761–793.
Berto, F. y G. Restall, 2018, “Negation on the Australian Plan”, Journal of Philosophical Logic, vol. 48, no. 6, pp. 1119–1144.
da Costa, N.C.A. y E.H. Alves, 1977, “A Semantical Analysis of the Calculi Cn”, Notre Dame Journal of Formal Logic, vol. 18, no. 4, pp. 621–630.
De, M. y H. Omori, 2018, “There Is More to Negation Than Modality”, Journal of Philosophical Logic, vol. 47, pp. 281–299.
Dummett, M., 1991, The Logical Basis of Metaphysics, Harvard University Press, Cambridge, Mass.
Estrada-González, L., 2020, “The Bochum Plan and the Foundations of Contra-Classical Logics”, CLE e-Prints, vol. 19, no. 1, pp. 1–22.
Estrada-González, L., 2011, “On the Meaning of Connectives: Apropos of a Non-
Necessitarianist Challenge”, Logica Universalis, vol. 5, no. 1, pp. 115–126.
Field, H., 2008, Saving Truth from Paradox, Oxford University Press, Oxford.
Font, J.M., 1997, “Belnap’s Four-Valued Logic and De Morgan Lattices”, Logic Journal of the IGPL, vol. 5, no. 3, pp. 413–440.
Francez, N., 2019, “Bilateralism, Trilateralism, Multilateralism and Polysequents”, Journal of Philosophical Logic, vol. 48, pp. 245–262.
Gentzen, G., 1964, “Investigations into Logical Deduction”, American Philosophical Quarterly, vol. 1, no. 4, pp. 288–306.
Hjortland, O., 2014, “Speech Acts, Categoricity, and the Meanings of Logical Connectives”, Notre Dame Journal of Formal Logic, vol. 55, no. 4, pp. 445–467.
Kremer, M., 1988, “Kripke and the Logic of Truth”, Journal of Philosophical Logic, vol. 17, no. 3, pp. 225–278.
Marcos, J., 2005, “On Negation: Pure Local Rules”, Journal of Applied Logic, vol. 11, pp. 185–219.
McGee, V., 1991, Truth, Vagueness and Paradox: An Essay on the Logic of Truth, Hackett, Indianápolis.
Omori, H. y H. Wansing, 2017, “40 Years of FDE: An Introductory Overview”, en H. Omori y H. Wansing (eds.), Studia Logica, vol. 105, pp. 1021–1049.
Omori, H. y H. Wansing (eds.), 2019, New Essays on Belnap-Dunn Logic, Springer, Berlín.
Paoli, F., 2019, “Bilattice Logics and Demi-Negation”, en H. Wansing y H. Omori (eds.), New Essays on Belnap-Dunn Logic, Springer, Berlín, pp. 233–253.
Paoli, F., 2003, “Quine and Slater on Paraconsistency and Deviance”, Journal of Philosophical Logic, vol. 32, pp. 531–548.
Paoli, F., 2002, Substructural Logics: A Primer, Kluwer, Dordrecht.
Priest, G., 2008, An Introduction to Non-Classical Logics, Cambridge University Press, Cambridge.
Priest, G., 2006, In Contradiction: A Study of the Transconsistent, 2a. ed., Oxford University Press, Oxford.
Priest, G., 1979, “The Logic of Paradox”, Journal of Philosophical Logic, vol. 8, no. 1, pp. 219–241.
Quine, W.V.O., 1970, Philosophy of Logic, Prentice Hall, Englewood Cliffs, Nueva Jersey.
Restall, G., 2015, “Assertion, Denial, Accepting, Rejecting, Symmetry and Paradox”, en C. Caret y O. Hjortland (eds.), Foundations of Logical Consequence, Oxford University Press, Oxford, pp. 310–321.
Restall, G., 2013, “Assertion, Denial and Non-Classical Theories”, en K. Tanaka y col (eds.), Paraconsistency: Logic and Applications. Logic, Epistemology, and the Unity of Science, Springer, Dordrecht.
Ripley, D., 2013, “Paradoxes and Failures of Cut”, Australasian Journal of Philosophy, vol. 91, no. 1, pp. 139–164.
Routley, R. y col., 1982, Relevant Logics and their Rivals, vol. 1, Ridgeview, Atascadero, Cal.
Shapiro, L., 2016a, “LP, K3, and FDE as Substructural Logics”, en P. Arazim y T. Lavicka (eds.), The Logica Yearbook 2015, College Publications, Londres.
Shapiro, L., 2016b, “The Very Idea of a Substructural Approach to Paradox”, Synthese. (doi: 10.1007/s11229-016-1230-x).
Suszko, R., 1975, “Remarks on Lukasiewicz’s Three-Valued Logic”, Bulletin of the Section of Logic, vol. 4, no. 3, pp. 87–90.
Teijeiro, P., 2020), “Not a Knot”, Thought: A Journal of Philosophy, vol. 9, no. 1, pp. 14–24.
Weber, Z., 2010, “A Paraconsistent Model of Vagueness”, Mind, vol. 119, no. 476, pp. 1025–1045.
Weber, Z. y col., 2014, “Tolerating Gluts”, Mind, vol. 123, no. 491, pp. 813–828.
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