Palabras clave
Lógica
Lógica multivaluada
Paraconsistencia
Lógica de três valores
Cómo citar
Resumen
En 1909, Peirce registró en unas páginas de su cuaderno de lógica algunos experimentos con matrices para la lógica proposicional de tres valores. Estas notas se reconocen hoy como uno de los primeros intentos de crear sistemas formales no clásicos. Sin embargo, aparte de los artículos publicados por Turquette en las décadas de 1970 y 1980, se ha avanzado muy poco hacia una comprensión exhaustiva de los aspectos formales de la lógica triádica de Peirce (como él la llamaba). Este trabajo pretende proponer un nuevo enfoque de las matrices de Peirce para la lógica proposicional triádica. Sugerimos que sus matrices lógicas dan lugar a tres sistemas diferentes, uno de los cuales -al que llamamos P3- es una lógica original y no explosiva. Además, mostraremos que el sistema P3 puede transformarse fácilmente en cálculos paraconsistentes y paracompletos, añadiéndole, respectivamente, operadores unarios de consistencia y negación intuicionista. Concluiremos con una discusión sobre las motivaciones filosóficas.
Citas
ANDERSON, A. R. and BELNAP, N. D. Entailment, v. 1. Princeton, New Jersey: Princeton University Press, 1975.
ANELLIS, I. “The genesis of the truth-table device”. Russell: The Journal of the Bertrand Russell Arquives, 24, pp. 55-70, 2004.
ANELLIS, I. “Peirce’s truth-functional analysis and the origin of the truth-table”, History and Philosophy of Logic, v. 33, n. 1, pp. 87-97, 2012.
ASENJO, F. G. “A calculus for antinomies”. Notre Dame Journal of Formal Logic, v. 16, n. 1, pp. 103-105, 1966.
BELIKOV, A. “Peirce’s triadic logic and its (overlooked) connexive expansion”. Logic and Logical Philosophy, 2021 (online first articles). Available at: Available at: https://apcz.umk.pl/czasopisma/index.php/LLP/article/view/LLP.2021.007 Accessed 16 June 2021.
BELL, J.L. A primer of infinitesimal analysis Second edition. Cambridge: Cambridge University Press, 2008.
BOLC, L.; BOROWIK, P. Many-valued logics, v. 1: theoretical foundations. New York: Springer-Verlag Berlin Heidelberg GmbH, 1992.
BURRIS, S.; SANKAPPANAVAR, H. P. A course in universal algebra New York: Springer-Verlag, 1981.
CARNIELLI, W.; CONIGLIO, M. E. Paraconsistent logic: consistent, contradiction and negation. Dordrecht: Springer, 2016.
CARNIELLI, W.; MARCOS, J.; DE AMO, S. “Formal inconsistency and evolutionary databases”. Logic and Logical Philosophy, v. 8, n. 8, pp. 115-152, 2000.
CARNIELLI, W.; MARCOS, J. “A taxonomy of C-systems”. In: CARNIELLI, W., CONIGLIO, M. E.; D’OTTAVIANO, I. M. L. (eds.). Paraconsistency: the logical way to the inconsistent (Lecture Notes in Pure and Applied Mathematics: Vol. 228). Boca Raton: CRC Press, 2002, pp. 01-94.
D’OTTAVIANO, I. M.L.; DA COSTA, N. C. A. “Sur un problème de Jáskowski”. Comptes Rendus de l’Académie de Sciences de Paris, (A-B) 270, pp. 1349-1353, 1970.
EISELE, C. “Introduction to volume 3”. In: PEIRCE, C. S. The New elements of mathematics, vol. III. The Hague: Mouton Publishers, 1976.
FISCH, M.; TURQUETTE, A. “Peirce’s triadic logic”. Transactions of the Charles S. Peirce Society, v. 2. n. 2, pp. 71-85, 1966.
HAVENEL, J. “Peirce’s clarifications of continuity”. Transactions of the Charles S. Peirce Society, v. 44, n. 1, pp. 133-86, 2008.
LANE, R. “Peirce’s triadic logic revisited”. Transactions of the Charles S. Peirce Society, v. 35, n. 2, pp. 284-311, 1999.
LANE, R. (2001). “Triadic logic”. In: BERGMAN, M. and QUEIROZ, J. (eds.). The Digital Encyclopedia of Peirce Studies New edition. The Commens Encyclopedia. Available in: http://www.commens.org/encyclopedia/article/ Accessed 05 April 2021
LANE, R. “Peirce’s modal shift: from set theory to pragmaticism”. Journal of the History of Philosophy, v. 45, n. 4, pp. 551-576, 2007.
ŁUKASIEWICZ, J. [1920]. “On three-valued logic”. In: BORKOWSKI, L. (ed.). Selected works Amsterdam: North-Holland, 1970, pp. 87-88.
MALINOWSKI, G. Many-valued logics Oxford: Clarendon Press, 1993.
ODLAND, B. C. “Peirce’s triadic logic: continuity, modality, and L”. Unpublished master's thesis. University of Calgary: Calgary, AB, 2020. Available in: Available in: http://hdl.handle.net/1880/112238 Accessed 10 April 2021.
PARKS, R. Z. “The mystery of Phi and Psi”. Transactions of the Charles S. Peirce Society, v. 7, n. 3, pp. 176-177, 1971.
PEIRCE, C. S. “On the algebra of logic”. American Journal of Mathematics, v. 3, n. 1, pp. 15-57, 1880.
PEIRCE, C. S. “On the algebra of logic: a contribution to the philosophy of notation”. American Journal of Mathematics, v. 7, n. 2, pp. 180-96, 1885.
PEIRCE, C. S. Collected Papers 8 vols. HARTSHORNE, Charles; HEISS, Paul and BURKS, Arthur (eds.). Cambridge: Harvard University Press, 1931-1958. [Cited as CP followed by volume and paragraph.]
PEIRCE, C. S. The New elements of mathematics The Hague: Mouton Publishers, 1976. [Cited as NEM followed by volume and page.]
PEIRCE, C. S. The Essential Peirce: selected philosophical writings, v. 1 (1867-1893). HOUSER, N. and KLOESEL, C. (eds.). Indiana University Press: Bloomington and Indianapolis, 1992. [Cited as EP followed by volume and page.]
PEIRCE, C. S. The Essential Peirce: selected philosophical writings, v. 2 (1893-1913). The Peirce Edition Project (ed.). Indiana University Press: Bloomington and Indianapolis, 1998. [Cited as EP followed by volume and page.]
PEIRCE, C. S. Philosophy of Mathematics: selected writings. MOORE, Matthew E. (ed.). Indiana University Press: Bloomington and Indianapolis, 2010. [Cited as PM followed by page.]
PEIRCE, C. S. Peirce logic notebook, Charles Sanders Peirce Papers MS Am 1632 (339). Houghton Library, Harvard University, Cambridge, Mass. Available at: https://nrs.harvard.edu/urn-3:FHCL.Hough:3686182 Accessed 10 April 2021.
POST, E. “Introduction to a general theory of elementary propositions”. American Journal of Mathematics, v. 43, n. 3, pp. 163-185, 1921.
PRIEST, G. “The logic of paradox”. Journal of Philosophical Logic, v. 8, n. 1, pp. 219-241, 1979.
RESCHER, N. Topics in philosophical logic Dordrecht, Holland: Springer Science+Business Media Dordrecht, 1968.
RODRIGUES, C. T. “Squaring the unknown: the generalization of logic according to G. Boole, A. De Morgan, and C. S. Peirce”. South American Journal of Logic, v. 3, n. 2, p. 1-67, 2017.
ROSSER, J. B.; TURQUETTE, A. R. Many-valued logics Amsterdam: North-Holland Publishing Company, 1952.
SALATIEL, J. R. “Tableau method of proof for Peirce’s three-valued propositional logic”. Unisinos Journal of Philosophy, v. 23, n. 1, pp. 1-10, 2022.
SOBOCINSKI, B. “Axiomatization of a partial system of three-valued calculus of propositions”, The Journal of Computing Systems, v. 1, pp. 23-55, 1952.
TURQUETTE, A. “Peirce's Phi and Psi operators for triadic logic”. Transactions of the Charles S. Peirce Society, v. 3, n, 2, p. 66-73, 1967.
TURQUETTE, A. “Peirce's complete systems of triadic logic”. Transactions of the Charles S. Peirce Society, v. 5, n. 4, p. 199-210, 1969.
TURQUETTE, A. “Dualism and trimorphism in Peirce's triadic logic”. Transactions of the Charles S. Peirce Society, v. 8, n. 3, pp. 131-140, 1972.
TURQUETTE, A. “Minimal axioms for Peirce's triadic logic“. Zeitschrift für mathematische Loßik und Grundlagen der Mathematik, v. 22, pp. 169-176, 1976.
TURQUETTE, A. “Alternative axioms for Peirce's triadic logic“. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, v. 24, pp. 443-444, 1978.
TURQUETTE, A. “Quantification for Peirce's preferred system of triadic logic”. Studia Logica, v. 40, pp. 373-382, 1981.
WÓJCICKI, R. Theory of logical calculi: basic theory of consequence operations. Dordrecht: Springer, 1988.
ZALAMEA, F. “Peirce's logic of continuity: Existential graphs and non-Cantorian continuum”. Review of Modern Logic, v. 9, n. 1-2, pp. 115-162, 2003.
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