Is Aristotelian Syllogistic an Axiomatized Mathematical Work?
DOI:
https://doi.org/10.48160/18532330me13.349Keywords:
mathematization, formalization, axiomatization, Aristotelian syllogisticAbstract
The aim of this paper is to clarify the metatheoretical characteristics of Aristotle's Prior Analytics. We start from a conceptual distinction between mathematization, formalization and axiomatization, from which it is possible to examine the Prior Analytics, establishing in what sense it is or is not a mathematized, formalized and/or axiomatized work. To clarify even further the conceptual distinction, we consider a mathematization (by Boole) and an axiomatization (by Sánchez Mazas), both of the Aristotelian syllogistic. In this way, we consider that the conceptual distinction with respect to Prior Analytics will be more precisely determined.
References
Aristóteles (s. IV a.C.), “Analíticos Primeros”, en Tratados de Lógica (Órganon) (trad. de Miguel Candel Sanmartín), tomo II, Madrid: Editorial Gredos, 1995, pp. 93-297.
Ávila, A. (2017), Una visión cuasiempirista de la matemática, México: Colofón.
Ávila, A. (2023), "¿Descubrir la estructura lógica de una teoría implica matematizarla?, Stoa 14(27): 17-33.
Bochenski, L. M. (1985), Historia de la lógica formal (trad. de Millán Bravo Lozano), Madrid: Editorial Gredos.
Boole, G. (1847), Análisis matemático de la lógica (trad. de Armando Asti Vera), Buenos Aires: Universidad Nacional de la Plata, 1960.
Boole, G. (1854), An Investigation of the laws of thought, London: Walton and Maberly.
Candel, M. (trad.) (1995), Tratados de Lógica (Organón) de Aristóteles, tomo II, Madrid: Editorial Gredos.
Cantor, G. (1883), “Foundation of a General Theory of Manifolds” (trad. de Uwe Parpart), Compaigner 9 (1976): 69–96.
Corcoran, J. (1974a), “Aristotelian Syllogisms: Valid Arguments or True Universalized Conditionals?”, Mind 83(330): 278- 81.
Corcoran, J. (1974b), “Aristotle’s Natural Deduction System”, en Corcoran, J. (ed.), Ancient Logic and Its Modern Interpretations, Dordrecht: Reidel, pp. 85-132.
Corcoran, J. (1992), “El nacimiento de la lógica: la concepción de la prueba en términos de verdad y consecuencia”, Ágora 11(2): 67-78.
Corcoran, J. (2003), “Aristotle’s Prior Analytics and Boole’s Laws of Thought”, History and Philosophy of Logic 24: 261-288.
Englebretsen, G. (1996), Something to Reckon with Logic of Terms, Canada: University of Ottawa Press.
Euclides (s. III a.C.), The Thirteen Books of the Elements, en Sir Thomas, L. H (Trad.), Great Books of the Western World of the Encyclopedia Britannica, Vol. II, William Benton Publisher, 1952, pp. 1-396. (Versión castellana de Juan D. García Bacca: Elementos de Geometría (precedidos por Los fundamentos de la Geometría de David Hilbert), México: UNAM, 1992.
Frege, G. (1879), Conceptografía, Los Fundamentos de la Aritmética y otros Estudios Filosóficos (trad. de Hugo Padilla), México: UNAM, 1972.
Gillings, R. J. (1972), Mathematics in the time of Pharaons, NY: Dover Publication.
Mueller, J. (1981), Philosophy of Mathematics and Deductive Structure in Euclid’s Elements, NY: MIT Press.
Neugebauer, O. (1957), The Exact Science in Antiquity, Providence, Rhode Island: Brown University Press.
Łukasiewicz, J. (1957), Aristotle’s Syllogistic, Oxford: Clarendon Press.
Ross, W.D. (1957), Aristotle’s Prior and Posterior Analytics, Oxford: Clarendon Press.
Sánchez Mazas, M. (1954), “La teoría del silogismo desarrollada en forma de álgebra”, Theoria 7/8: 95-104.
Smiley, T.J. (1973), “What is a Syllogism?”, Journal of Philosophical Logic 2: 136-154.
Wittgenstein, L. (1922), Tractatus Logico-philosophicus (trad. de Enrique Tierno Galván), Madrid: Alianza Universidad, 1980.
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