The proof methods in Aristotle’s Prior Analytics and its normative nature
DOI:
https://doi.org/10.15448/1984-6746.2020.3.35620Keywords:
Logic, Syllogism, Proof, NormativityAbstract
This article is divided into two steps. The first has two objectives. The first objective is to present three methods of proof present in Aristotle’s First Analytical the direct, reductio ad impossibile and ekthesis, in addition, a method of counterproof. The second objective is to provide a notation and deduction schemes familiar to contemporary logic, easy to access, understand and relatively neutral to interpretations in order to demonstrate that syllogistics preserves interesting deduction tools and intuitively fertile questions for today’s philosophical research, particularly, to those who wish to understand philosophical readings of Aristotle’s logic such as those found in Łukasiewicz (1957) and Corcoran (2009). The second step aims to provide a normative interpretation for Aristotelian syllogistics. I argue in favor of this reading, the way in which the deduction paths described in the methods can be read as authorizations, commitments and incompatibilities in the inferences, in turn, guided by logical principles and by the value of the components of the syllogism. I conclude, therefore, that syllogism has the role of explaining and demonstrating reasoning in view of certain norms.
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References
ANGIONI, L. Introdução à Teoria da Predicação em Aristóteles. São Paulo: UNICAMP, 2006.
ARISTÓFANES. As Nuvens. Tradução Gilda Maria Reale Strazynski. São Paulo: Nova Cultural, 1987. (Coleção os Pensadores).
ARISTÓTELES. The Complete Works of Aristotle. Ed. Jonathan Barnes. New Jersey: Princeton University Press, 1995. 2 v.
ARISTÓTELES. Órganon. Trad. Edson Bini. São Paulo: Edipro, 2010.
ARISTÓTELES. Metafísica. 3 v. Trad. para o Italiano de Giovanni Reale; Trad. para o Português de Marcelo Perine. São Paulo: Loyola, 2002.
BARNES, J. (org.) Aristóteles. São Paulo: Ideias & Letras, 2009.
BÉZIAU, J.-Y. New Light on the Square of Oppositions and its Nameless Corner. Logical Investigations, [s. l.], v. 10, p. 218-233.,2003.
BLANCHÊ, R.; DUBUCS, J. História da Lógica: de Aristóteles a Bertrand Russel. Lisboa: Edições 70, 1996.
BRANDOM, Robert B. Articulating Reasons: An Introduction to Inferencialism. Cambridge: Harvard University Press, 2000. DOI: https://doi.org/10.4159/9780674028739
BRANDOM, Robert B. Making it Explicit: Reasoning, Representing and Discursive Commitment. Cambridge: Harvard University Press, 1998.
COPI, I. Introdução à lógica. São Paulo: Mestre Jou, 1978.
CORCORAN, J. Logical form. In: AUDI, R. (ed.). Cambridge Dictionary of Philosophy. 2. ed. Cambridge University Press, Cambridge, 1999.
CORCORAN, J. Aristotle’s demonstrative logic. History and Philosophy of Logic, Londres, v. 30, p.1-20, 2009. https://doi.org/10.1080/01445340802228362. DOI: https://doi.org/10.1080/01445340802228362
CORCORAN, J. Aristotle’s Prototype Rule-Based Underlying Logic. Logica Universalis, Basel, v. 12, n. 1-2, p. 9-35, 2018. https://doi.org/10.1007/s11787-018-0189-4. DOI: https://doi.org/10.1007/s11787-018-0189-4
HINTIKKA, J. Aristotelian induction. Rev. Int. Philos. [s. l.], v. 34, p. 422-439, 1980.
KNEALE, M.; KNEALE, W. O Desenvolvimento da Lógica, 3. ed. Lisboa: Calouste Gulbenkian, 1968.
LAGERLUND, H. Medieval Theories of the Syllogism. In: The Stanford Encyclopedia of Philosophy (Winter 2017 Edition). Disponível em: https://plato.stanford.edu/archives/win2017/entries/medieval-syllogism/. Acessado em: 05 set. 2019.
LUKASIEWICZ, J. Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Oxford: Oxford University Press, 1957.
MORTARI, C.A. Introdução à Lógica. 2. ed. São Paulo: Ed. Unesp, 2016.
PATZIG, G. Aristotle’s Theory of the Syllogism. Trans. Jonathan Barnes. Dordrecht: D. Reidel, 1969. DOI: https://doi.org/10.1007/978-94-017-0787-9
PLATÃO. A República. 2. ed. Tradução Edson Bini. São Paulo: Edipro, 2012.
PLATÃO. Protágoras. Tradução Daniel R. N. Lopes. São Paulo: Perspectiva, 2017.
SMITH, R. Aristotle’s Logic. In: The Stanford Encyclopedia of Philosophy. Summer 2019 Edition. Disponível em: https://plato.stanford.edu/archives/sum2019/entries/aristotle-logic/. Acessado em: 05 set. 2019.
SMITH, R. What Is Aristotelian Ecthesis? History and Philosophy of Logic, Londres, v.3, n. 2, p.113–127. 1982. https://doi.org/10.1080/01445348208837035. DOI: https://doi.org/10.1080/01445348208837035
ŻŁARNECKA–BIAŁY, E. Aristotle’s Proofs by Ecthesis. Bulletin of the Section of Logic, Lodz, v. 22, n.1, p. 40-44, 1993.
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