Proofs by Reductio ad Impossibile in Aristotle’s Prior Analytics

Authors

DOI:

https://doi.org/10.11606/issn.1981-9471.v15i2p53-76

Keywords:

reductio ad impossibile, Aristotle, Prior Analytics

Abstract

This paper aims at clarifying the procedure of proofs by reductio ad impossibile in Aristotle’s Prior Analytics, especially elucidating what can be taken as impossibility in such proofs. Traditional interpretation has it that the impossibility in Aristotle’s reductio proofs must be a contradiction. I argue for an alternative interpretation according to which both contrarieties and contradictions are suitable as the impossibility required by the proofs in question. I also present a definition of proof by reductio ad impossibile in accordance with the alternative interpretation.

Downloads

Download data is not yet available.

References

Aristoteles. Aristotelis Categoriae et Liber de Interpretatione. Ed. L. Minio-Paluello. Oxford: Clarendon Press, 1949.

Aristoteles. Aristotelis Topica et Sophistici Elenchi. Ed. W. D. Ross. Oxford: Clarendon Press, 1958.

Aristoteles. Aristotelis Analytica Priora et Posteriora. Ed. W. D. Ross. Oxford: Clarendon Press, 1964.

Aristotle. Categories and De Interpretatione. Trans. J. L. Ackrill. Oxford: Clarendon Press, 1963.

Aristotle. Prior Analytics. Trans. R. Smith. Indianapolis: Hackett Publishing Company, 1989.

Aristotle. Topics. Books I and VIII. Trans. R. Smith. Oxford: Clarendon Press, 1997.

Aristotle. Prior Analytics. Book I. Trans. G. Striker. Oxford: Clarendon Press, 2009.

Corcoran, J. Completeness of an Ancient Logic. The Journal of Symbolic Logic, Vol. 37, No. 4, pp. 696-702, 1972.

Corcoran, J. A Mathematical Model of Aristotle’s Syllogistic. Archiv für Geschichte der Philosophie, Vol. 55, No.2, pp. 191-219, 1973.

Corcoran, J. Aristotle's Natural Deduction System. In: J. Corcoran (ed.). Ancient Logic and its Modern Interpretations. pp. 85-132. Dordrecht: D. Reidel Publishing Company, 1974.

Corcoran, J. Aristotle’s Demonstrative Logic. History and Philosophy of Logic, Vol. 30, No. 1, pp. 1-20, 2009.

Crivelli, P. Aristotle’s Logic. In: C. Shields (ed.). The Oxford Handbook of Aristotle. Oxford: Oxford University Press, 2012.

Dyckhoff, R. Indirect proof and inversions of syllogisms. Bulletin of Symbolic Logic, Vol. 25, No. 2, pp. 196-207, 2019.

Ferreira, M. R. F. O que são silogismos perfeitos? doispontos, Vol. 10, No. 2, pp. 189-224, 2013.

Malink, M. Aristotle's Modal Syllogistic. Cambridge, MA: Harvard University Press, 2013.

Mignucci, M. Aristotle on the Existential Import of Propositions. Phronesis, Vol. 52, No. 2, pp. 121-138, 2007.

Ockham, G. Opera Philosophica I – Summa Logicae. Ed. P. Boehner, G. Gál and S. Brown. St. Bonaventure, N.Y.: Editiones Instituti Franciscani Universitatis S. Bonaventurae, 1974.

Patzig, G. Aristotle’s Theory of the Syllogism: a logico-philological study of book A of the Prior Analytics. Trans. J. Barnes. Dordrecht: Springer Science+Business Media, 1968.

Read, S. Aristotle's Theory of the Assertoric Syllogism. Unpublished, pp. 1-26, 2017, (Available at https://www.st-andrews.ac.uk/~slr/The_Syllogism.pdf).

Smiley, T. J. What Is a Syllogism? Journal of Philosophical Logic, Vol. 2, No. 1, pp. 136-54, 1973.

Smith, R. Logic. In: J. Barnes (ed.). The Cambridge Companion to Aristotle. pp. 27-65. Cambridge: Cambridge University Press, 1995.

von Plato, J. Elements of Logical Reasoning. Cambridge: Cambridge University Press, 2013.

von Plato, J. Aristotle’s deductive logic: A proof-theoretical study. In: D. Probst and P. Schuster (eds.). Concepts of Proof in Mathematics, Philosophy, and Computer Science. pp. 323-46. Berlin: De Gruyter, 2016.

von Plato, J. The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age. Princeton: Princeton University Press, 2017.

Downloads

Published

2021-10-14

How to Cite

Mesquita Neto, A. (2021). Proofs by Reductio ad Impossibile in Aristotle’s Prior Analytics. Journal of Ancient Philosophy, 15(2), 53-76. https://doi.org/10.11606/issn.1981-9471.v15i2p53-76

Issue

Section

Articles