Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T22:10:59.808Z Has data issue: false hasContentIssue false

Aristotle and Łukasiewicz on Existential Import

Published online by Cambridge University Press:  22 September 2015

STEPHEN READ*
Affiliation:
UNIVERSITY OF ST. ANDREWS [email protected]

Abstract:

Jan Łukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing the contemporary understanding of Aristotle's logical systems. However, Łukasiewicz's interpretation is based on a number of tendentious claims, not least, on the claim that the syllogistic was intended to apply only to nonempty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition.

Type
Articles
Copyright
Copyright © American Philosophical Association 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aristotle. (1963) Categories and On Interpretation. Translated with Notes by Ackrill, J. L.. Clarendon Aristotle Series. Oxford: Clarendon Press.Google Scholar
Aristotle. (2009) Prior Analytics Book I. Translated with an Introduction and Commentary by Striker, Gisela. Clarendon Aristotle Series. Oxford: Clarendon Press.Google Scholar
Avicenna. (2013) (Ibn Sina) Al-’Ibara. Translated and Introduced by Bäck, Allan. Munich: Philosophia Verlag.Google Scholar
Bednarowski, W. (1949) ‘Review of Annales Universitatis Mariae Curie-Sklodowska, Lublin, Polonia. Section F, vol. 1 no. 3’. Mind, 58, 542–45.Google Scholar
Bednarowski, W. (1956) ‘Hamilton's Quantification of the Predicate’. Aristotelian Society Proceedings, 56, 217–40.Google Scholar
Bochenski, I. (1962) A History of Formal Logic. Translated and edited by Thomas, Ivo. New York: Chelsea Publishing.Google Scholar
Buridan, J. (2001) Summulae de Dialectica. English translation by Klima, G.. New Haven: Yale University Press.Google Scholar
Buridan, J. (2014) Tractatus de Consequentiis. English translation by Read, Stephen., New York: Fordham University Press.Google Scholar
Burley, W. (2000) On the Purity of the Art of Logic. English translation by Spade, P. V.. New Haven: Yale University Press.Google Scholar
Church, A. (1965) ‘The History of the Question of Existential Import of Categorical Propositions’. In Bar-Hillel, Y., ed., Logic, Methodology and Philosophy of Science: Proceedings of the 1964 International Congress, 417–24. Amsterdam: North-Holland Publishing.Google Scholar
Corcoran, J. (1974) ‘Aristotle's Natural Deduction System’. In Corcoran, J., ed., Ancient Logic and its Modern Interpretations, 85131. Dordrecht: Reidel.Google Scholar
Geach, P. (1950) ‘Subject and Predicate’. Mind, 59, 461–82.Google Scholar
Hodges, W. (2011) ‘Interview’. The Reasoner, 5, 179–83.Google Scholar
Hodges, W. (2012) ‘Affirmative and Negative in Ibn Sina’. In Novaes, C. Dutilh and Hjortland, O., eds., Insolubles and Consequences, 119–34. London: College Publications.Google Scholar
Keynes, J. N. (1884) Studies and Exercises in Formal Logic. London: Macmillan.Google Scholar
Kneale, W., and Kneale, M.. (1962) The Development of Logic. Oxford: Oxford University Press.Google Scholar
Londey, D., and Johanson, C.. (1987) The Logic of Apuleius. Leiden: Brill.Google Scholar
Łukasiewicz, J. (1923) ‘Review of Śleszyński’. Ruch Filosoficczny, 8:107–8.Google Scholar
Łukasiewicz, J. (1951) Aristotle's Syllogistic. Oxford: Clarendon Press.Google Scholar
Łukasiewicz, J. (1957) Aristotle's Syllogistic. 2nd enlarged edition. Oxford: Clarendon Press.Google Scholar
Łukasiewicz, J. (1963) Elements of Mathematical Logic. Translated by Wojtasiewicz, Olgierd from the Polish of the second edition, 1958, edited by Słupecki, Jerzy. First edition, Warsaw 1929. Oxford: Pergamon Press.Google Scholar
Martin, J. N. (2004) Themes in Neoplatonic and Aristotelian Logic. Aldershot: Ashgate.Google Scholar
Moody, E. A. (1953) Truth and Consequence in Mediaeval Logic. Amsterdam: North-Holland.Google Scholar
Ockham, G. de. (1974) Summa Logicae. Edited by Boehner, P. et al. St. Bonaventure: Franciscan Institute Publications.Google Scholar
Ockham, G. de. (2007) Demonstration and Scientific Knowledge in William of Ockham. English translation by Longeway, John Lee. Notre Dame: University of Notre Dame.Google Scholar
Parsons, T. (2008a) ‘Things That Are Right with the Traditional Square of Opposition’. Logica Universalis, 2, 311.Google Scholar
Parsons, T. (2008b) ‘The Traditional Square of Opposition’. In Zalta, E. N., ed., The Stanford Encyclopedia of Philosophy. Fall 2008 edition.Google Scholar
Patzig, G. (1968) Aristotle's Theory of the Syllogism. Dordrecht: Reidel.Google Scholar
Prior, A. (1962) Formal Logic. Oxford: Clarendon Press.Google Scholar
Rescher, N. (1963) Al-Farabi's Short Commentary on Aristotle's Prior Analytics. Translated from the original Arabic with introduction by Rescher, Nicholas. Pittsburgh: University of Pittsburgh Press.Google Scholar
Ross, W., ed. (1928) Aristotle's Organon. Volume 1 of The Works of Aristotle. Categories and On Interpretation. Tr. Edghill, E. M., Prior Analytics. Tr. Jenkinson, A. J., Posterior Analytics. Tr. Mure, G. R. G., Topics and Sophistical Refutations. Translated by Pickard-Cambridge, W. A.. Oxford: Oxford University Press.Google Scholar
Seuren, P. (2010) The Logic of Language. Oxford: Oxford University Press.Google Scholar
Śleszyński, J. (1921) O Logice Tradycyjnej [On traditional logic]. Krakow: Wydawnictwo Towaratystwa Filozofucznego w Krakowie.Google Scholar
Smiley, T. (1973) ‘What is a Syllogism?’. Journal of Philosophical Logic, 2, 155–80.Google Scholar
Smith, R. (2009) ‘Aristotle's Logic’. In Zalta, E. N., ed., The Stanford Encyclopedia of Philosophy. Spring 2009 edition.Google Scholar
Strawson, P. (1950) ‘On Referring’. Mind, 59, 320–44.Google Scholar
Thom, P. (1981) The Syllogism. Munich: Philosophia Verlag.Google Scholar
Thompson, M. (1953) ‘On Aristotle's Square of Opposition’. Philosophical Review, 62, 251–65.Google Scholar
Wedin, M. (1996) ‘Negation and Quantification in Aristotle’. History and Philosophy of Logic, 11, 131–50.CrossRefGoogle Scholar
Wu, J. S. (1969) ‘The Problem of Existential Import (from George Boole to P. F. Strawson)’. Notre Dame Journal of Formal Logic, 10, 415–24.Google Scholar