What is the O-Corner Interpretation and Does it Save the Traditional Square of Opposition?

Year 2019, Issue: 51, 37 - 59, 31.12.2019

Yavuz Recep Başoğlu

Abstract

To salvage traditional logic and traditional square of opposition from the problem of existential import, logicians have been offering solutions for centuries. In this paper, firstly it will be argued that as far as we know, the historically first solution proposed by Abelard in 11th century and by Seuren in 2002 is actually a version of the O-Corner Interpretation of traditional logic, which is generally attributed to the 14th century logician Ockham. Secondly, it will be advocated that two systems of Abelard and of Ockham have the same logical power. Lastly, the main claim will be that Abelard’s and Seuren’s system shall be favored over Ockham’s system.

Keywords

Problem of existential import, the o-corner interpretation, traditional logic, Abelard, Ockham, traditional square of opposition

O-Köşesi Yorumu Nedir ve Geleneksel Karşıtlık Karesini Kurtarabilir mi?

Abstract

Geleneksel mantığı ve geleneksel karşıtlık karesini, varlıksal varsayım denen problemden kurtarmak için, mantıkçılar yüzyıllardır çözüm üretmekteler. Bu çalışmada, ilk, bildiğimiz kadarıyla tarihsel ilk çözüm olan ve 11. yüzyılda Abelard ve 2002’de Seuren tarafından önerilen sistemin aslında 14. yüzyıl mantıkçısı olan Ockham’a atfedilen geleneksel mantığın O-köşesi yorumunun bir versiyonu olduğu savunulacaktır. Daha sonra, bu iki sistemin mantıksal güçlerinin eşit olduğu iddia edilecektir. En son olarak da, Abelard ve Seuren’in sisteminin Ockham’ınkine tercih edilmesi gerektiği asıl iddiamız olacaktır.

Keywords

Varlıksal varsayım problemi, o-köşesi yorumu, geleneksel mantık, Abelard, Ockham, geleneksel karşıtlık karesi

References

• Aristotle. Aristotle: Categories on interpretation. Prior analytics. Translated by Cooke, H.P., Tredennick, H. London: Harvard University Press, 1938.
• Aristotle. Categories and De interpretatione. Translated by J.L.Ackrill. Oxford: Clarendon Press, 1975.
• Ashworth, E. Jeniffer. “Existential assumptions in late medieval logic.” American Philosophical Quarterly 10(2) (1973): 141-147.
• Ashworth, E. Jennifer. Language and Logic in the Post-medieval Period. Dortrecht: Reidel Publishing, 1974.
• Bäck, Allan. Aristotle’s theory of predication. Leiden: Brill, 2000. Caroll, Lewis. Symbolic Logic, Part I, Elementary. New York: NY Dover Publications, 1958 [1896].
• Chatti, Saloua and Schang, Fabian. “The cube the square and the problem of existential import.” History and Philosophy of Logic 34(2) (2013):101-132.
• Church, Alonzo. “The history of the question of existential import of categorical propositions.” In Logic, Methodology, and Philosophy of Science: Proceedings of the 1964 International Congress, edited by Y. BarHillel, 417-24. Amsterdam: North-Holland, 1965.
• Copi, Irving M. and Cohen, Carl. Introduction to Logic: Study Guide. US: Macmillan,1994. Copi, Irving M. Introduction to Logic. New York: Macmillan, 1953.
• De Rijk, Lambertus Marie. Petrus Abaelardus, Dialectica. First Complete Edition of the Parisian Manuscript. Assen: Van Gorcum/Hak and Prakke, 1956.
• Horn, Laurence R. A natural history of negation. Chicago: University of Chicago Press, 1989.
• Horn, Laurence R. “All john’s children are as bald as the king of france: Existential import and the geometry of opposition.” Chicago Linguistics Society 33 (1997): 155-179. Hudson Mulder, Dwayne. “The existential assumpions of traditional logic.” History and Philosophy of Logic, 17(1-2) (1996):141-154.
• Hughes, G. Edward. and Londey, David. The elements of formal logic. New York: Harper and Raw, 1965.
• Johnson, William Ernest. Logic, vol. 1. Cambridge: Cambridge University Press, 1921.
• Keynes, John Neville. Studies and Exercises in Formal Logic. London: Macmillan, 1906.
• Klima, Gyula. “Existence and reference in medieval logic.” In New essays in free logic, edited by Morscher, E. and Hieke, A., 197-226. Dortrecht: Springer, 2001.
• Klima, Gyula. John Buridan. New York: Oxford University Press, 2008.
• Klima, Gyula. “Consequence”. In The Cambridge Companion to Medieval Logic, edited by Catarina Dutilh Novaes and Stephen Read, 316-41. Cambridge: Cambridge University Press, 2016.
• Klima, Gyula. Ars artium: essays in philosophical semantics, mediaeval and modern. Budapest: Institute of Philosopher, Hungarian Academy of Sciences, 1988.
• Kneale, William and Kneale, Martha, The development of logic. London: Oxford University Press, 1962.
• Londey, David G. and Johanson, Carmen J. The logic of Apuleius: Including a complete Latin text and English translation of the Peri Hermeneias of Apuleius of Madaura. Leiden: Brill Archive,1987.
• Moody, Ernest A. Truth and Consequence in Mediaeval Logic. Amsterdam: North-Holland Publishing Company, 1953.
• Morrison, John J. “The existential import of a proposition in Aristotelian logic.” Philosophy and Phenomenological Research, 15(3) (1995):386-393.
• Ockham, W. (1998). Ockham’s Theory of Propositions: Part 2 of the Summa Logicae. Translated by Alfred J. Freddoso and Henry Shuurman. Indiana: St. Augustine’s Press, 1998.
• Parsons, Terence. “Things that are right with the traditional square of oppositions.” Logica Universalis, 2(1) (2008) :3-11. Parsons, Terence. Articulating medieval logic. Oxford: Oxford University Press, 2014.
• Parsons, Terence. “The traditional square of opposition.” In The Stanford Encyclopedia of Philosophy Summer 2017 edition. Edited by Zalta, E.N. Metaphysics Research Lab, Stanford University, 2017.
• Read, Stephan. “Aristotle and Lukasiewicz on existential import.” Journal of the American Philosophical Association 1(3) (2015):535-544.
• Seuren, Pieter A. “The logic of thinking.” Koninklijke Nederlandse Akademie van Wetenschappen, Mededelingen van de Afdelig Letterkunde, Niuwe Reeks, 65(9) (2002):5-35.
• Seuren, Pieter. A. The Logic of Language: Language From Within, volume 2. New York: Oxford Univerity Press, 2009.
• Seuren, Pieter A. “Does a leaking o-corner save the square?” in Around and beyond the square of opposition, edited by Béziau, J.Y., and Jacquette, D. Basel: Springer, 2012
• Seuren, Pieter A. From Whorf to Montague: Explorations in the theory of language. Oxford: Oxford University Press, 2013. Strawson, Peter Frederick. Introduction to Logical Theory. New York: Routledge, 2011.
• Thom, Paul. The syllogism. München: Philosophie Verlag, 1981. Thomson, Manley. “Aristotle’s square of oppositions.” Philosophical Review 62 (1953):251-265.
• Wedin, Michael V. “Negation and quantification in Aristotle.” History and Philosophy of Logic 11(2) (1990) :131-150.