Abstract
In 1910, Jan Łukasiewicz published a groundbreaking book, On the Principle of Contradiction in Aristotle. The book contained a critique of the traditional attitude to the Principle of Non-Contradiction, and a reevaluation of its significance in the light of contemporary developments in logic. In the first half of the book, Łukasiewicz produced an analysis of Aristotle’s defence of the Principle in the Metaphysics, showing its deep inadequacy. In the second half of the book, Łukasiewicz, in his own terms, considers the pros and cons of the principle. The present paper provides an analysis and commentary on the second half of the book. Łukasiewicz is seen to be badly torn. Though he eventually endorses the principle, he does so, not in virtue of the evidence he considers, but in despite of it. In particular, he considers arguments against the Principle, drawn from Hegel, Meinong, and the paradoxes of self-reference, but rejects them for what appear to be patently inadequate reasons.
It is surprising how strongly certain opinions can persist within the sciences that are not only incorrectly formulated and without justification but which are plainly false—most likely, as I believe, because what has been declared in the past is repeated uncritically again and again.
Jan Łukasiewicz (Heine 2013, p. 125).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Łukasiewicz (1910a). He was 21 at the time.
- 2.
Heine (2013), p. 81. Quotations and page references in what follows are to this translation. All italics are original.
- 3.
Introduction, pp. 84–5.
- 4.
Introduction, pp. 86–7.
- 5.
Łukasiewicz (1910b).
- 6.
Heine (2013).
- 7.
Chapter XI, p. 153.
- 8.
Chapter XIV, p. 178.
- 9.
Indeed, I do not agree with it. See Priest (1998), esp. 1.5–1.10.
- 10.
Chapter X, pp. 145–6.
- 11.
An. Post. 77a10-23. Aristotle’s claim bears a small—and opaque—qualification. Łukasiewicz argues that this does not seriously limit the categorical claim.
- 12.
See Chalmers (2013), esp. Chap. 1.
- 13.
Chap. XVI, p. 192.
- 14.
In the first half of the book Łukasiewicz finds three versions of the PNC in Aristotle. Logical: A and ¬A cannot be true together. Metaphysical: an object cannot both have and not have a property. Psychological: no one can believe A and ¬A. The third, he argues, is just factually false. The first two are, however, equivalent, and provide the subject of the following discussion.
- 15.
Chap. I, p. 89.
- 16.
Chap. XVII, p. 201.
- 17.
Chap. XVII, pp. 205–6.
- 18.
Łukasiewicz attended lectures by Meinong in Graz in 1908–1909 (see Simons 1989).
- 19.
See Priest (2005), esp. the Preface.
- 20.
See Priest (1995), p. 126 of 2nd ed.
- 21.
He notes that the argument for the Russell paradox uses the Principle of Excluded Middle: the Russell set is either a member of itself or it is not. Since construction objects are incomplete, perhaps he had doubts about this.
- 22.
Enquiry Concerning Human Understanding, Part X, Sect. 1.
- 23.
p. 216. Łukasiewicz’ text then refers back to Chap. V, where he has quoted a passage from Hegel’s Logic expressing the point even more explicitly.
- 24.
See Priest (1987), 12.2.
- 25.
Łukasiewicz makes the point only concerning the experience of an object being in two places at the same time. But he might equally have applied the thought to instantaneous situations, thus attempting a solution to the Arrow Paradox.
- 26.
One might, I suppose, suggest that the length which is the arrow, is not made up of points. So much the worse for contemporary science. And supposing spatial distance to be quantized drives us into the arms of another of Zeno’s paradoxs anyway: the Stadium.
- 27.
Chap. XX, p. 230.
- 28.
What my evidence must do is cause the judge to reject the claim that I was at the scene of the murder. However, the distinction between asserting a negated sentence and denial—the linguistic correlate of rejection—is not on Łukasiewicz’ radar. (For more on the distinction, see Priest 1987, 7.3, 2006, 6.2.).
- 29.
An Enquiry Concerning Human Understanding, Sect. X.
- 30.
Chapter XIII, pp. 170–1.
- 31.
A draft of this paper was read to the Melbourne Logic Group, July 2014. Thanks go to the members of the group for their helpful discussion.
References
Chalmers, A. (2013). What is this thing called science? (4th ed.). Brisbane: University of Queensland Press.
Heine, H. (2013). Jan Łukasiewicz and the principle of contradiction (Ph.D. Thesis, University of Melbourne, 2013).
Łukasiewicz, J. (1910a). O Zasadzie Sprzeczności u Arystotelesa. Kraków: Akademia Umiejętności (2nd ed.). In J. Woleński (Ed.), Warsaw: PWN, 1987. Translated as: Über den Satz vom Widerspruch bei Aristoteles. Hildesheim: Olms, 1993. Del Principio di Contradizzione in Aristotele. Macerata: Quodlibet, 2003.
Łukasiewicz, J. (1910b). Über den Satz von Widerspruch bei Aristoteles. Bulletin Internationale de l’Académie des Sciences de Cracovie, Classe de Philosophie, 15–38. Translated as: On the Principle of Contradiction in Aristotle. Review of Metaphysics 24: 485–509 (1970/71). Aristotle on the Law of Contradiction. Articles on Aristotle 3. Metaphysics, eds. J. Barnes, M. Schofield, and R. Sorabji, 50–62. London: Duckworth, 1979.
Priest, G. (1987). In contradiction. The Hague: Martinus Nijhoff (2nd ed.). Oxford: Oxford University Press, 2006.
Priest, G. (1995). Beyond the limits of thought. Cambridge: Cambridge University Press (2nd. ed., Oxford: Oxford University Press, 2002).
Priest, G. (1998). To Be and not to be—that is the answer: Aristotle on the law of non-contradiction. Philosophiegeschichte und Logische Analyse 1: 91–130. (Reprinted as ch. 1 of Priest 2006).
Priest, G. (2005). Towards non-being. Oxford: Oxford University Press.
Priest, G. (2006). Doubt truth to be a liar. Oxford: Oxford University Press.
Simons, P. (1989). Łukasiewicz, Meinong and many-valued logic. In K. Szaniawski (Ed.), The Vienna circle and the Lvov-Warsaw School (pp. 249–91). Dortrecht: Kluwer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Priest, G. (2016). Torn by Reason: Łukasiewicz on the Principle of Contradiction. In: Costreie, S. (eds) Early Analytic Philosophy - New Perspectives on the Tradition. The Western Ontario Series in Philosophy of Science, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-24214-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-24214-9_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24212-5
Online ISBN: 978-3-319-24214-9
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)