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Łukasiewicz and the Several Senses of Possibility

Published online by Cambridge University Press:  29 January 2015

Peter Simons
Peter Simons*
Affiliation:
Trinity College Dublin, Ireland. E-mail: psimons@tcd.ie
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Abstract

The most famous achievement of Jan Łukasiewicz (1878–1956) was to give the first rigorous formulation of many-valued logic. In this paper I discuss his motivations for this, which were philosophical, and the legacy of his work.

Type
Focus: Logic and Philosophy in Poland
Information
European Review , Volume 23 , Issue 1 , February 2015 , pp. 114 - 124
Copyright
© Academia Europaea 2015 

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References

Selected Works by Łukasiewicz

Collections

Z zagadnień logiki i filozofii. Pisma wybrane. [Topics in Logic and Philosophy. Selected Writings], edited by J. Słupecki (Warsaw: PWN, 1961). [Abbreviated below as Z].Google Scholar
Selected Works, edited by L. Borkowski (Amsterdam: North-Holland, 1970). [Abbreviated below as SW].Google Scholar
Logika i Metafizyka. Miscellanea. [Logic and Metaphysics. A Miscellany], edited by J. J. Jadacki (Warsaw: Towarzystwo Naukowe Warszawskie, 1998).Google Scholar
Pamiętnik [Diary], edited by J. J. Jadacki and P. Surma (Warsaw: Semper, 2013) [Contains reminiscences, written mainly around 1949, keyed to certain days of the year, along with miscellaneous recollections by others, assorted biographical and chronological details, and copious photographs].Google Scholar

Monographs

O zasadzie sprzeczności u Arystotelesa, Studium krytyczne. [On the Principle of Contradiction in Aristotle. A Critical Study.] Kraków: Akademia Umiejętności, 1910. 2nd ed., edited by J. Woleński (Warsaw: PWN, 1987). Translations: Über den Satz vom Widerspruch bei Aristoteles (Hildesheim: Olms, 1993); Del principio di contradizzione in Aristotele (Macerata: Quodlibet, 2003).Google Scholar
Die logischen Grundlagen der Wahrscheinlichkeitsrechnung (Kraków: Spółka Wydawnicza Polska, 1913). Translation: Logical Foundations of Probability Theory, in SW, 16–63.Google Scholar
Elementy logiki matematycznej. Skrypt autoryzowany, edited by M. Presburger (Warsaw: Wydawnictwo Koła Matematyczno-Fizycznego Słuchaczów Uniwersytetu Warszawskiego, 1929). 2nd edition, edited by J. Słupecki (Warsaw: PWN, 1958). Translation: Elements of Mathematical Logic (Oxford: Pergamon Press, 1966).Google Scholar
Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic (Oxford: Clarendon Press, 1951; 2nd, enlarged edition, 1957).Google Scholar

Papers

O zasadzie wyłączonego środka. Przegłąd Filozoficzne 13(1910), 372–373. Translation: On the principle of the excluded middle. History and Philosophy of Logic, 8(1987), pp. 67–69.Google Scholar
Über den Satz von Widerspruch bei Aristoteles. Bulletin internationale de l’Académie des Sciences de Cracovie, Classe de Philosophie (1910), pp. 15–38. Translation: On the principle of contradiction in Aristotle. Review of Metaphysics, 24(1970/71), pp. 485–509; Aristotle on the law of contradiction. In: J. Barnes, M. Schofield and R. Sorabji (eds), Articles on Aristotle 3. Metaphysics (London: Duckworth, 1979), pp. 50–62.Google Scholar
Treść wykładu pożegnalnego wygłoszonego w auli Uniwersytetu Warszawskiego 7 marca 1918 r. Pro arte et studio 3(1918), pp. 3–4. Translation: Farewell lecture delivered in the Warsaw University Lecture Hall on March 7, 1918, in SW, pp. 84–86.Google Scholar
O pojęciu możliwości, Ruch Filozoficzne, 5(1920), pp. 169–170. Translation: On the concept of possibility, in PL, pp. 15–16.Google Scholar
O logice trójwartościowej, Ruch Filozoficzne, 5(1920), pp. 170–171. Translation: On three-valued logic, in PL, pp. 16–18, and in SW, pp. 87–88.Google Scholar
Interpretacja liczbowa teorii zdań, Ruch Filozoficzne, 7(1922/23), pp. 92–93. Translation: A numerical interpretation of the theory of propositions, in SW, pp. 129–130.Google Scholar
(with A. Tarski) Untersuchungen über den Aussagenkalkül, Comptes rendus de la Société des Sciences et des Lettres de Varsovie, cl. iii, 23 (1930), 1–21. Translation: Investigations into the Sentential Calculus, in SW, pp. 131–152.Google Scholar
Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls, Comptes rendus de la Société des Sciences et des Lettres de Varsovie, cl. iii, 23 (1930), pp. 51–77. Translation: Philosophical remarks on many-valued systems of propositional logic. In: S. McCall (ed.), Polish Logic, 1920–1939. [Abbreviated below as PL.] (Oxford: Clarendon, 1967), pp. 40–65, and in SW, pp. 153–78.Google Scholar
Geneza logiki trójwartościowej [The origins of three-valued logic]. Nauka Polska, 24(1939), pp. 215–223.Google Scholar
A system of modal logic, The Journal of Computing Systems, 1(1953), pp. 111–149, reprinted in SW, pp. 352–390.Google Scholar
Arithmetic and modal logic, The Journal of Computing Systems, 1(1954), pp. 213–219, reprinted in SW, pp. 391–400.Google Scholar
On a controversial problem of Aristotle’s modal syllogistic, Dominican Studies, 7(1954), pp. 114–128.Google Scholar
O determinizmie, in Z, pp. 114–126. Translation: On determinism, in PL, pp. 19–39, and in SW, pp. 110–128.Google Scholar