Jan Łukasiewicz

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Jan Łukasiewicz 1935

Jan Łukasiewicz [ jan wukaˈɕɛvʲitʃ ] (born  December 21, 1878 in Lemberg , †  February 13, 1956 in Dublin ) was a Polish philosopher , mathematician and logician .


From 1915 to 1939, Łukasiewicz was a professor at the Universities of Lviv and Warsaw , and was twice rector at the latter. His work there was dominated by the Lemberg-Warsaw School , whose basic research on mathematical logic made the University of Warsaw a center of logic in the period after the First World War . Alfred Tarski was one of his students and later colleagues . In 1919, Łukasiewicz was Polish Minister of Education for a short time.

In 1938 the University of Münster awarded him an honorary doctorate in philosophy. During the occupation after the German invasion of Poland , he worked at the secret Warsaw Underground University ( Tajny Uniwersytet Warszawski ). He experienced the end of the war in Hembsen , where his friend German mathematicians had taken him for his own safety. In 1949 he went to Dublin, where he was offered a professorship at the university and worked for the rest of his life.

He later introduced the so-called Polish notation (prefix notation), in which the operator of an expression (e.g. a mathematical formula) is written in front of the operand and thus does not need parentheses: instead of 8 + 5 , you write + 8 5 . The reverse Polish notation (postfix notation) was derived from this later , in which the operators are written after their operands (e.g. 8 5 + ).

Jan Łukasiewicz formalized the trivalent logic Ł 3 in 1920 and created the first multi-valued and thus non-classical logical calculus . His work also dealt with classical logic . Independent of Bernays and Post , he proved the completeness and consistency of classical propositional logic .

In his multi-valued logics he used truth value functions , which are now known as Łukasiewicz-Tarski negation and Łukasiewicz-Tarski implication .

Jan Łukasiewicz also wrote groundbreaking works on the history of logic. He reconstructed the Aristotelian syllogistics and discovered next to Martha Kneale the importance of stoic logic, which he considered to be the earliest historical form of propositional logic (today priority is assigned to the "dialecticians" Diodoros Kronos and Philo of Megara ). With this reassessment, he freed the Stoa from the old and persistent judgment that it had introduced a sterile formalism into logic and added a new chapter to the history of logic.


  • Jan Łukasiewicz, Alfred Tarski: Studies on the propositional calculus , Comptes Rendus Séances Société des Sciences et Lettres Varsovie, Cl. III, 23 (1930), pp. 30-50.
  • Jan Łukasiewicz: Philosophical remarks on multi-valued systems of the propositional calculus . In: Comptes rend. d. séances dl Soc. d. Sciences et d. Lettres d. Vars. Cl. III . 1930
  • Jan Łukasiewicz: Z historii logiki zdań . In: Przegl. filoz. 37 (1934), pp. 417–437 (German: On the history of propositional logic . In: Knowledge , Volume 5, 1935, pp. 111–131). (Discovery of the stoic join logic)
  • Jan Łukasiewicz: Aristotle's syllogistic. From the standpoint of modern formal logic . Oxford: Clarendon Press, 1951.
  • Jan Łukasiewicz: Elements of mathematical logic . Transl. from the Polish by Olgierd Wojtasiewicz. Oxford [u. a.]: Pergamon Press / Warszawa: Państwowe Wydawnictwo Naukowe, 1963 (= Internat. Series of monographs on pure and applied mathematics; 31). (Ubs. Of 'Elementy logiki matematycznej')
  • Jan Łukasiewicz: Selected works . Ed. by Ludwig Borkowski. Amsterdam, London: North-Holland Publ. Comp./Warszawa: Pol. Scientif. Publ., 1970 (= Studies in logic and the foundations of mathematics). ISBN 0-7204-2252-3
  • Jan Łukasiewicz: About the principle of contradiction in Aristotle . Hildesheim u. a .: Olms, 1993 (= on the modern interpretation of Aristotelian logic; 5) (excerpt from 'O zasadzie sprzeczności u Arystotelesa'. Studyum krytyczne. Kraków, 1910)


  • Hans-Christoph Schmidt am Busch, Kai F. Wehmeier : Heinrich Scholz and Jan Łukasiewicz . In: Forum (for Eastern European History of Ideas and Contemporary History) , Volume 11, Number 2, 2007, pp. 107–125. Translation: "On the Relations between Heinrich Scholz and Jan Łukasiewicz," History and Philosophy of Logic 28 (2007), 67–81.
  • Frederick Seddon: Aristotle & Łukasiewicz on the Principle of Contradiction (= Modern Logic, 1996) ISBN 1-884905-04-8
  • Mieszko Tałasiewicz: Jan Łukasiewicz - The Quest for the Form of Science , in: Wladyslaw Krajewski (ed.): Polish Philosophers of Science and Nature in the 20th Century , Amsterdam-New York: Rodopi 2001, pages 27-35 ISBN 90-420 -1497-0
  • Jan Wolenski (Ed.): Philosophical Logic in Poland , Kluwer 1994 ISBN 0-7923-2293-2

Web links

Individual evidence

  1. “The decidability of propositional logic, through the use of truth tables, was known to Frege and Peirce; a proof of its decidability is attributable to Jan Łukasiewicz and Emil Post independently in 1921. ”(“ Logic ”, in: Encyclopaedia Britannica, 15th ed. 2003, volume 23, page 279, column 2)