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Jan Łukasiewicz

Jan Łukasiewicz
Łukasiewicz in 1935
Born21 December 1878
Died13 February 1956(1956-02-13) (aged 77)
Alma materLemberg University
Era20th-century philosophy
RegionWestern philosophy
SchoolLwów–Warsaw school
Analytical philosophy
Main interests
Philosophical logic, mathematical logic and history of logic
Notable ideas
Polish notation
Łukasiewicz logic
Łukasiewicz–Moisil algebra
Reductive reasoning

Jan Łukasiewicz (Polish: [ˈjan wukaˈɕɛvit͡ʂ] ; 21 December 1878 – 13 February 1956) was a Polish logician and philosopher who is best known for Polish notation and Łukasiewicz logic.[1] His work centred on philosophical logic, mathematical logic and history of logic.[2] He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle, offering one of the earliest systems of many-valued logic. Contemporary research on Aristotelian logic also builds on innovative works by Łukasiewicz, which applied methods from modern logic to the formalization of Aristotle's syllogistic.[3]

The Łukasiewicz approach was reinvigorated in the early 1970s in a series of papers by John Corcoran and Timothy Smiley that inform modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009.[4] Łukasiewicz is regarded as one of the most important historians of logic.


He was born in Lemberg in Austria-Hungary (now Lviv, Ukraine; Polish: Lwów) and was the only child of Paweł Łukasiewicz, a captain in the Austrian army, and Leopoldina, née Holtzer, the daughter of a civil servant. His family was Roman Catholic.[citation needed]

He finished his gymnasium studies in philology and in 1897 went on to Lemberg University, where he studied philosophy and mathematics. He was a pupil of the philosopher Kazimierz Twardowski.[5]

In 1902, he received a Doctor of Philosophy degree under the patronage of Emperor Franz Joseph I of Austria, who gave him a special doctoral ring with diamonds.[6]

He spent three years as a private teacher, and in 1905, he received a scholarship to complete his philosophy studies at the University of Berlin and the University of Louvain in Belgium.[6]

Łukasiewicz continued studying for his habilitation qualification and in 1906 submitted his thesis to the University of Lemberg. That year, he was appointed a lecturer at the University of Lemberg, where he was eventually appointed Extraordinary Professor by Emperor Franz Joseph I. He taught there until the First World War.[6]

In 1915, he was invited to lecture as a full professor at the University of Warsaw, which the German occupation authorities had reopened after it had been closed down by the Tsarist government in the 19th century.[6]

In 1919, Łukasiewicz left the university to serve as Polish Minister of Religious Denominations and Public Education in Paderewski's government until 1920. Łukasiewicz led the development of a Polish curriculum replacing the Russian, German and Austrian curricula that had been used in partitioned Poland. The Łukasiewicz curriculum emphasized the early acquisition of logical and mathematical concepts.[citation needed]

In 1928, he married Regina Barwińska.[6]

He remained a professor at the University of Warsaw from 1920 until 1939, when the family house was destroyed by German bombs, and the university was closed by the German occupation. He had been a rector of the university twice during which Łukasiewicz and Stanisław Leśniewski had founded the Lwów–Warsaw school of logic, which was later made famous internationally by Alfred Tarski, who had been a student of Leśniewski.

During the start of the Second World War, he worked at the Warsaw Underground University. After the Nazi occupation authorities had closed the university, he earned a meager living in the Warsaw city archive. His friendship with Heinrich Scholz (German professor of mathematical logic) helped him, too, and it was Scholz who arranged for the Łukasiewicz family's passage to Germany in 1944 (Łukasiewicz was fearful of the Red Army advance). Jan Łukasiewicz and his wife wanted to move to Switzerland but were unable to get permission from the German authorities. They thus spent the last months of the war in Münster, Germany. After the end of the war, unwilling to return to a Soviet-controlled Poland, they moved first to Belgium, where Łukasiewicz taught logic at a provisional Polish Scientific Institute.[6]

In February 1946, at the invitation of Irish political leader Éamon de Valera, Łukasiewicz and his wife relocated to Dublin, where they remained until his death there a decade later. In Ireland, he briefly served as Professor of Mathematical Logic at the Royal Irish Academy (a position created for him). His duties involved giving frequent public lectures.[7]

During this period, his book Elements of Mathematical Logic was published in English by Macmillan (1963, translated from Polish by Olgierd Wojtasiewicz).

Jan Łukasiewicz died on 13 February 1956. He was buried in Mount Jerome Cemetery, in Dublin. At the urging of the Armenian community in Poland, his remains were repatriated to Poland 66 years later. He was reburied on 22 November 2022 in Warsaw's Old Powązki Cemetery.[8]

From October to December 2022, the Royal Irish Academy in Dublin hosted an exhibition on his life and work.[9]

Łukasiewicz's papers (post-1945) are held by the University of Manchester Library.


A number of axiomatizations of classical propositional logic are due to Łukasiewicz. A particularly elegant axiomatization features a mere three axioms and is still invoked to the present day. He was a pioneer investigator of multi-valued logics; his three-valued propositional calculus, introduced in 1917, was the first explicitly axiomatized non-classical logical calculus. He wrote on the philosophy of science, and his approach to the making of scientific theories was similar to the thinking of Karl Popper.

Łukasiewicz invented the Polish notation (named after his nationality) for the logical connectives around 1920. A quotation from a paper by Jan Łukasiewicz in 1931[10]: 367, Footnote 3) [11]: 180, Footnote 3)  states how the notation was invented:

I came upon the idea of a parenthesis-free notation in 1924. I used that notation for the first time in my article Łukasiewicz (1), p. 610, footnote.

The reference cited by Łukasiewicz, i.e., Łukasiewicz (1),[12] is apparently a lithographed report in Polish. The referring paper[10] by Łukasiewicz was reviewed by Henry A. Pogorzelski in the Journal of Symbolic Logic in 1965.[13]

In Łukasiewicz's 1951 book, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, he mentions that the principle of his notation was to write the functors before the arguments to avoid brackets (i.e., parentheses) and that he had employed his notation in his logical papers since 1929.[3]: 78  He then goes on to cite, as an example, a 1930 paper he wrote with Alfred Tarski on the sentential calculus.[14]

This notation is the root of the idea of the recursive stack, a last-in, first-out computer memory store proposed by several researchers including Turing, Bauer and Hamblin, and first implemented in 1957. In 1960, Łukasiewicz's notation concepts and stacks were used as the basis of the Burroughs B5000 computer designed by Robert S. Barton and his team at Burroughs Corporation in Pasadena, California. The concepts also led to the design of the English Electric multi-programmed KDF9 computer system of 1963, which had two such hardware register stacks. A similar concept underlies the reverse Polish notation (RPN, a postfix notation) of the Friden EC-130 calculator and its successors, many Hewlett-Packard calculators, the Lisp and Forth programming languages, and the PostScript page description language.


Warsaw University Library – at entrance (seen from rear) are pillared statues of Lwów-Warsaw School philosophers (right to left) Kazimierz Twardowski, Jan Łukasiewicz, Alfred Tarski, Stanisław Leśniewski.

In 2008 the Polish Information Processing Society established the Jan Łukasiewicz Award, to be presented to the most innovative Polish IT companies.[15]

From 1999 to 2004, the Department of Computer Science building at UCD was called the Łukasiewicz Building, until all campus buildings were renamed after the disciplines they housed.

His model of 3-valued logic allowed for formulating Kleene's ternary logic and a meta-model of empiricism, mathematics and logic, i.e. senary logic.[16]


Selected works


  • Łukasiewicz, Jan (1951). Aristotle's Syllogistic from the Standpoint of Modern Formal Logic. Oxford University Press. 2nd Edition, enlarged, 1957. Reprinted by Garland Publishing in 1987. ISBN 0-8240-6924-2
  • Łukasiewicz, Jan (1928). Elementy logiki matematycznej (in Polish). Warsaw, Państwowe Wydawnictwo Naukowe. OCLC 11322101.
  • Łukasiewicz, Jan (1964) [1963]. Elements of Mathematical Logic. Translated from Polish by Olgierd Wojtasiewicz. New York, Macmillan. OCLC 671498.
  • Łukasiewicz, Jan (1970). Ludwik Borkowski (ed.). Selected Works. North-Holland Pub. Co. ISBN 0-7204-2252-3. OCLC 115237.
  • Łukasiewicz, Jan (1998). Jacek Jadacki (ed.). Logika i metafizyka. Miscellanea (in Polish). Warsaw, WFiS UW. ISBN 83-910113-3-X.


  • 1903 "On Induction as Inversion of Deduction"
  • 1906 "Analysis and Construction of the Concept of Cause"
  • 1910 "On Aristotle's Principle of Contradiction"
  • 1913 "On the Reversibility of the Relation of Ground and Consequence"
  • 1920 "On Three-valued Logic"
  • 1921 "Two-valued Logic"
  • 1922 "A Numerical Interpretation of the Theory of Propositions"
  • 1928 "Concerning the Method in Philosophy"
  • 1929 "Elements of Mathematical Logic"
  • 1929 "On Importance and Requirements of Mathematical Logic"
  • 1930 "Philosophical Remarks on Many-Valued Systems of Propositional Logic"
  • 1930 "Investigations into the Sentential Calculus" ["Untersuchungen über den Aussagenkalkül"], with Alfred Tarski
  • 1931 "Comments on Nicod's Axiom and the 'Generalizing Deduction'"
  • 1934 "On Science"
  • 1934 "Importance of Logical Analysis for Knowledge"
  • 1934 "Outlines of the History of the Propositional Logic"
  • 1936 "Logistic and Philosophy"
  • 1937 "In Defense of the Logistic"
  • 1938 "On Descartes's Philosophy"
  • 1943 "The Shortest Axiom of the Implicational Calculus of Propositions"
  • 1951 "On Variable Functors of Propositional Arguments"
  • 1952 "On the Intuitionistic Theory of Deduction"
  • 1953 "A System of Modal Logic"
  • 1954 "On a Controversial Problem of Aristotle's Modal Syllogistic"

See also


  1. ^ "Home from home – An Irishman’s Diary on Polish logician, mathematician and philosopher Jan Lukasiewicz" by Oliver O’Hanlon, The Irish Times, 2019-04-08
  2. ^ Jan Łukasiewicz on Porta Polonica
  3. ^ a b Łukasiewicz, Jan (1957) [1951]. Aristotle's Syllogistic from the Standpoint of Modern Formal Logic (2 ed.). Oxford University Press. (Reprinted by Garland Publishing in 1987, ISBN 0-8240-6924-2.)
  4. ^ Review of "Aristotle, Prior Analytics: Book I, Gisela Striker (translation and commentary), Oxford UP, 2009, 268pp., $39.95 (pbk), ISBN 978-0-19-925041-7." in the Notre Dame Philosophical Reviews, 2010.02.02 Archived 2011-06-15 at the Wayback Machine.
  5. ^ Jan Łukasiewicz at the Mathematics Genealogy Project
  6. ^ a b c d e f "Jan Łukasiewicz". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. 2021.
  7. ^ Jan Łukasiewicz Stanford Encyclopedia of Philosophy
  8. ^ at the Old Powązki Cemetery, Prof. Jan Łukasiewicz Polskie Radio 24, 22-11-2022
  9. ^ Jan Łukasiewicz, Professor of Mathematical Logic at the Royal Irish Academy 07 November 2022, Royal Irish Academy
  10. ^ a b Łukasiewicz, Jan (1931). "Uwagi o aksjomacie Nicoda i 'dedukcji uogólniającej'" [Comments on Nicod's Axiom and on 'Generalizing Deduction']. Księga pamiątkowa Polskiego Towarzystwa Filozoficznego We Lwowie, 12. II. 1904-12. II. 1929 (in Polish). Lwów: Wydawnictwo Polskie Towarzystwo Filozoficzne. pp. 366–383.
  11. ^ Łukasiewicz, Jan (1970). "Comments on Nicod's Axiom and on 'Generalizing Deduction'". In Borkowski, L. (ed.). Selected Works. Amsterdam and London/Warszawa: North-Holland Publishing Company/Polish Scientific Publishers. pp. 179–196.
  12. ^ Łukasiewicz, Jan (1929). "O znaczeniu i potrzebach logiki matematycznej". Nauka Polska (in Polish). 10: 604–620.
  13. ^ Pogorzelski, H. A., "Reviewed work(s): Remarks on Nicod's Axiom and on "Generalizing Deduction" by Jan Łukasiewicz; Jerzy Słupecki; Państwowe Wydawnictwo Naukowe", The Journal of Symbolic Logic, Vol. 30, No. 3 (September 1965), pp. 376–377. This paper by Jan Łukasiewicz was re-published in Warsaw in 1961 in a volume edited by Jerzy Słupecki. It had been published originally in 1931 in Polish.
  14. ^ Łukasiewicz, Jan; Tarski, Alfred, "Untersuchungen über den Aussagenkalkül" ["Investigations into the sentential calculus"], Comptes Rendus des séances de la Société des Sciences et des Lettres de Varsovie, Vol. 23 (1930) Cl. III, pp. 31–32. This paper can be found translated into English in Chapter IV "Investigations into the Sentential Calculus", pp.39-59, in Logic, Semantics, Metamathematics: Papers from 1923 to 1938 by Alfred Tarski, translated into English by J. H. Woodger, Oxford University Press, 1956; 2nd edition, Hackett Publishing Company, 1983
  15. ^ "2009 International Multiconference on Computer Science and Information Technology (IMCSIT)", conference report
  16. ^ Zi, Jan (2019), Models of 6-valued measures: 6-kinds of information, Kindle Direct Publishing Science

Further reading

  • Kotarbiński, Tadeusz, "Jan Łukasiewicz's Works on the History of Logic", Studia Logica 8 (1958), 57–63 JSTOR 20013605. (7 pages)
  • Kwiatkowski, Tadeusz, "Jan Łukasiewicz – A historian of logic", Organon 16–17 (1980–1981), 169–188.
  • Łukasiewicz, Jan; Heine, Holger R. (2021). The Principle of Contradiction in Aristotle: A Critical Study. Honolulu, Hawaii: Topos Productions. ISBN 978-1943354061.
  • Marshall Jr., David, "Łukasiewicz, Leibniz and the arithmetization of the syllogism", Notre Dame Journal of Formal Logic 18 (2) (1977), 235–242.
  • Seddon, Frederick (1996). Aristotle & Łukasiewicz on the Principle of Contradiction. Ames, Iowa: Modern Logic Pub. ISBN 1-884905-04-8. OCLC 37533856.
  • Woleński, Jan (1994). Philosophical Logic in Poland. Kluwer Academic Publishers. ISBN 0-7923-2293-2. OCLC 27938071.
  • Woleński, Jan (1994). "Jan Łukasiewicz on the Liar Paradox, Logical Consequence, Truth and Induction". Modern Logic (4): 394–400.
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