Jan Łukasiewicz

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Jan Łukasiewicz
Jan Łukasiewicz.jpg
Born21 December 1878
Died13 February 1956(1956-02-13) (aged 77)
Dublin, Ireland
Alma materLwów University
EraContemporary philosophy
RegionWestern philosophy
SchoolLwów–Warsaw school
Analytical philosophy
Main interests
Philosophical logic, mathematical logic and history of logic
Notable ideas
Polish notation, Łukasiewicz logic

Jan Łukasiewicz (Polish: [ˈjan wukaˈɕɛvʲitʂ]; 21 December 1878 – 13 February 1956) was a Polish logician and philosopher born in Lemberg, a city in the Galician kingdom of Austria-Hungary (now Lviv, Ukraine). His work centred on philosophical logic, mathematical logic, and history of logic. He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Łukasiewicz of a revolutionary paradigm. The Łukasiewicz approach was reinvigorated in the early 1970s in a series of papers by John Corcoran and Timothy Smiley—which inform modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009.[1] Łukasiewicz is regarded as one of the most important historians of logic.


He grew up in 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.

He finished his gymnasium studies in philology and in 1897 went on to Lwów University (which, before the Polish partitions, had been in Poland), where he studied philosophy and mathematics. He was a pupil of philosopher Kazimierz Twardowski.

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.

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.

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

In 1915 he was invited to lecture as a full professor at the University of Warsaw which had re-opened after being closed down by the Tsarist government in the 19th century.

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

In 1928 he married Regina Barwińska.

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 under German occupation. He had been a rector of the university twice. In this period Łukasiewicz and Stanisław Leśniewski founded the Lwów–Warsaw school of logic which was later made internationally famous by Alfred Tarski who had been Leśniewski's student.

At the beginning of World War II he worked at the Warsaw Underground University as part of the secret system of education in Poland during World War II.

He and his wife wanted to move to Switzerland but couldn't get permission from the German authorities. Instead, in the summer of 1944, they left Poland with the help of Heinrich Scholz and spent the last few months of the war in Münster, Germany hoping to somehow go on further, perhaps to Switzerland.

Following the war, he emigrated to Ireland and worked at University College Dublin (UCD) until his death.

Jan Łukasiewicz's papers (post-1945 only) 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. There is a quotation from his paper, Remarks on Nicod's Axiom and on "Generalizing Deduction", page 180;

"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 above is apparently a lithographed report in Polish. The referring paper by Łukasiewicz Remarks on Nicod's Axiom and on "Generalizing Deduction", originally published in Polish in 1931,[2] was later reviewed by H. A. Pogorzelski in the Journal of Symbolic Logic in 1965.[3]

In Łukasiewicz 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 and that he had employed his notation in his logical papers since 1929.[4] He then goes on to cite, as an example, a 1930 paper he wrote with Alfred Tarski on the sentential calculus.[5]

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 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 Forth programming language, and the PostScript page description language.


In 2008 the Polish Information Processing Society established the Jan Łukasiewicz Award, to be presented to the most innovative Polish IT companies.[6]

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.


Selected works[edit]


  • 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[edit]


  1. ^ *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.
  2. ^ Łukasiewicz, Jan, "Uwagi o aksjomacie Nicoda i 'dedukcji uogólniającej'", ("Remarks on Nicod's Axiom and the "Generalizing Deduction"), Księga pamiątkowa Polskiego Towarzystwa Filozoficznego, Lwów 1931.
  3. ^ 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 (Sep. 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.
  4. ^ Cf. Łukasiewicz, (1951) Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Chapter IV "Aristotle's System in Symbolic Form" (section on "Explanation of the Symbolism"), p.78 and on.
  5. ^ 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
  6. ^ "2009 International Multiconference on Computer Science and Information Technology (IMCSIT)", conference report


Further reading[edit]

  • Borkowski, L.; Słupecki, J., "The logical works of J. Łukasiewicz", Studia Logica 8 (1958), 7–56.
  • Kotarbiński, T., "Jan Łukasiewicz's works on the history of logic", Studia Logica 8 (1958), 57–62.
  • Kwiatkowski, T., "Jan Łukasiewicz – A historian of logic", Organon 16–17 (1980–1981), 169–188.
  • Marshall, D., "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, "Jan Łukasiewicz on the Liar Paradox, Logical Consequence, Truth and Induction", Modern Logic 4 (1994), 394–400.

External links[edit]