Jan Łukasiewicz ({{IPA|pol|ˈjan wukaˈɕɛvit͡ʂ|lang|LL-Q809 (pol)-Gower-Jan Łukasiewicz.wav}}; 21 December 1878 – 13 February 1956) was a Polish logician and philosopher who is best known for Polish notation and Łukasiewicz logic. 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, 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.{{sfn|Łukasiewicz|1957}}

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. Łukasiewicz is regarded as one of the most important historians of logic.

Life

He was born in Lwów in Austria-Hungary (now Lviv, Ukraine) 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.{{fact|date=January 2022}}

He finished his gymnasium studies in philology and in 1897 went on to Lwów University, where he studied philosophy and mathematics. He was a pupil of the 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 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.

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.

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.{{fact|date=January 2022}}

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 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 German 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). As it became increasingly clear that Germany would lose the war, Łukasiewicz and his wife tried 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.

In February 1946, at the invitation of Irish political leader Éamon de Valera (himself a mathematician by profession), 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.

During this period, his book Elements of Mathematical Logic was published in English by Macmillan (1963, translated from Polish by Olgierd Wojtasiewicz).{{sfn|Łukasiewicz|1964}}

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.[https://polskieradio24.pl/5/1222/artykul/3074635,na-starych-powazkach-spocznie-dzis-prof-jan-lukasiewiczToday, at the Old Powązki Cemetery, Prof. Jan Łukasiewicz] Polskie Radio 24, 2022-11-22

From October to December 2022, the Royal Irish Academy in Dublin hosted an exhibition on his life and work.[https://www.ria.ie/news/library-library-blog/jan-lukasiewicz-professor-mathematical-logic-royal-irish-academy Jan Łukasiewicz, Professor of Mathematical Logic at the Royal Irish Academy] {{Webarchive|url=https://web.archive.org/web/20240116020230/https://www.ria.ie/news/library-library-blog/jan-lukasiewicz-professor-mathematical-logic-royal-irish-academy |date=2024-01-16}} 7 November 2022, Royal Irish Academy

Łukasiewicz's [https://www.library.manchester.ac.uk/rylands/special-collections/a-to-z/detail/?mms_id=992983876595601631 papers] (post-1945) are held by the University of Manchester Library.

Work

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{{sfn|Łukasiewicz|1931|page=367|loc=Footnote 3}}{{sfn|Łukasiewicz|1970|page=180|loc=Footnote 3}} states how the notation was invented:

{{blockquote|text=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.|author={{harvnb|Łukasiewicz|1970|page=180|loc=Footnote 3}}}}

The reference cited by Łukasiewicz, i.e., Łukasiewicz (1),{{sfn|Łukasiewicz|1929}} is apparently a lithographed report in Polish. The referring paper{{sfn|Łukasiewicz|1931}} by Łukasiewicz was reviewed by Henry A. Pogorzelski in the Journal of Symbolic Logic in 1965.

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.{{sfn|Łukasiewicz|1957|page=78}} He then goes on to cite, as an example, a 1930 paper he wrote with Alfred Tarski on the sentential calculus.{{refn|{{harvnb|Łukasiewicz|Tarski|1930}} {{in lang|de}}. Translation: {{harvnb|Łukasiewicz|Tarski|1956}}}}

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.

Recognition

File:20070206 uw buw hall glowny biblioteki.jpg – 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.

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 three-valued logic allowed for formulating Kleene's ternary logic and a meta-model of empiricism, mathematics and logic, i.e. senary logic.

Chronology

1878 born in Lemberg (now Lviv)
1890–1902 studies with Kazimierz Twardowski in Lemberg (Lwów, L'viv)
1902 doctorate (mathematics and philosophy), University of Lemberg with the highest distinction possible
1906 habilitation thesis completed, University of Lemberg
1906 becomes a lecturer
1910 essays on the principle of non-contradiction and the excluded middle
1911 extraordinary professor at Lemberg
1915 invited to the newly reopened University of Warsaw
1916 new Kingdom of Poland declared
1917 develops three-valued propositional calculus
1919 Polish Minister of Education
1920–1939 professor at Warsaw University founds with Stanisław Leśniewski the Lwów–Warsaw school of logic (see also Alfred Tarski, Stefan Banach, Hugo Steinhaus, Zygmunt Janiszewski, Stefan Mazurkiewicz)
1928 marries Regina Barwińska
1944 flees to Germany and settles in Hembsen, in the Nethegau, where he was brought for his own safety.
1946 exile in Belgium
1946 held a chair at the Royal Irish Academy in Dublin.
1953 writes autobiography
1956 dies in Dublin

Selected works

=Books=

{{cite book | mode=cs2 |last=Łukasiewicz |first=Jan | title=Elementy logiki matematycznej |trans-title=Elements of Mathematical Logic | location =Warsaw | publisher=Państwowe Wydawnictwo Naukowe | year=1928 | language=pl}}

{{cite book | mode=cs2 |last=Łukasiewicz |first=Jan | author-mask=1 | title=Aristotle's Syllogistic from the Standpoint of Modern Formal Logic | publisher= Oxford University Press |edition=2nd, enlarged | year=1957| orig-year=1951|isbn=9780198241447}} (Reprinted by Garland Publishing in 1987, {{ISBN|0-8240-6924-2}})

{{cite book | mode=cs2 |last=Łukasiewicz | first=Jan | author-mask=1 | year=1964 | orig-year=1958 | edition=2nd| title= Elementy logiki matematycznej | language=pl | trans-title=Elements of Mathematical Logic | translator-last=Wojtasiewicz | translator-first=Olgierd |location=New York | publisher=Macmillan | oclc=671498 | lccn=63-10013}}

{{cite book | mode=cs2 |last=Łukasiewicz |first=Jan | author-mask=1 |editor=Jacek Jadacki | title=Logika i metafizyka. Miscellanea | publisher=Warsaw, WFiS UW | year=1998 | language=pl | isbn=83-910113-3-X }}

=Papers=

{{citation | last=Łukasiewicz | first=Jan | year=1903 | title=On Induction as Inversion of Deduction }}

{{cite thesis | mode=cs2 | last=Łukasiewicz | first=Jan | author-mask=1 | year=1906 | title=Analysis and Construction of the Concept of Cause}}

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1910 | title=On the Principle of the Excluded Middle | journal=History and Philosophy of Logic | volume=8 (1987) | pages=67–69 }}

{{cite journal | mode=cs2 | last=Łukasiewicz | first=Jan | author-mask=1 | year=1910 | title=On the Principle of Contradiction in Aristotle | journal=Review of Metaphysics | volume=24 (1971) |issue=3 | pages=485–509|translator-last= Wedin|translator-first=Vernon|jstor=20125812 }}

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1912 | title=Creative Elements in Science}} (included in {{harvnb|Łukasiewicz|1970|pages=1–15}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1913 | title=On the Reversibility of the Relation of Ground and Consequence }}

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1913 | title=Logical Foundations of Probability Theory}} (included in {{harvnb|Łukasiewicz|1970|pages=16–63}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1915 | title=On Science }})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1916 | title=On the Concept of Magnitude}} (included in {{harvnb|Łukasiewicz|1970|pages=64–83}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1918 | title=Farewell Lecture by Professor Jan Lukasiewicz, delivered in the Warsaw University Lecture Hall on March 7, 1918}} (included in {{harvnb|Łukasiewicz|1970|pages=84–86}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1920 | title=On Three-valued Logic }} (included in {{harvnb|Łukasiewicz|1970|pages=87–88}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1921 | title=Two-valued Logic }} (included in {{harvnb|Łukasiewicz|1970|pages=89–109}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1922| title=On Determinism|quote=published for the first time in 1961 }} (included in {{harvnb|Łukasiewicz|1970|pages=110–128}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1922 | title=A Numerical Interpretation of the Theory of Propositions }} (included in {{harvnb|Łukasiewicz|1970|pages=129–130}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1928 | title=Concerning the Method in Philosophy}}

{{cite journal | mode=cs2 | last=Łukasiewicz |first=Jan | author-mask=1 |title=O znaczeniu i potrzebach logiki matematycznej |trans-title=On Importance and Requirements of Mathematical Logic|journal=Nauka Polska |date=1929 |volume=10 |pages=604–620 |language=Polish |url=https://www.sbc.org.pl/dlibra/publication/22955/edition/20205/content?format_id=2}}

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1930 | title=Philosophical Remarks on Many-Valued Systems of Propositional Logic }}

{{cite journal | mode=cs2 | last1=Łukasiewicz | first1=Jan | author1-mask=1 | last2=Tarski | first2=Alfred | year=1930 |title=Untersuchungen über den Aussagenkalkül |language=de| trans-title=Investigations into the Sentential Calculus|journal=Comptes Rendus des séances de la Société des Sciences et des Lettres de Varsovie|volume=23|issue=Cl. III| pages=31–32}} (included in {{harvnb|Łukasiewicz|1970|pages=131–152}})

:{{cite book | mode=cs2 | last1=Łukasiewicz | first1=Jan | author1-mask=1 | last2=Tarski | first2=Alfred | year=1956|orig-year=1930 |title=Logic, Semantics, Metamathematics: Papers from 1923 to 1938 by Alfred Tarski|chapter= Chapter IV: Investigations into the Sentential Calculus|translator-first=Woodger|translator-last=J. H.|publisher=Oxford University Press|pages=39–59}}

:{{cite book | mode=cs2 |last1=Łukasiewicz | first1=Jan | author1-mask=1 | last2=Tarski | first2=Alfred | year=1983|orig-year=1930 |title=Logic, Semantics, Metamathematics: Papers from 1923 to 1938 by Alfred Tarski|chapter= Chapter IV: Investigations into the Sentential Calculus|editor-first=Corcoran|editor-last=John|translator-first=Woodger|translator-last=J. H.|publisher=Hackett Publishing Company|pages=38–59|isbn=0915144-76-X|url=https://books.google.com/books?id=2uhra9PEFZsC|access-date=2025-04-07|edition=2nd}}

{{cite journal | mode=cs2 | last=Łukasiewicz | first=Jan | author-mask=1 | year=1930 | title=Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls | trans-title= Philosophical Remarks on Many-Valued Systems of Propositional Logic| journal=Comptes rendus de la Société des Sciences et des Lettres de Varsovie, cl. III | volume=23 | pages=51–77}} (included in {{harvnb|Łukasiewicz|1970|pages=153–178}})

{{cite encyclopedia | mode=cs2 |last=Łukasiewicz |first=Jan | author-mask=1 |url=https://sbc.org.pl/dlibra/docmetadata?showContent=true&id=18864 |title=Uwagi o aksjomacie Nicoda i 'dedukcji uogólniającej' |trans-title=Comments on Nicod's Axiom and on 'Generalizing Deduction' |encyclopedia=Księga pamiątkowa Polskiego Towarzystwa Filozoficznego We Lwowie, 12. II. 1904-12. II. 1929 |date=1931|publisher=Wydawnictwo Polskie Towarzystwo Filozoficzne |location=Lwów |pages=366–383 |language=Polish}} (included in {{harvnb|Łukasiewicz|1970|pages=179–196}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1934 | title=Importance of Logical Analysis for Knowledge }}

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1934 | title=Outlines of the History of the Propositional Logic }} (included in {{harvnb|Łukasiewicz|1970|pages=197–217}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1936 | title=Logistic and Philosophy }} (included in {{harvnb|Łukasiewicz|1970|pages=218–235}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1937 | title=In Defense of Logistic }} (included in {{harvnb|Łukasiewicz|1970|pages=236–249}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year= 1938| title=The Equivalential Calculus}} (included in {{harvnb|Łukasiewicz|1970|pages=250–277}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year= 1927| title=Logic and the Problem of the Foundations of Mathematics}} (included in {{harvnb|Łukasiewicz|1970|pages=278–294}})

{{cite journal | mode=cs2 | last=Łukasiewicz | first=Jan | author-mask=1 | year=1948 | title=The Shortest Axiom of the Implicational Calculus of Propositions|journal=Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences|volume=52|publisher=Royal Irish Academy|pages=25–33|jstor=20488489}} (included in {{harvnb|Łukasiewicz|1970|pages=295–305}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year= 1950| title=On the System of Axioms of the Implicational Propositional Calculus}} (included in {{harvnb|Łukasiewicz|1970|pages=306–310}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1938 | title=On Descartes's Philosophy }}

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1951 | title=On Variable Functors of Propositional Arguments }} (included in {{harvnb|Łukasiewicz|1970|pages=311–324}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1952 | title=On the Intuitionistic Theory of Deduction }} (included in {{harvnb|Łukasiewicz|1970|pages=325–340}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1953 | title=Formalization of Mathematical Theories}} (included in {{harvnb|Łukasiewicz|1970|pages=341–351}})

{{cite journal | mode=cs2 | last=Łukasiewicz | first=Jan | author-mask=1 | year=1953 | title=A System of Modal Logic | url=https://archive.org/details/journal-of-computing-systems_1953-07_1_3/page/111/ | journal=The Journal of Computing Systems | volume=1 | issue=3 | pages=111–149 | access-date=2025-03-24}} (included in {{harvnb|Łukasiewicz|1970|pages=352–390}})

{{cite book | mode=cs2 |last=Łukasiewicz | first=Jan | author-mask=1 | year=1954 | title=Arithmetic and Modal Logic}} (included in {{harvnb|Łukasiewicz|1970|pages=391–400}})

{{citation | last=Łukasiewicz | first=Jan | author-mask=1 | year=1954 | title=On a Controversial Problem of Aristotle's Modal Syllogistic}}

{{cite book | mode=cs2 |last=Łukasiewicz | first=Jan | author-mask=1 | year=1970 | title=Selected Works | language=en | pages=405|url=https://archive.org/details/selectedworks0000ukas/page/n5/ | editor-last=Borkowski | editor-first=L. | editor-link=:pl:Ludwik Borkowski | location=Amsterdam and London/Warszawa | publisher=North-Holland Publishing Company/Polish Scientific Publishers | isbn=978-0720422528 |lccn=74-96734|oclc=115237|quote=Contains List of Publications by Jan Łukasiewicz, pp. 401–405}}

References

{{Reflist|refs=

"[https://www.irishtimes.com/opinion/home-from-home-an-irishman-s-diary-on-polish-logician-mathematician-and-philosopher-jan-lukasiewicz-1.3853608 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

[https://www.porta-polonica.de/en/atlas-of-remembrance-places/jan-lukasiewicz?page=2 Jan Łukasiewicz on Porta Polonica]

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, [https://ndpr.nd.edu/review.cfm?id=18787 2010.02.02] {{Webarchive|url=https://web.archive.org/web/20110615062213/http://ndpr.nd.edu/review.cfm?id=18787 |date=2011-06-15}}.

{{Cite SEP|mode=cs2 |url-id=lukasiewicz|title=Jan Łukasiewicz|last=Simons|first=Peter|date=Spring 2023}}

{{cite journal | mode=cs2 |last=Pogorzelski | first=H. A. | date=September 1965|jstor=2269644|title=Remarks on Nicod's Axiom and on "Generalizing Deduction" by Jan Łukasiewicz, Jerzy Słupecki, Państwowe Wydawnictwo Naukowe|journal=Journal of Symbolic Logic|volume=30|issue=3|pages=376–377|doi=10.2307/2269644}}

[http://2010.imcsit.org/pg/331/261 "2009 International Multiconference on Computer Science and Information Technology (IMCSIT)"], conference report

{{citation |title=Models of 6-valued measures: 6-kinds of information |author-first=Jan |author-last=Zi |publisher=Kindle Direct Publishing Science |date=2019 |url=https://www.amazon.com/dp/B081PT2CPR}}

}}

External links

{{cite SEP|url-id=lukasiewicz|title=Jan Łukasiewicz|author-last=Simons|author-first=Peter|author-link=Peter Simons (academic)|date=Spring 2023}}
{{MacTutor Biography|id=Lukasiewicz}}
[https://web.archive.org/web/20091127190318/http://segr-did2.fmag.unict.it/~polphil/PolPhil/Lukas/Lukas.html Łukasiewicz entry at Polish Philosophy Page], ed. by Francesco Coniglione (University of Catania)
{{MathGenealogy |id=13346}}

Category:20th-century Polish mathematicians

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Category:Polish logicians

Category:Philosophers of logic

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Category:Academics of University College Dublin

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Category:Scientists from Lviv

Category:1878 births

Category:1956 deaths

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