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Jan Łukasiewicz

December 04, 2023

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.

Life edit

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.

Work edit

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.

Recognition edit

 
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]

Chronology edit

Selected works edit

Books 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.

Papers edit

  • 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

References edit

  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 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 edit

  • "Curriculum Vitae of Jan Łukasiewicz", Rome, Italy: Metalogicon journal, (1994) VII, 2 (July–December issue).
  • Craig, Edward (general editor), "Article: Jan Łukasiewicz", Routledge Encyclopedia of Philosophy, 1998, Volume 5, pp. 860–863.
  • Borkowski, Ludwik [pl]; Słupecki, Jerzy, "The Logical Works of J. Łukasiewicz", Studia Logica 8 (1958), 7–56. JSTOR 20013604. (51 pages)
  • 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 1943354065.
  • 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.

External links edit

December 04, 2023
Łukasiewicz, polish, ˈjan, wukaˈɕɛvit, december, 1878, february, 1956, polish, logician, philosopher, best, known, polish, notation, Łukasiewicz, logic, work, centred, philosophical, logic, mathematical, logic, history, logic, thought, innovatively, about, tra. Jan Lukasiewicz Polish ˈjan wukaˈɕɛvit ʂ 21 December 1878 13 February 1956 was a Polish logician and philosopher who is best known for Polish notation and Lukasiewicz 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 Lukasiewicz which applied methods from modern logic to the formalization of Aristotle s syllogistic 3 Jan Lukasiewicz1935Born21 December 1878Lemberg Kingdom of Galicia and Lodomeria Austria HungaryDied13 February 1956 1956 02 13 aged 77 Dublin Republic of IrelandNationalityPolishAlma materLemberg UniversityEra20th century philosophyRegionWestern philosophy Polish philosophySchoolLwow Warsaw schoolAnalytical philosophyMain interestsPhilosophical logic mathematical logic and history of logicNotable ideasPolish notationLukasiewicz logicLukasiewicz Moisil algebraReductive reasoningThe Lukasiewicz 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 Lukasiewicz is regarded as one of the most important historians of logic Contents 1 Life 2 Work 3 Recognition 4 Chronology 5 Selected works 5 1 Books 5 2 Papers 6 See also 7 References 8 Further reading 9 External linksLife editHe was born in Lemberg in Austria Hungary now Lviv Ukraine Polish Lwow and was the only child of Pawel Lukasiewicz a captain in the Austrian army and Leopoldina nee 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 Lukasiewicz 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 Lukasiewicz left the university to serve as Polish Minister of Religious Denominations and Public Education in Paderewski s government until 1920 Lukasiewicz led the development of a Polish curriculum replacing the Russian German and Austrian curricula that had been used in partitioned Poland The Lukasiewicz curriculum emphasized the early acquisition of logical and mathematical concepts citation needed In 1928 he married Regina Barwinska 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 Lukasiewicz and Stanislaw Lesniewski had founded the Lwow Warsaw school of logic which was later made famous internationally by Alfred Tarski who had been a student of Lesniewski 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 Lukasiewicz family s passage to Germany in 1944 Lukasiewicz was fearful of the Red Army advance Jan Lukasiewicz 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 Munster Germany After the end of the war unwilling to return to a Soviet controlled Poland they moved first to Belgium where Lukasiewicz taught logic at a provisional Polish Scientific Institute 6 In February 1946 at the invitation of Irish political leader Eamon de Valera Lukasiewicz 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 Lukasiewicz 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 Powazki Cemetery 8 From October to December 2022 the Royal Irish Academy in Dublin hosted an exhibition on his life and work 9 Lukasiewicz s papers post 1945 are held by the University of Manchester Library Work editA number of axiomatizations of classical propositional logic are due to Lukasiewicz 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 Lukasiewicz invented the Polish notation named after his nationality for the logical connectives around 1920 A quotation from a paper by Jan Lukasiewicz 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 Lukasiewicz 1 p 610 footnote The reference cited by Lukasiewicz i e Lukasiewicz 1 12 is apparently a lithographed report in Polish The referring paper 10 by Lukasiewicz was reviewed by Henry A Pogorzelski in the Journal of Symbolic Logic in 1965 13 In Lukasiewicz 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 Lukasiewicz 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 edit nbsp Warsaw University Library at entrance seen from rear are pillared statues of Lwow Warsaw School philosophers right to left Kazimierz Twardowski Jan Lukasiewicz Alfred Tarski Stanislaw Lesniewski In 2008 the Polish Information Processing Society established the Jan Lukasiewicz 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 Lukasiewicz 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 Chronology edit1878 born in Lemberg now Lviv 1890 1902 studies with Kazimierz Twardowski in Lemberg Lwow 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 Stanislaw Lesniewski the Lwow Warsaw school of logic see also Alfred Tarski Stefan Banach Hugo Steinhaus Zygmunt Janiszewski Stefan Mazurkiewicz 1928 marries Regina Barwinska 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 DublinSelected works editBooks edit Lukasiewicz 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 Lukasiewicz Jan 1928 Elementy logiki matematycznej in Polish Warsaw Panstwowe Wydawnictwo Naukowe OCLC 11322101 Lukasiewicz Jan 1964 1963 Elements of Mathematical Logic Translated from Polish by Olgierd Wojtasiewicz New York Macmillan OCLC 671498 Lukasiewicz Jan 1970 Ludwik Borkowski ed Selected Works North Holland Pub Co ISBN 0 7204 2252 3 OCLC 115237 Lukasiewicz Jan 1998 Jacek Jadacki ed Logika i metafizyka Miscellanea in Polish Warsaw WFiS UW ISBN 83 910113 3 X Papers edit 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 uber den Aussagenkalkul 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 editHistory of philosophy in Poland List of Poles Logical operators Truth function 27114 LukasiewiczReferences edit 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 Jan Lukasiewicz on Porta Polonica a b Lukasiewicz 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 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 Jan Lukasiewicz at the Mathematics Genealogy Project a b c d e f Jan Lukasiewicz The Stanford Encyclopedia of Philosophy Metaphysics Research Lab Stanford University 2021 Jan Lukasiewicz Stanford Encyclopedia of Philosophy at the Old Powazki Cemetery Prof Jan Lukasiewicz Polskie Radio 24 22 11 2022 Jan Lukasiewicz Professor of Mathematical Logic at the Royal Irish Academy 07 November 2022 Royal Irish Academy a b Lukasiewicz Jan 1931 Uwagi o aksjomacie Nicoda i dedukcji uogolniajacej Comments on Nicod s Axiom and on Generalizing Deduction Ksiega pamiatkowa Polskiego Towarzystwa Filozoficznego We Lwowie 12 II 1904 12 II 1929 in Polish Lwow Wydawnictwo Polskie Towarzystwo Filozoficzne pp 366 383 Lukasiewicz 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 Lukasiewicz Jan 1929 O znaczeniu i potrzebach logiki matematycznej Nauka Polska in Polish 10 604 620 Pogorzelski H A Reviewed work s Remarks on Nicod s Axiom and on Generalizing Deduction by Jan Lukasiewicz Jerzy Slupecki Panstwowe Wydawnictwo Naukowe The Journal of Symbolic Logic Vol 30 No 3 September 1965 pp 376 377 This paper by Jan Lukasiewicz was re published in Warsaw in 1961 in a volume edited by Jerzy Slupecki It had been published originally in 1931 in Polish Lukasiewicz Jan Tarski Alfred Untersuchungen uber den Aussagenkalkul Investigations into the sentential calculus Comptes Rendus des seances de la Societe 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 2009 International Multiconference on Computer Science and Information Technology IMCSIT conference report Zi Jan 2019 Models of 6 valued measures 6 kinds of information Kindle Direct Publishing ScienceFurther reading edit Curriculum Vitae of Jan Lukasiewicz Rome Italy Metalogicon journal 1994 VII 2 July December issue Craig Edward general editor Article Jan Lukasiewicz Routledge Encyclopedia of Philosophy 1998 Volume 5 pp 860 863 Borkowski Ludwik pl Slupecki Jerzy The Logical Works of J Lukasiewicz Studia Logica 8 1958 7 56 JSTOR 20013604 51 pages Kotarbinski Tadeusz Jan Lukasiewicz s Works on the History of Logic Studia Logica 8 1958 57 63 JSTOR 20013605 7 pages Kwiatkowski Tadeusz Jan Lukasiewicz A historian of logic Organon 16 17 1980 1981 169 188 Lukasiewicz Jan Heine Holger R 2021 The Principle of Contradiction in Aristotle A Critical Study Honolulu Hawaii Topos Productions ISBN 1943354065 Marshall Jr David Lukasiewicz Leibniz and the arithmetization of the syllogism Notre Dame Journal of Formal Logic 18 2 1977 235 242 Seddon Frederick 1996 Aristotle amp Lukasiewicz on the Principle of Contradiction Ames Iowa Modern Logic Pub ISBN 1 884905 04 8 OCLC 37533856 Wolenski Jan 1994 Philosophical Logic in Poland Kluwer Academic Publishers ISBN 0 7923 2293 2 OCLC 27938071 Wolenski Jan 1994 Jan Lukasiewicz on the Liar Paradox Logical Consequence Truth and Induction Modern Logic 4 394 400 External links editSimons Peter Jan Lukasiewicz In Zalta Edward N ed Stanford Encyclopedia of Philosophy O Connor John J Robertson Edmund F Jan Lukasiewicz MacTutor History of Mathematics Archive University of St Andrews Lukasiewicz entry at Polish Philosophy Page ed by Francesco Coniglione University of Catania Jan Lukasiewicz at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Jan Lukasiewicz amp oldid 1187826301, wikipedia, wiki, book, books, library,

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