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	Lukasiewicz (Site not responding. Last check: 2007-11-07)
		Jan Lukasiewicz's father, Luke Lukasiewicz, was a captain in the Austrian army.
		Lukasiewicz was Polish Minister of Education in 1919 and a professor at Warsaw University from 1920 to 1939.
		Lukasiewicz introduced the 'Polish notation' which allowed expressions to be written unambiguously without the use of brackets and his studies were to form the basis for Tarski's work.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Lukasiewicz.html (626 words)

	Jan Lukasiewicz
		Jan Lukasiewicz is known all over the world as the founder of the first non-classical logical calculus, the so-called trivalent or polivalent logic, and as one of the most prominent and significative logicians of this century.
		Lukasiewicz occupied one of the two chairs of Philosophy at the new University of Warsaw, establishing fruitful relationships with the University's mathematicians and gathering round himself a group of young scholars, the most outstanding of whom was to be Alfred Tarski.
		Lukasiewicz, J. "Curriculum vitae of Jan Lukasiewicz", Metalogicon 7 (2) (1994), pp.
	www.fmag.unict.it /~polphil/PolPhil/Lukas/Lukas.html (789 words)

	Jan Łukasiewicz - Wikipedia, the free encyclopedia
		Jan Łukasiewicz (born 21 December 1878 - 13 February 1956) was a Polish mathematician born in Lwów, Galicia (now L'viv, Ukraine).
		Jan Łukasiewicz: Elements of Mathematical Logic, Warsaw, Państwowe Wydawnictwo Naukowe, 1963
		This page was last modified 09:11, 13 October 2005.
	en.wikipedia.org /wiki/Jan_Lukasiewicz (328 words)

	Lukasiewicz, Aristotle, and Contradiction - Owen LeBlanc
		Lukasiewicz was asked to come to London to be Lejewski's external examiner, and there Lejewski presented him with a copy of The Principle of Contradiction in Aristotle which he had obtained there.
		Lukasiewicz suffered from severe kidney problems, and he was unable to complete the translation before he died in Dublin on February 13, 1956.
		Lukasiewicz argues that although Aristotle does not state this explicitly, the ontological and logical principles of contradiction are equivalent on Aristotelian grounds.
	evans-experientialism.freewebspace.com /leblanc.htm (5428 words)

	References for Lukasiewicz (Site not responding. Last check: 2007-11-07)
		J Lukasiewicz, Curriculum vitae of Jan Lukasiewicz, Metalogicon 7 (2) (1994), 133-137.
		D Marshall, Lukasiewicz, Leibniz and the arithmetization of the syllogism, Notre Dame J. Formal Logic 18 (2) (1977), 235-242.
		J Slupecki, Jan Lukasiewicz (Polish), Wiadomosci matematyczne (2) 15 (1972), 73-78.
	www-groups.dcs.st-and.ac.uk /history/References/Lukasiewicz.html (159 words)

	Jan Lukasiewicz
		Jan Lukasiewicz (pronounced Wu-cash-ay-vich) was born on December 21st, 1878 in the city of Lwow in Poland.
		As a young man, Lukasiewicz studied mathematics and philosophy at the local University and was awarded a doctorate in 1902.
		Lukasiewicz survived long enough to witness the arrival of the computer era and the application of some of his ideas.
	www.calculator.org /Lukasiewicz.html (472 words)

	Thomistic Institute 1999:
		Lukasiewicz transported the methodology of the Lvov Department of Philosophy to Warsaw, with an added commitment to the essential role of logic.
		Lukasiewicz' project was not the rejection of metaphysics, but its revision.
		Jan Salamucha's paper on the ex motu proof for the existence of God provides a good example of what the members of the Cracow Circle were trying to do [3].
	www.nd.edu /Departments/Maritain/ti99/pouivet.htm (2058 words)

	[No title]
		In the early 1900's, Lukasiewicz described a three-valued logic, along with the mathematics to accompany it.
		Lukasiewicz felt that three- and infinite-valued logics were the most intriguing, but he ultimately settled on a four-valued logic because it seemed to be the most easily adaptable to Aristotlean logic.
		His insight, apparently missed by Lukasiewicz, was to use the integral range [-1, 0 +1] rather than [0, 1, 2].
	www.ortech-engr.com /fuzzy/tutor.txt (2691 words)

	ieo homepage
		The Warsaw school of mathematical logic, with Jan Lukasiewicz, Stanislaw Lesniewski, and Alfred Tarski, is regarded as the core of this movement; moreover, Kazimierz Ajdukiewicz, Tadeusz Czezowski, Tadeusz Kotarbinski, and Zygmunt Zawirski are counted as belonging to its more philosophical wing.
		This was exactly Lukasiewicz's point who complained that Descartes and Kant corrupted philosophy by their preoccupation with theory of knowledge, neglecting ontology.
		Lukasiewicz himself was a devout catholic, but he radically opposed the view that logic led to any atheistic consequences.
	www.unifr.ch /ieo/ieo-veta/40jah/texte.wolenski.html (3374 words)

	CHAPTER THREE - THE TRIVALENT LOGIC OF AYMARA (Site not responding. Last check: 2007-11-07)
		The research of the Polish thinker J. Lukasiewicz was a sharp departure from the Aristotelian interpretation of logic.
		Next, Lukasiewicz discusses the definitions of his trivalent propositional calculus, which is based on just two three-valued logical propositions, negation and implication, and from which he developed all the remaining propositions necessary for a complete logical system.
		Lukasiewicz used mathematics to generallze bivalent truth-tables and define trivalent truth-values from which he developed a new system of logic which, unlike Aristotle's, can only be understood using formulas.
	www.aymara.org /biblio/igr/igr3.html (2570 words)

	Word for Word (Site not responding. Last check: 2007-11-07)
		The original notation was developed by one Jan Lukasiewicz (pictured) who was born in 1878 in what is now the Ukraine.
		Lukasiewicz was Polish Education Minister in 1919, a professor at Warsaw University from 1920 to 1939, and a master of logic as well as mathematics.
		I don't know whether Lukasiewicz named his notation, or whether it was named by others, and since the name Lukasiewicz doesn't spring from the pages of my encyclopaedia I don't know whether he was of Polish ethnic stock, or even if he considered himself to be Polish.
	plateaupress.com.au /wfw/polish.htm (353 words)

	Web Sites Guide ODP > Science> Math> Logic and Foundations> History> People> Lukasiewicz, Jan
		Jan Lukasiewicz - Biography from the MacTutor History of Mathematics archive.
		Logic and determinism in Jan Lukasiewicz's philosophy - An Essay from Alessandro Becchi, PhD Student Florence University - Department of Philosophy.
		Lukasiewicz in Dublin - An International Conference on the work of Jan Lukasiewicz - Dublin, July 7-10 1996.
	www.websitesguide.info /Science/Math/Logic_and_Foundations/History/People/Lukasiewicz,_Jan (118 words)

	Philosophy Of Jan Harrison - (Site not responding. Last check: 2007-11-07)
		The Influence of Realist Philosophy on Jan Hus and His Predecessors in Bohemia...
		Jan Zwicky was born 1955 in Alberta and raised there.
		Kansas City, Kan., were Thursday, Jan. 11, at Porter Funeral...
	philosophy.fmqg.com /index.php?k=philosophy-of-jan-harrison (932 words)

	Stanislaw Lesniewski
		Lesniewski attributed the discovery of his true intellectual vocation to the influence of Jan Lukasiewicz, also a pupil of Twardowski and then a privat dozent at the University of Lwów.
		Already learned in the history of logic, to which he was to make outstanding contributions, Lukasiewicz was at the time studying the work of the German logicians Gottlob Frege and Ernst Schröder, the importance of which he was mainly responsible for making known in Poland, and teaching his first course in mathematical logic.
		From it he became interested in the problem posed by the discovery of the antinomies, or paradoxes, in logic and mathematics that threatened to undermine the foundations of all deductive science.
	www.cs.ualberta.ca /~piotr/Mizar/mirror/http/sum/lesniewski.html (1218 words)

	CSISS Classics - Lotfi Zadeh: Fuzzy logic-Incoporating Real-World Vagueness
		In the early 1900s, Lukasiewicz extended on to the conventional bi-valued logic of Aristotle and proposed a tri-valued logic in his paper in 1920 titled On three-valued logic where a new truth value was added to the truth logic 0 and false logic 1.
		Explicit formulation and systematic investigation of many-valued logics began with writings of Jan Lukasiewicz and Emil Post in the 1920s and D. Bochvar, Jerzy Stupecki, and Stephen Kleene in the late 1930s.
		Lukasiewicz experimented with four and five valued logic and hypothesized the possibility of infinite-valued logic.
	www.csiss.org /classics/content/68 (1118 words)

	Lukasiewicz \| Aristotle's Syllogistic \| Book #20400 (Site not responding. Last check: 2007-11-07)
		Jan Lukasiewicz (1878-1956) was one of the most important and innovative logicians of this century.
		The first, 'historical' part of the work expounds the Aristotelian doctrines and explains them from the standpoint of modern formal logic; the following 'systematic' section, intended by Lukasiewicz as an introduction to modern formal logic, explains the modern theories necessary for an understanding of Aristotle's syllogistic and includes the proof of decision by Slupecki.
		The final chapters contain the exposition of the modal system Lukasiewicz created in order to be "able to explain the difficulties and correct the errors of the Aristotelian modal syllogistic."
	www.powellschicago.com /html/reprints/20400.html (163 words)

	Directory - Science: Math: Logic and Foundations: History: People: Lukasiewicz, Jan
		Jan Lukasiewicz · cached · Biography from the MacTutor History of Mathematics archive.
		Logic and determinism in Jan Lukasiewicz's philosophy · An Essay from Alessandro Becchi, PhD Student Florence University - Department of Philosophy.
		Lukasiewicz in Dublin · cached · An International Conference on the work of Jan Lukasiewicz - Dublin, July 7-10 1996.
	www.incywincy.com /default?p=169982 (94 words)

	Polish notation - a Whatis.com definition - see also: Polish logic, prefix notation, postfix notation
		Polish notation, also known as prefix notation, is a symbolic logic invented by Polish mathematician Jan Lukasiewicz in the 1920's.
		In the 1960's, engineers at Hewlett-Packard decided that it would be easier for end-users to learn Jan Lukasiewicz' logic system than to try and use the Order of Operations on a calculator.
		They modified Jan Lukasiewicz's system for a calculator keyboard by placing the instructions (operators) after the data.
	searchcio.techtarget.com /sDefinition/0,,sid19_gci824619,00.html (403 words)

	Jan Lukasiewicz (Site not responding. Last check: 2007-11-07)
		- "Curriculum vitae of Jan Lukasiewicz", Rassegna di Scienze Filosofiche, XXX, 2-3, 1977, pp.23-9.
		- A. Schiaparelli, "Aspetti della critica di Jan Lukasiewicz al principio aristotelico di non contraddizione", Elenchos, 1, 1994, pp.
		Coniglione, "Filosofia e scienza in Jan Lukasiewicz", Epistemologia, 17, 1, 1994, pp.
	eber.kul.lublin.pl /~polhome/PolPhil/Lukas/Lukas.html (564 words)

	Reverse Polish Notation
		The rules of algebra have been used for centuries and is familiar to most everyone.
		In the 1920's, Jan Lukasiewicz developed a formal logic system which allowed mathematical expressions to be specified without parentheses by placing the operators before (prefix notation) or after (postfix notation) the operands.
		Prefix notation is known as Polish Notation after the nationality of Lukasiewicz.
	home.att.net /~srschmitt/reversepolish.html (491 words)

	UniFI - Dipartimento di Filosofia - Persone - Alessandro Becchi (Site not responding. Last check: 2007-11-07)
		I am actually working on my PhD thesis; it is concerned with the relationship between the logical principle of bivalence and the metaphysical thesis of determinism, both in an historical perspective and in a theoretical one.
		The second section is based on the contributions that the Polish philosophers and logicians Kotarbinski, Lesniewski and Lukasiewicz gave to the problem at issue, reaching - in the case of Lukasiewicz - to the development of the first three-valued system of propositional logic.
		The third section tries to put into a sharper focus certain aspects of the main problem by means of some conceptual instruments devised in the framework of analytic philosophy (truth-bearers, truth-makers, philosophy of time, theory of negation).
	www.philos.unifi.it /persone/becchi.htm (690 words)

	biography e jan matzeliger (Site not responding. Last check: 2007-11-07)
		Jan Matzeliger was born in Paramaribo, Dutch Guiana on September...
		When Jan was 18 years old, he began working in...
		Kavandi, Janet L. Lukasiewicz, Jan. Matzeliger, Jan. Pierce, Jane Means Appleton...
	www.biography-search.com /5/biography219.html (300 words)

	O. Le Blanc, Lukasiewicz, Aristotle, and Contradiction
		In 1910 the Polish philosopher Jan Lukasiewicz (1878-1956) published his first book, 0 Zasadzie Sprzecznosci u Arystotelesa: Studium Krytyczne, which means On the Principle of Contradiction in Aristotle: A Critical Study.
		Lukasiewicz did publish in 1910, the year in which the book appeared, a German summary of it, which is twenty-three pages long, about one tenth of the length of the book (Lukasiewicz 1910a).
		Finally, that this work is still of interest today, so that if I am able to complete a translation of the book, you might be willing to read it.
	www.fmag.unict.it /~polphil/PolPhil/Lukas/LeBlanc.html (5417 words)

	Jan Lukasiewicz - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-07)
		Habra o no por fin manana una batalla naval?(Aristóteles; Jan Lukasiewicz) : An article from: Revista de Filosofía de la Universidad de Costa Rica
		Collected Works of Jan Lukasiewicz (Western Phiosophy Series)
		Aristotle & Lukasiewicz on the Principle of Contradiction
	encyclopedia.worldsearch.com /jan_lukasiewicz.htm (161 words)

	The medieval theories of supposition and mental language
		Two developments which have taken place during the past thirty years have rescued medieval logic from oblivion and have stimulated a steadily increasing study of its content.
		In the year 1935 J. Salamucha, a pupil of Lukasiewicz, published a detailed study of the propositional logic of William of Ockham, and in that same year the present writer published (as his doctoral dissertation) the first modern study of Ockham's logical writings as a whole.
		A second development, which has taken place during the past thirty years within modern logic itself, has been the extension of logical investigations into the fields of semantics, modal logic, and philosophy of language, which turn out to be the areas in which the medieval logicians made their most interesting contributions.
	www.formalontology.it /supposition.htm (960 words)

	Polish Facts and Figures in World War II, Part III
		Jan Matejko (1839-1893), creator of a series of monumental visions of Poland's glorious past;
		Emil Mlynarski and Artur Rodzinski are well-known Polish conductors, while the de Reszke brothers, Adam Didur, Jan Kiepura, Ada Sari and Sembrich-Kochanska are well-known Polish singers of international repute.
		Among contemporary Polish poets mention should be made of Stanislaw Balinski, Jan Lechon, Kazimierz Wierzynski, Julian Tuwim and Antoni Slonimski.
	republika.pl /unpack/1/dok02c.html (2923 words)

	The Cracow Circle (Site not responding. Last check: 2007-11-07)
		Jan F. Drewnowski, Neoscholasticism and the Demands of Modern Science (1937)
		The book traced the fundamental outlines of a philosophical programme which drew on Lukasiewicz's standpoint and proposed to introduce a range of semiotic problems into gnoseological and ontological thought by reflecting on human knowledge as a system of signs.
		It also clearly expressed the non-philosophical role of contemporary logic, a thesis which was to be one of the most typical of the School, in opposition to those who wished to bind logic to the specific expressions of Neopositivism.
	eber.kul.lublin.pl /~polhome/PolPhil/Cracow/Cracow.html (1411 words)

	Lukasiewicz and Modal Logic (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		/ Lukasiewicz's four-valued modal logic is surveyed and analyzed.
		1 Introduction The Polish philosopher and logician Jan / Lukasiewicz (Lw'ow, 1878 -- Dublin, 1956) is one of the fathers of modern many-valued logic, and some of the systems he introduced are presently a topic of deep investigation.
		1 andpoint of modern formal logic, 2nd enlarged edition (context) - Lukasiewicz, from et al.
	citeseer.ist.psu.edu /309038.html (412 words)

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