Stanisław Leśniewski (; 30 March 1886 – 13 May 1939) was a Polish
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
,
philosopher
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
and
logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arg ...
. A professor of mathematics at the
University of Warsaw
The University of Warsaw (, ) is a public university, public research university in Warsaw, Poland. Established on November 19, 1816, it is the largest institution of higher learning in the country, offering 37 different fields of study as well ...
, he was a leading representative of the
Lwów–Warsaw School of Logic and is known for coining and introducing the concept of
mereology
Mereology (; from Greek μέρος 'part' (root: μερε-, ''mere-'') and the suffix ''-logy'', 'study, discussion, science') is the philosophical study of part-whole relationships, also called ''parthood relationships''. As a branch of metaphys ...
as part of a comprehensive framework for logic and mathematics.
Life
Leśniewski was born on 28 March 1886 at
Serpukhov
Serpukhov ( rus, Серпухов, p=ˈsʲerpʊxəf) is a types of inhabited localities in Russia, city in Moscow Oblast, Russia, located at the confluence of the Oka River, Oka and the Nara (Oka), Nara Rivers, 99 kilometers (62 miles) south fro ...
, near
Moscow
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...
, to father Izydor, an engineer working on the construction of the
Trans-Siberian Railway
The Trans-Siberian Railway, historically known as the Great Siberian Route and often shortened to Transsib, is a large railway system that connects European Russia to the Russian Far East. Spanning a length of over , it is the longest railway ...
, and mother Helena (''née'' Palczewska). Leśniewski went to a high school in
Irkutsk
Irkutsk ( ; rus, Иркутск, p=ɪrˈkutsk; Buryat language, Buryat and , ''Erhüü'', ) is the largest city and administrative center of Irkutsk Oblast, Russia. With a population of 587,891 Irkutsk is the List of cities and towns in Russ ...
. Later he attended lectures by
Hans Cornelius at the
Ludwig Maximilian University of Munich
The Ludwig Maximilian University of Munich (simply University of Munich, LMU or LMU Munich; ) is a public university, public research university in Munich, Bavaria, Germany. Originally established as the University of Ingolstadt in 1472 by Duke ...
and lectures by
Wacław Sierpiński
Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a Polish mathematician. He was known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions ...
at
Lviv University.
Leśniewski belonged to the first generation of the
Lwów–Warsaw School of logic founded by
Kazimierz Twardowski
Kazimierz Jerzy Skrzypna-Twardowski (; 20 October 1866 – 11 February 1938) was a Polish philosopher, psychologist, logician, and rector of the Lwów University. He was initially affiliated with Alexius Meinong's Graz School of object theory. ...
. Together with
Alfred Tarski
Alfred Tarski (; ; born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
and
Jan Łukasiewicz
Jan Łukasiewicz (; 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 logi ...
, he formed a trio which made the
University of Warsaw
The University of Warsaw (, ) is a public university, public research university in Warsaw, Poland. Established on November 19, 1816, it is the largest institution of higher learning in the country, offering 37 different fields of study as well ...
, during the
interbellum
In the history of the 20th century, the interwar period, also known as the interbellum (), lasted from 11 November 1918 to 1 September 1939 (20 years, 9 months, 21 days) – from the end of World War I (WWI) to the beginning of World War II ( ...
, perhaps the most important research center in the world for
formal logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
. Despite that, Leśniewski's growing anti-semitism later caused the deterioration of the relationship with Tarski.
His main contribution was the construction of three nested
formal system
A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms.
In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in ma ...
s, to which he gave the Greek-derived names of protothetic,
ontology
Ontology is the philosophical study of existence, being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of realit ...
, and
mereology
Mereology (; from Greek μέρος 'part' (root: μερε-, ''mere-'') and the suffix ''-logy'', 'study, discussion, science') is the philosophical study of part-whole relationships, also called ''parthood relationships''. As a branch of metaphys ...
. ("Calculus of names" is sometimes used instead of ontology, a term widely employed in
metaphysics
Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...
in a very different sense.) A good textbook presentation of these systems is that by
Simons (1987), who compares and contrasts them with the variants of
mereology
Mereology (; from Greek μέρος 'part' (root: μερε-, ''mere-'') and the suffix ''-logy'', 'study, discussion, science') is the philosophical study of part-whole relationships, also called ''parthood relationships''. As a branch of metaphys ...
, more popular nowadays, descending from the ''calculus of individuals'' of Leonard and Goodman. Simons clarifies something that is very difficult to determine by reading Leśniewski and his students, namely that Polish mereology is a
first-order theory
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, giving rise to a formal system that combines the language with deduct ...
equivalent to what is now called classical extensional
mereology
Mereology (; from Greek μέρος 'part' (root: μερε-, ''mere-'') and the suffix ''-logy'', 'study, discussion, science') is the philosophical study of part-whole relationships, also called ''parthood relationships''. As a branch of metaphys ...
(modulo choice of language).
While he did publish a fair body of work (Leśniewski, 1992, is his collected works in English translation), some of it in German, the leading language for mathematics of his day, his writings had limited impact because of their enigmatic style and highly idiosyncratic notation. Leśniewski was also a radical
nominalist
In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are two main versions of nominalism. One denies the existence of universals—that which can be inst ...
: he rejected
axiomatic set theory
Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
at a time when that theory was in full flower. He pointed to
Russell's paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains ...
and the like in support of his rejection, and devised his three formal systems as a concrete alternative to set theory. Even though
Alfred Tarski
Alfred Tarski (; ; born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
was his sole doctoral pupil, Leśniewski nevertheless strongly influenced an entire generation of Polish logicians and mathematicians via his teaching at the University of Warsaw. It is mainly thanks to the writings of his students (e.g., Srzednicki and Rickey 1984) that Leśniewski's thought is known.
During the
Polish–Soviet War
The Polish–Soviet War (14 February 1919 – 18 March 1921) was fought primarily between the Second Polish Republic and the Russian Soviet Federative Socialist Republic, following World War I and the Russian Revolution.
After the collapse ...
of 1919-21, Leśniewski served the cause of Poland's independence by breaking
Soviet Russian cipher
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s for the
Polish General Staff
Polish General Staff, formally known as the General Staff of the Polish Armed Forces ( Polish: ''Sztab Generalny Wojska Polskiego'') is the highest professional body within the Polish Armed Forces. Organizationally, it is an integral part of the M ...
's
Cipher Bureau.
Leśniewski died suddenly of cancer, shortly before the German
invasion of Poland
The invasion of Poland, also known as the September Campaign, Polish Campaign, and Polish Defensive War of 1939 (1 September – 6 October 1939), was a joint attack on the Second Polish Republic, Republic of Poland by Nazi Germany, the Slovak R ...
, which resulted in the destruction of his ''
Nachlass
''Nachlass'' (, older spelling ''Nachlaß'') is a German language, German word, used in academia to describe the collection of manuscripts, notes, correspondence, and so on left behind when a scholar dies. The word is a compound word, compound in ...
''. He was buried at Warsaw's
Powązki Cemetery
Powązki Cemetery (; ), also known as Stare Powązki (), is a historic necropolis located in Wola district, in the western part of Warsaw, Poland. It is the most famous cemetery in the city and one of the oldest, having been established in 179 ...
.
Works
* 1988. ''Lecture Notes in Logic''. Kluwer
Table of Contents.* 1992. ''Collected Works''. 2 vols. Kluwer
* 1929, "Über Funktionen, deren Felder Gruppen mit Rücksicht auf diese Funktionen sind", Fundamenta Mathematicae 13: 319-32.
* 1929, "Grundzüge eines neuen Systems der Grundlagen der Mathematik", Fundamenta Mathematicae 14: 1-81.
* 1929, "Über Funktionen, deren Felder Abelsche Gruppen in bezug auf diese Funktionen sind", Fundamenta Mathematicae 14: 242-51.
See also
*
History of philosophy in Poland
*
List of Poles
This is a partial list of notable Polish people, Polish or Polish language, Polish-speaking or -writing people. People of partial Polish heritage have their respective ancestries credited.
Physics
*Miedziak Antal
* Czesław Białobrzesk ...
References
Bibliography
*
Ivor Grattan-Guinness
Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic.
Life
Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his ...
, 2000. ''In Search of Mathematical Roots''. Princeton: Princeton University Press.
* Luschei, Eugene, 1962. ''The Logical Systems of Lesniewski''. Amsterdam: North-Holland.
* Miéville, Denis, 1984. "Un Développement des Systèmes Logiques de Stanislas Lesniewski", Peter Lang, European University Studies.
* Simons, Peter, 1987. ''Parts: A Study in Ontology''. New York: Oxford University Press.
* Srzednicki, J. T. J., and
Rickey, V. F., (eds.), 1984. ''Lesniewski's Systems: Ontology and Mereology''. Dordrecht: Kluwer.
* Surma, Stanislaw J. (editor) (1977/8) "On Leśniewski's Systems, Proceedings of XXII Conference on History of Logic",
Studia Logica
''Studia Logica'' (full name: ''Studia Logica, An International Journal for Symbolic Logic'') is a scientific journal publishing papers employing formal tools from Mathematics and Logic. The scope of papers published in Studia Logica covers all sc ...
36(4): 247–426
* Urbaniak, Rafal, 2013. ''Leśniewski's Systems of Logic and Foundations of Mathematics'', Dordrecht: Springer.
* Wolenski, Jan, 1989. ''Logic and Philosophy in the Lwow-Warsaw School''. Dordrecht: Kluwer.
External links
*
*
*
* Betti, Arianna, 2001,
Sempiternal Truth: The Bolzano-Twardowski-Lesniewski connection.by Francesco Coniglione and Arianna Betti.
* Raul Corazzon's Theory and History of Ontology web page
Includes the English translations and selected bibliography of the secondary literature.
*
{{DEFAULTSORT:Lesniewski, Stanislaw
1886 births
1939 deaths
20th-century Polish philosophers
People from Serpukhov
Polish logicians
Polish mathematicians
Cipher Bureau (Poland)
University of Warsaw alumni
Deaths from cancer in Poland