Stanislaw Lesniewski
Encyclopedia
Stanisław Leśniewski was a Polish
mathematician
, philosopher and logician.
Leśniewski went to a high school in Irkutsk
. Later he attended lectures by Hans Cornelius
at the Ludwig Maximilian University of Munich and lectures by Wacław Sierpiński at the Lviv University
.
. Together with Alfred Tarski
and Jan Łukasiewicz, he formed the troika which made the University of Warsaw
, during the Interbellum, perhaps the most important research center in the world for formal logic
.
His main contribution was the construction of three nested formal system
s, to which he gave the Greek-derived names of protothetic, ontology, and mereology
. ("Calculus of names" is sometimes used instead of ontology
, a term widely employed in metaphysics
in a very different sense.) A good textbook presentation of these systems is Simons (1987), who compares and contrasts them with the variants of mereology
, 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
isomorphic to what is now called classical extensional mereology
.
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: he rejected axiomatic set theory at a time when that theory was in full flower. He pointed to Russell's paradox
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
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
of 1919-21, Leśniewski served the cause of Poland's independence by breaking Soviet Russian cipher
s for the Polish General Staff
's Cipher Bureau
.
Leśniewski died suddenly of cancer, shortly before the German invasion of Poland
, which resulted in the destruction of his Nachlass
.
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, philosopher and logician.
Leśniewski went to a high school in Irkutsk
Irkutsk
Irkutsk is a city and the administrative center of Irkutsk Oblast, Russia, one of the largest cities in Siberia. Population: .-History:In 1652, Ivan Pokhabov built a zimovye near the site of Irkutsk for gold trading and for the collection of fur taxes from the Buryats. In 1661, Yakov Pokhabov...
. Later he attended lectures by Hans Cornelius
Hans Cornelius
Johannes Wilhelm Cornelius was a German neo-Kantian philosopher.Born in Munich, he originally studied mathematics, physics, and chemistry, graduating with a Ph.D. in 1886, before turning to philosophy...
at the Ludwig Maximilian University of Munich and lectures by Wacław Sierpiński at the Lviv University
Lviv University
The Lviv University or officially the Ivan Franko National University of Lviv is the oldest continuously operating university in Ukraine...
.
Life
Leśniewski belonged to the first generation of the Lwów-Warsaw School of logic founded by Kazimierz TwardowskiKazimierz Twardowski
Kazimierz Jerzy Skrzypna-Twardowski was a Polish philosopher and logician.-Life:Twardowski's family belonged to the Ogończyk coat-of-arms.Twardowski studied philosophy in Vienna with Franz Brentano and Robert Zimmermann...
. Together with Alfred Tarski
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
and Jan Łukasiewicz, he formed the troika which made the University of Warsaw
University of Warsaw
The University of Warsaw is the largest university in Poland and one of the most prestigious, ranked as best Polish university in 2010 and 2011...
, during the Interbellum, perhaps the most important research center in the world for formal logic
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...
.
His main contribution was the construction of three nested formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
s, to which he gave the Greek-derived names of protothetic, ontology, and mereology
Mereology
In philosophy and mathematical logic, mereology treats parts and the wholes they form...
. ("Calculus of names" is sometimes used instead of ontology
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
, a term widely employed in metaphysics
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
in a very different sense.) A good textbook presentation of these systems is Simons (1987), who compares and contrasts them with the variants of mereology
Mereology
In philosophy and mathematical logic, mereology treats parts and the wholes they form...
, 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
First-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
isomorphic to what is now called classical extensional mereology
Mereology
In philosophy and mathematical logic, mereology treats parts and the wholes they form...
.
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: he rejected axiomatic set theory at a time when that theory was in full flower. He pointed to Russell's paradox
Russell's paradox
In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction...
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
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
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
Polish-Soviet War
The Polish–Soviet War was an armed conflict between Soviet Russia and Soviet Ukraine and the Second Polish Republic and the Ukrainian People's Republic—four states in post–World War I Europe...
of 1919-21, Leśniewski served the cause of Poland's independence by breaking Soviet Russian cipher
Cipher
In cryptography, a cipher 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. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...
s for the Polish General Staff
General Staff
A military staff, often referred to as General Staff, Army Staff, Navy Staff or Air Staff within the individual services, is a group of officers and enlisted personnel that provides a bi-directional flow of information between a commanding officer and subordinate military units...
's Cipher Bureau
Biuro Szyfrów
The Biuro Szyfrów was the interwar Polish General Staff's agency charged with both cryptography and cryptology ....
.
Leśniewski died suddenly of cancer, shortly before the German invasion of Poland
Invasion of Poland (1939)
The Invasion of Poland, also known as the September Campaign or 1939 Defensive War in Poland and the Poland Campaign in Germany, was an invasion of Poland by Germany, the Soviet Union, and a small Slovak contingent that marked the start of World War II in Europe...
, which resulted in the destruction of his Nachlass
Nachlass
Nachlass is a 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 in German: nach means 'after', and the verb lassen means 'leave'. The plural can be either Nachlasse or Nachlässe...
.
Works
- 1988. Lecture Notes in Logic. Kluwer. Table of Contents.
- 1992. Collected Works. 2 vols. Kluwer. Table of Contents.
- 1929, "Über Funktionen, deren Felder Gruppen mit Rücksicht auf diese Funktionen sind", Fundamenta MathematicaeFundamenta MathematicaeFundamenta Mathematicae is a scientific journal of mathematics with a special focus on the foundations of mathematics. At present, it concentrates on papers devoted to set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems...
XIII: 319-32. - 1929, "Grundzüge eines neuen Systems der Grundlagen der Mathematik", Fundamenta Mathematicae XIV: 1-81.
- 1929, "Über Funktionen, deren Felder Abelsche Gruppen in bezug auf diese Funktionen sind", Fundamenta Mathematicae XIV: 242-51.
See also
- History of philosophy in Poland
- List of Poles
External links
- Betti, Arianna, 2001, "Sempiternal Truth: The Bolzano-Twardowski-Lesniewski connection."
- Polish Philosophy: Stanislaw Lesniewski by Francesco Coniglione and Arianna Betti.
- Raul Corazzon's Theory and History of Ontology web page: Lesniewski.
- Selected bibliography of and about Lesniewski. Includes the English translations and selected bibliography of the secondary literature.
- Rafal Urbaniak's Leśniewski’s Systems of Logic and Mereology; History and Re-evaluation.