Stanisław Jaśkowski (Polish pronunciation: ; 22 April 1906, in

Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...

– 16 November 1965, in Warsaw) was a Polish

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 ...

who made important contributions to

proof theory Proof theory is a major branchAccording to , proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. consists of four corresponding parts, with part D being about "Proof The ...

and formal semantics. He was a student of

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 ...

and a member of the Lwów–Warsaw School of Logic. He is regarded as one of the founders of

natural deduction In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use ...

, which he discovered independently of

Gerhard Gentzen Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died ...

in the 1930s. He is also known for his research into

paraconsistent logic Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion where anything can be proven true. Specifically, paraconsistent logic is the subfield of log ...

. Upon his death, his name was added to the Genius Wall of Fame. He was the President (rector) of the Nicolaus Copernicus University in

Toruń Toruń is a city on the Vistula River in north-central Poland and a World Heritage Sites of Poland, UNESCO World Heritage Site. Its population was 196,935 as of December 2021. Previously, it was the capital of the Toruń Voivodeship (1975–199 ...

Life and career

He was born in 1906 in

to father Feliks Jaśkowski and mother Kazimiera (nee Dzierzbicka). In 1924, he graduated from high school in

Zakopane Zakopane (Gorals#Language, Podhale Goral: ''Zokopane'') is a town in the south of Poland, in the southern part of the Podhale region at the foot of the Tatra Mountains. From 1975 to 1998, it was part of Nowy Sącz Voivodeship; since 1999, it has ...

and enrolled 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 ...

to study

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. He was taught

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

under

and participated in the Polish Mathematicians' Congresses in

Lviv Lviv ( or ; ; ; see #Names and symbols, below for other names) is the largest city in western Ukraine, as well as the List of cities in Ukraine, fifth-largest city in Ukraine, with a population of It serves as the administrative centre of ...

(1927) and

Vilnius Vilnius ( , ) is the capital of and List of cities in Lithuania#Cities, largest city in Lithuania and the List of cities in the Baltic states by population, most-populous city in the Baltic states. The city's estimated January 2025 population w ...

(1931). After the outbreak of

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

, he participated in the September Campaign as a volunteer. In 1942, he was briefly imprisoned by the Germans. In 1945, he continued his scientific career at the

University of Toruń A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...

where he defended his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

and assumed the post of the head of the Faculty of Mathematical Logic. Since 1950, he collaborated with the State Institute of Mathematics of the

Polish Academy of Sciences The Polish Academy of Sciences (, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of distinguished scholars a ...

(PAN). Between 1959–1962, he served as the Rector of the University. He was among the founders and served as the first President of the

Polish Mathematical Society The Polish Mathematical Society () is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). History The society was ...

's branch in Toruń. Jaśkowski is considered to be one of the founders of

, which he discovered independently of

in the 1930s. Gentzen's approach initially became more popular with logicians because it could be used to prove the

cut-elimination theorem The cut-elimination theorem (or Gentzen's ''Hauptsatz'') is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in part I of his landmark 1935 paper "Investigations in Logical Ded ...

. However, Jaśkowski's is closer to the way that proofs are done in practice. He was also one of the first to propose a formal calculus of inconsistency-tolerant (or paraconsistent) logic. Furthermore, Jaśkowski was a pioneer in the investigation of both

intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems ...

and

free logic A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter propert ...

. He died in 1965 in

and was buried at the

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

''On the Rules of Suppositions in Formal 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 ...

1, 1934 pp. 5–32 (reprinted in: Storrs McCall (ed.), ''Polish Logic 1920-1939'', Oxford University Press, 1967 pp. 232–258 * ''Investigations into the System of Intuitionist Logic'' 1936 (translated in: Storrs McCall (ed.), ''Polish Logic 1920-1939'', Oxford University Press, 1967 pp. 259–263 * ''A propositional Calculus for Inconsistent Deductive Systems'' 1948 (reprinted in: Studia Logica, 24 1969, pp 143–157 and in: Logic and Logical Philosophy 7, 1999 pp. 35–56) * ''On the Discussive Conjunction in the Propositional Calculus for Inconsistent Deductive Systems'' 1949 (reprinted in: Logic and Logical Philosophy 7, 1999 pp. 57–59) * ''On Formulas in which no Individual Variable occurs more than Twice'',

Journal of Symbolic Logic The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zent ...

, 31, 1966, pp. 1–6) ; in Polish: * ''O symetrii w zdobnictwie i przyrodzie - matematyczna teoria ornamentów'' (English title: ''On Symmetry in Art and Nature''), PWS, Warszawa, 1952 (book 168 pages) * ''Matematyczna teoria ornamentów'' (English title: ''Mathematical Theory of Ornaments''), PWN, Warszawa, 1957 (book 100 pages)

References

Sources

* * * Jerzy Kotas, August Pieczkowski. ''Scientific works of Stanisław Jaśkowski'', Studia Logica 21, 1967, 7-15

External links

Polish Logic of the Postwar Period
{{DEFAULTSORT:Jaskowski, Stanislaw 1906 births 1965 deaths Writers from Warsaw Polish logicians Polish mathematicians University of Warsaw alumni Academic staff of Nicolaus Copernicus University in Toruń Paraconsistent logic 20th-century Polish philosophers

Life and career

Works

See also

References

Sources

External links