Stanisław Leśniewski

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Stanisław Leśniewski
Stanisław Leśniewski.jpg
Born(1886-03-30)March 30, 1886
DiedMay 13, 1939(1939-05-13) (aged 53)
Alma materLviv University
Known forCalculus of names
Scientific career
InstitutionsUniversity of Warsaw
Doctoral advisorKazimierz Twardowski
Doctoral studentsAlfred Tarski
InfluencedDenis Miéville

Stanisław Leśniewski (March 30, 1886 – May 13, 1939) 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.

Leśniewski belonged to the first generation of the Lwów-Warsaw School of logic founded by Kazimierz Twardowski. 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 systems, 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 that by 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 ciphers 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.


  • 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 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[edit]


  • Ivor Grattan-Guinness, 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 36(4): 247–426 MR0476370
  • 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[edit]