Stanisław Leśniewski

Works

• 1916Foundations of the General Theory of Sets I

  The first presentation of mereology: classes understood as wholes made of parts, a way out of Russell’s paradox.

Position

Leśniewski wanted a logic free of the paradoxes and of what he regarded as the unclarities of “Principia Mathematica”. He built three systems on one another: protothetic, a propositional calculus with quantifiers over propositions and connectives; ontology, a calculus of names built on a single copula “is” (ε) that admits empty and general names; and mereology, a theory of collective classes in which a class is a whole made of its parts, not an abstract set. Russell’s paradox arises, he argued, because the distributive and the collective sense of “class” are confused. His nominalism admitted only concrete individuals, and he required that every formula be built by explicit rules, definitions included, and that using an expression be strictly distinguished from mentioning it. These standards shaped Tarski, whose analysis of the semantic paradoxes and of the concept of truth drew on them, and Kotarbiński’s reism. Mereology was developed further by Henry Leonard and Nelson Goodman (1940) and by Peter Simons (1987) and belongs today to the standard tools of formal ontology. His idiosyncratic notation, the few publications and the loss of his papers limited his reception.

Life & context

Stanisław Leśniewski was born on 30 March 1886 in Serpukhov near Moscow, where his father, a Polish engineer, was working on the construction of a railway; he went to school in Irkutsk in Siberia. From 1904 he studied mathematics and philosophy at several universities in Germany and Switzerland, among them Leipzig, Zurich, Heidelberg and Munich, before moving to Lwów, where he took his doctorate under Kazimierz Twardowski in 1912 with a thesis on existential sentences. Łukasiewicz’s book on the principle of contradiction in Aristotle (1910) acquainted him with Russell’s paradox, which turned him from the philosophical analysis of language to the foundations of logic and mathematics. During the First World War he taught at Polish schools in Moscow, where his first account of mereology appeared in 1916. In 1919 he became professor of the philosophy of mathematics at the University of Warsaw, where he taught until his death; Alfred Tarski took his doctorate under him in 1924. From the 1920s Leśniewski supported the authoritarian rule of Józef Piłsudski, and from about 1930 his views took on an antisemitic tinge; a letter to Twardowski of 1935 voices it, together with a personal antipathy towards Tarski, whose candidacy for a chair in Lwów he had earlier supported (P. Simons, Stanford Encyclopedia of Philosophy). His systems were published only in part, above all in the series “On the Foundations of Mathematics” (1927–31). He died of cancer in Warsaw on 13 May 1939; most of his manuscripts were destroyed during the Warsaw Uprising of 1944.

Further main works

• Contribution to the Analysis of Existential Propositions (Przyczynek do analizy zdań egzystencjalnych, 1911)
• On the Foundations of Mathematics (O podstawach matematyki, 1927–31)
• Outline of a New System of the Foundations of Mathematics (Grundzüge eines neuen Systems der Grundlagen der Mathematik, 1929)
• On the Foundations of Ontology (Über die Grundlagen der Ontologie, 1930)