Background

Chwistek was born on June 13, 1884, in Krakow, Poland, the son of Bronisław i Emilia Majewski. Bronisław Chwistek was a doctor, who opened one of the first hydrotherapy plants in Zakopane in the villa "Gerlach" on Krupówki. His mother was a pianist and painter, a student of Jan Matejko and Karol Mikulski.

Education

From 1903 to 1904, Chwistek studied at the Krakow Academy of Fine Arts under Józef Mehoffer. He later studied philosophy and mathematics at the Jagiellonian University. In 1906 he received a doctorate in the thesis on axioms.

Career

An acute thinker who was strongly opposed to metaphysics and idealistic philosophy, Chwistek was professor oflogic at the University of Lvov from 1930 to 1940, when he took refuge in the Soviet Union. In 1921 he published his theory of the plurality of realities.

Rejecting the idea of one reality, he distinguished four main concepts of reality: natural reality, physical reality, reality of sensation, and reality of images. These concepts should not be confused, and each has its proper sphere of application. He used this theory to classify movements and styles in art. He maintained that aesthetic evaluation should be based not on reality but on form.

From 1919 to 1920 he was coeditor of the periodical Formisci. Under the influence of Poincaré, Chwistek developed a strictly nominalistic attitude toward science, particularly logic and mathematics. In 1921 he observed that for the removal of Russell’s paradox in the theory of classes, the simplified theory of types suffices. Dissatisfied with Russell’s foundation of mathematics, in which he rejected such idealistic elements as the axiom of reducibility in the theory of types, Chwistek proposed his theory of constructive types in 1924. His main contribution was the foundation of logic and mathematics on his system of rational semantics.

Chwistek also developed his theory of the multiplicity of realities first with regard to the arts. He distinguished four basic types of realities, then matched them with four basic types of painting.

Achievements

• In the 1920's-1930's, many European philosophers attempted to reform traditional philosophy by means of mathematical logic. Leon Chwistek did not believe that such reform could succeed. He thought that reality could not be described in one homogeneous system, based on the principles of formal logic, because there was not one reality but many.

Works

More photos

• book

  • The Plurality of Realities: Collected Essays

    (The Plurality of Realities contains four texts by Leon Ch...)

  • The Limits of Science: Outline of Logic and of the Methodology of the Exact Sciences

Views

In logic, Chwistek proposed a certain simplification of the Russellian theory of types; he also elaborated his own version of the pure theory of types. He made a suggestion of bracket less logical notation. He introduced the precision notion of semantics. Using the method of explication by formalization he created an axiomatic system of elementary semantics. He also made an exact rendering of rules of definition.

In the field of the foundations of mathematics he was the creator of the so-called rational metamathematics. In semiotics he described the peculiarities of natural languages: their indefiniteness, ambiguity and self-contradiction.

His epistemology was founded on broad empiricism and realism. In ontology, his conception of plurality of realities influenced the further discussion on the idea of possible worlds. In the philosophy of mathematics he was a defender of nominalism.

Connections

Chwistek married Olga, sister of Hugo Steinhaus and daughter of Alina Dawidowiczowa, a doctor of mathematics, a painter and author of memories.

Father:

Bronisława Chwistek

Mother:

Emilia Chwistek

Spouse:

Olga Dawidowiczowa

References

• Leon Chwistek. Nowe kierunki w sztuce
• Dictionary of Scientific Biography Volume 3
  1971