Leon Chwistek


From Antinomies of Formal Logic (1921)* by Leon Chwistek

When Bertrand Russell published his theory of logical types,1 it might have appeared that the difficulties which had since ancient times been inherent in the foundations of logic were finally resolved. Nevertheless some additional assumptions of Russell's theory, known collectively as the principle of reducibility, could have at once inspired a certain distrust in view of their utterly arbitrary character.   (Etc.)   Henri Poincaré, the first critic of the theory of types, spoke against the axiom of reducibility, making the objection that Russell introduced a synthetic a priori statement into the axioms of logic.2 A few years later I drew attention to some paradoxical consequences which follow from the acceptance of the axiom of reducibility.3   (Etc.)

     1 'Mathematical logic as based on the theory of types', American Journal of Mathematics, 30 (1908), pp. 222-62.
      2 H. Poincaré, Dernières Pensées, ch. iv.
      3 'Zasada sprzecznosci w swietle nowszych badan Bertranda Russella' (The principle of non-contradiction in the light of Bertrand Russell's recent investigations), Rozprawy Akademii Umiejetnosci 30, Cracow, 1912, pp. 270-334.

* This paper appeared originally under the title 'Antynomje logiki formalnej' in Przeglad Filozoficzny 24 (1921), pp. 164-71.   Translated by Z. Jordan with certain small changes in notation.

Editor Storrs McCall, Oxford 1967, p. 338.


From Geschichte der Logik, 1931 by Heinrich Scholz

[..]   Poland has lately become the main country and Warsaw the main bastion of research in symbolic logic by virtue of the work of Jan Łukasiewicz. We can only refer to the pertinent treatises . . . in the Fundamenta Mathematicae of which volume 16 appeared in Warszawa during 1930. They all are geared to undergirding the foundations of mathematics. Also Leon Chwistek: The Theory of Constructive Types, Principles of Logic and Mathematics (Cracow, University Press, 1925) must at least be alluded to.

English version, Concise History of Logic,
Translator Kurt Leidecker.
New York : Philosophical Library 1961, p. 82.


From A NON-ARISTOTELIAN SYSTEM (etc), 1931 by Alfred Korzybski

" Here we find the main importance of the semantic fact established by Skarzenski,** that the 'logical' freedom from contradiction becomes a semantic problem of one-value. "


      **Quoted by Chwistek in his Neue Grundlagen der Logic und Mathematik.

Supplement III, Science and Sanity 1933,
pp. 753-754


From The Nature of Mathematics, 1933 by Max Black

A critical survey of Principia Mathematica and allied views on the nature of mathematics, with supplementary accounts of the Formalist and Intuitionist doctrines. The contributions of Chwistek, Ramsey, Wittgenstein, Weyl, and others to logistic theory are described and considered . . (etc).

London : Routledge & Kegan Paul 1933,
the front cover.


From SCIENCE AND SANITY, 1933 by Alfred Korzybski

" The term 'semantic' is derived from the Greek Semantikos, 'significant', from Semainein 'to signify', 'to mean', and was introduced into literature by Michel Bréal in his Essai de Sémantique. The term has been variously used in a more or less general or restricted sense by different writers. Of late, this term has been used by the Polish School of Mathematicians, and particularly L. Chwistek (See Supplement III), A. F. Bentley, and has been given a medical application by Henry Head in the study of different forms of Aphasias. 'Aphasia', from the Greek aphasia, 'speechlessness', is used to describe disorders incomprehension or expression of written and spoken language (etc). (pp. 19-20)

* * *

The structural notion of 'infinite', 'infinity', is of great semantic importance and lately has again become a subject of heated mathematical debates. My examination of this subject is from the point of view of a [non-A]-system, general semantic, and a a theory of sanity which completely eliminates identification. In Supplement III, I give a more detailed [non-A] analysis of the problem already anticipated by Brouwer, Weyl, Chwistek, and others. (Etc). (p. 204)

* * *

"The Polish school of mathematicians has produced the extension of the traditional two-valued A 'logic' to three-, and many-valued 'logic' ; Chwistek has based a new foundation of mathematics and a new theory of aggregates on his semantic methods ; but even these writers disregarded the general problems of non-elementalism, non-identity, and the necessity for a full-fledged [non-A]-system before their formulations can become free from paradoxes, valid and applied to life". (p. 541)

From Bibliography

100. CHWISTEK, L.   Wielosc Rzeczywistosci,   Kraków.
101.     The Theory of Constructive Types (Principles of Logic and Mathematics),
        2 parts.   Ann. soc. polonaise de mathématique.   Kraków.   1924, 1925.
102.     Über die Hypothesen der Mengenlehre.   Math. Zeit.   B. 25, H. 3. Berlin,
103.     Une Méthode métamathématique d'analyse.   C. R. du Iier congrès des
        math, des pays Slaves.
  Warsaw. 1929
104.     Neue Grundlagen der Logik und Mathematik, Part I. Math. Zeit. B. 30,
        H. 5. Berlin, 1929. Part II, B. 34, H. 4. Berlin.   1932.

(page 770)


From Mathematical Logic in Poland, etc. 1944 by Zbigniew Jordan

While I am writing these words Chwistek's tall and bulky figure still floats before my eyes. He was full of fun, eager to discuss for hours as well as enjoy life, and he knew perfectly how to do it.  .  .  . he possessed some qualities lending themselves to legend. The younger of us used to refer to him as 'this Renaissance man', (etc). He did not shun the limelight, nor avoid a fight whenever his pugnacious spirits saw an opportunity for it. Numberless anecdotes were told about him. When he was a young man, says one of them, he was asked by his mother what he would like to do. He replied that he was anxious to become a painter. But his mother thought that besides being a painter he must have a profession to secure his living. Chwistek was reported to have agreed with his mother's opinion and to be anxious to act in accordance with her wishes. Consequently he matriculated to read mathematics.

POLISH LOGIC 1920-1939, ed. Storrs McCall,
Oxford 1967, pp. 388-9.



Author Chwistek, Leon, 1884-1944. Title Zagadnienia kultury duchowej w Polsce. Publisher Warszawa, Gebethner i Wolff, 1933. Description 206 p.

Author Chwistek, Leon, 1884-1944. Title La méthode générale des sciences positives; l'esprit de la sémantique. Publisher Paris, Hermann, 1946. Description 42 p. 25 cm. Series Actualités scientifiques et industrielles,1014 Logique et methodologie,6 Series Logique et methodologie,6 Actualités scientifiques et industrielles,1014. Language French

Author Chwistek, Leon, 1884-1944. Title The limits of science; outline of logic and of the methodology of the exact sciences. [Tr. from the Polish by Helen Charlotte Brodie and Arthur P. Coleman] Introd. and appendix by Helen Charlotte Brodie. Publisher London, K. Paul, Trench, Trubner [1948] Description lvii, 347 p. diagrs. 23 cm. Series International library of psychology, philosophy, and scientific method Note "First published in 1935 under the title Granice nauki. The present edition has been revised and supplemented by the author." Note H.C. Brodie's thesis--Columbia Univ.
Note Bibliography of Chwistek's articles and books: p. [xvii]-xix. Bibliographical footnotes.

Author Chwistek, Leon, 1884-1944. Title Wielość rzeczywistości w sztuce, i inne szkice literackie. Ilustrowane rysunkami i akwarelami autora. Wybrał i przedm. poprzedził Karol Estreicher. Edition [Wyd. 1. Publisher Warszawa] Czytelnik, 1960. Description 258 p. illus. 21 cm. Subject Aesthetics.

Author Chwistek, Leon, 1884-1944. Title Pisma filozoficzne i logiczne. Wyboru dokonał i wstepem poprzedził Kazimierz Pasenkiewicz. Edition [Wyd. 1.] Publisher Warszawa, Państwowe Wydawn. Naukowe, 1961-1963. Description 2 v. port. 25 cm. Note Includes indexes (v. 2) Note Includes bibliographical references.


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Last updated 27 August 2004

W. Paul Tabaka
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