Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-19T11:32:39.451Z Has data issue: false hasContentIssue false
  • English
  • Français

GÖDEL ON MANY-VALUED LOGIC

Part of: Mathematical Logic and Foundations Philosophical aspects of logic and foundations General logic

Published online by Cambridge University Press:  22 February 2021

TIM LETHEN
TIM LETHEN*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HELSINKI FI-00014 HELSINKI, FINLAND
*
E-mail: tim.lethen@gmx.de
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper collects and presents unpublished notes of Kurt Gödel concerning the field of many-valued logic. In order to get a picture as complete as possible, both formal and philosophical notes, transcribed from the Gabelsberger shorthand system, are included.

Keywords

many-valued logicKurt Gödel

MSC classification

Primary: 03-03: Historical (must also be assigned at least one classification number from Section 01)
Secondary: 03A05: Philosophical and critical 03B50: Many-valued logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 3 , September 2023 , pp. 655 - 671
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Bernays, P. (1918). Beiträge zur axiomatischen Behandlung des Logik-Kalküls. Habilitationsschrift, Universität Göttingen. Bernays Nachlass, WHS, Bibliothek, ETH Zürich, Hs. 973.192. Printed in: Ewald, W. and Sieg, W., editors. (2013). David Hilbert’s Lectures on the Foundations of Arithmetic and Logic 1917–1933. Berlin: Springer, pp. 231–269.Google Scholar
Bernays, P. (1926). Axiomatische Untersuchung des Aussagen-Kalküls der ‘Principia Mathematica’. Mathematische Zeitschrift, 25, 305–320.Google Scholar
Bochvar, D. A. (1938). Ob odnom tréchznačnom isčislénii i égo priménénii k analizu paradoksov klassičéskogo rasširennogo funkcjonal’nogo isčislénija. Matématičéskij Sbornik, 4(46), 287–308. English translation in [4].Google Scholar
Bochvar, D. A. & Bergmann, M. (1981). On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus. History and Philosophy of Logic, 2(1–2), 87–112.Google Scholar
Ciucci, D. & Dubois, D. (2013). A map of dependencies among three-valued logics. Information Sciences, 250, 162–177.Google Scholar
Engelen, E.-M. (2019). Kurt Gödel—Philosophische Notizbücher, Vol. 1: Philosophie I Maximen 0. Berlin: De Gruyter.Google Scholar
Feferman, S., et al., editors (1995). Kurt Gödel, Collected Works. Vol. III. Unpublished Essays and Lectures. New York: Oxford University Press.Google Scholar
Gödel, K. (1932). Zum intuitionistischen Aussagenkalkül. Anzeiger der Akademie der Wissenschaften in Wien, 69, 65–66.Google Scholar
Gödel, K. (2021). Results on foundations. Edited by Maria Hämeen-Anttila and Jan von Plato. In preparation.Google Scholar
Gottwald, S. (2001). A Treatise on Many-Valued Logics. Studies in Logic and Computation, Vol. 9. Baldock: Research Studies Press.Google Scholar
Grelling, K. (1936). Der Typusbegriff im Lichte der neuen Logik, von C. G. Hempel & P. Oppenheim (Besprechung). Erkenntnis, 6, 266–268.Google Scholar
Hempel, C. G. & Oppenheim, P. (1936). Der Typusbegriff im Lichte der neuen Logik. Leiden: Sijthoff.Google Scholar
Heyting, A. (1930). Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte Preußische Akademie der Wissenschaften Berlin, physikalisch-mathematische Klasse II, 42–56.Google Scholar
Heyting, A. (1934). Mathematische Grundlagenforschung: Intuitionismus, Beweistheorie. Berlin: Springer.Google Scholar
Jaśkowski, S. (1936). Recherches sur le système de la logique intuitioniste. Actes du Congrès International de Philosophie Scientifique, 6, 58–61. English translation in [16].Google Scholar
Jaśkowski, S. (1975). Investigations into the system of intuitionist logic. Studia Logica: An International Journal for Symbolic Logic, 34(2), 117–120.Google Scholar
Kleene, S. C. (1938). On a notation for ordinal numbers. The Journal of Symbolic Logic, 3, 150–155.Google Scholar
Kleene, S. C. (1952). Introduction to Metamathematics. Amsterdam: North-Holland.Google Scholar
Lethen, T. (2020a). Kurt Gödel on logical, theological, and physical antinomies. Submitted for publication.Google Scholar
Lethen, T. (2020b). Gespräche, Vorträge, Séancen: Kurt Gödels Wiener Protokolle 1937/38—Transkriptionen und Kommentare. Cham: Springer. To appear.Google Scholar
Lethen, T. (2020c). Mistakes in the bible—Kurt Gödel’s biblical studies. Submitted for publication.Google Scholar
Lethen, T. (2020d). Kurt Gödel’s dogmatic logic. In: Ramharter, E., editor. Vienna Circle and Religion. Cham: Springer. To appear.Google Scholar
Łukasiewicz, J. (1920). O logice trójwartościowej, Ruch Filozoficny, 5, 170–171. English translation in [27].Google Scholar
Łukasiewicz, J. (1930). Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls. Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Cl. iii, 23, 51–77. English translation in [27].Google Scholar
Łukasiewicz, J. & Tarski, A. (1930). Untersuchungen über den Aussagenkalkül. Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Cl. iii, 23, 30–50.Google Scholar
Malinowski, G. (1993). Many-Valued Logics. Oxford: Oxford University Press.Google Scholar
McCall, S. (1967). Polish Logic, 1920–1939. Oxford: Oxford University Press.Google Scholar
Post, E. L. (1921). Introduction to a general theory of elementary propositions. American Journal of Mathematics, 43(3), 163–185.Google Scholar
von Plato, J. (2020). Can Mathematics be Proved Consistent? Gödel’s Shorthand Notes & Lectures on Incompleteness. Berlin: Springer.Google Scholar
von Plato, J. (2017). The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age. Princeton: Princeton University Press.Google Scholar
von Plato, J. (2021). Gödel’s Unfinished Book on Foundational Research in Mathematics. Vienna Circle Institute Library, Vol. 8. Cham: Springer. To appear.Google Scholar
Zach, R. (1999). Completeness before post: Bernays, Hilbert, and the development of propositional logic. The Bulletin of Symbolic Logic, 5(3), 331–366.Google Scholar