Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-22T16:09:05.643Z Has data issue: false hasContentIssue false
  • English
  • Français

HUSSERL AND GÖDEL’S INCOMPLETENESS THEOREMS

Published online by Cambridge University Press:  03 July 2017

MIRJA HARTIMO
MIRJA HARTIMO*
Affiliation:
Norwegian University of Life Sciences
*
*NORWEGIAN UNIVERSITY OF LIFE SCIENCES PO BOX 5003 1432 AAS, NORWAY E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper examines Husserl’s interactions with logicians in the 1930s in order to assess Husserl’s awareness of Gödel’s incompleteness theorems. While there is no mention about the results in Husserl’s known exchanges with Hilbert, Weyl, or Zermelo, the most likely source about them for Husserl is Felix Kaufmann (1895–1949). Husserl’s interactions with Kaufmann show that Husserl may have learned about the results from him, but not necessarily so. Ultimately Husserl’s reading marks on Friedrich Waismann’s Einführung in das mathematische Denken: die Begriffsbildung der modernen Mathematik, 1936, show that he knew about them before his death in 1938.

Keywords

01A6003-0303A05Edmund HusserlGödel’s incompleteness theoremsFelix KaufmannFriedrich Waismann
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 4 , December 2017 , pp. 638 - 650
Copyright
Copyright © Association for Symbolic Logic 2017 

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

van Atten, M. (2015). Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Cham, Heidelberg, New York, Dordrecht, London: Springer.Google Scholar
van Atten, M. & Kennedy, J. ([2003] 2015). On the philosophical development of Kurt Gödel. In van Atten, M. Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Cham, Heidelberg, New York, Dordrecht, London: Springer, pp. 95–145.Google Scholar
Cavaillés, J. (1970). On logic and the theory of science. In Kockelmans, J. J. and Kisiel, T. J., editors. Translated by Kisiel, Theodore J.. Phenomenology and the Natural Sciences. Evanston: Northwestern University Press, pp. 353–409.Google Scholar
Dawson, J. W Jr.. (1984). The reception of Gödel’s incompleteness theorems. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1984, 253–271.Google Scholar
Ebbinghaus, H.-D. in cooperation with Volker Peckhaus (2007). Ernst Zermelo, An Approach to his Life and Work. Berlin, Heidelberg, New York: Springer.Google Scholar
Eley, L. (1970). Einleitung des Herausgebers. In Husserl, E. Philosophie der Arithmetik, mit ergänzenden Texten (1890–1901). Husserliana Band XII. Den Haag: Martinus Nijhoff, pp. XIII–XXVIX.CrossRefGoogle Scholar
Feferman, S. (2008). Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert’s program. Dialectica, 62(2), 179–203.Google Scholar
Gödel, K. (1990). Remarks before the Princeton Bicentennial Conference on the problems of mathematics, 1946. In Feferman, S., Dawson, J. W. Jr, Kleene, S. C., Moore, G. H., Solovay, R. M., and van Heijenoort, J., editors. Collected Works, Volume II, Publications 1938–1974. Oxford: Clarendon Press, pp. 150–153.Google Scholar
Hartimo, M. (2007). Towards completeness: Husserl on theories of manifolds 1890–1901. Synthese, 156, 281–310.Google Scholar
Hartimo, M. (2016). Husserl on completeness, definitely. Synthese, doi: 10.1007/s11229-016-1278-7.Google Scholar
Hartimo, M. (Forthcoming in 2017). Deeply Respectful Friendship: Husserl and Hilbert on the foundations of mathematics. In Centrone, S., editor. Essays on Husserl’s Logic and Philosophy of Mathematics. Synthese Library. Springer.Google Scholar
Husserl, E. (1950/1983). Ideen zu einer reinen Phänomenologie und phäneomenologischen Philosophie. Erstes Buch. Allgemeine Einführung in die reine Phänomenologie. Herausgegeben von Walter Biemel. Husserliana Band III. Haag: Martinus Nijhoff, 1950. English translation: Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy. First book. General Introduction to a Pure Phenomenology. The Hague, Boston, Lancaster: Martinus Nijhoff, 1983.Google Scholar
Husserl, E. (1974/1969). Formale and transzendentale Logik. Versuch einer Kritik der logischen Vernunft. Husserliana Band 17. The Hague, Netherlands: Martinus Nijhoff, 1974. English translation: Formal and Transcendental Logic, transl. by Dorion Cairns. The Hague: Martinus Nijhoff, 1969.Google Scholar
Husserl, E. (1976/1970). Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie. Eine Einleitung in die phänomenologische Philosophie. Herausgegeben von Walter Biemel. Husserliana Band VI. Haag: Martinus Nijhoff, 1976. English translation: The Crisis of European Sciences and Transcendental Phenomenology. An Introduction to Phenomenological Philosophy. Translated by David Carr. Evanston: Northwestern University Press, 1970.CrossRefGoogle Scholar
Husserl, E. (1994a). Briefwechsel. Husserliana Dokumente Band III, III. Die Göttinger Schule, edited by Schuhmann, E. and Schuhmann, K.. Dordrecht, Boston, London: Kluwer Academic Publishers.Google Scholar
Husserl, E. (1994b). Briefwechsel. Husserliana Dokumente Band III, IV. Die Freiburger Schüler, edited by Schuhmann, E. and Schuhmann, K.. Dordrecht, Boston, London: Kluwer Academic Publishers.Google Scholar
Husserl, E. (1994c). Briefwechsel. Husserliana Dokumente Band III, VII. Wissenschaftlerkorrespondenz, edited by Schuhmann, E. and Schuhmann, K.. Dordrecht, Boston, London: Kluwer Academic Publishers.Google Scholar
Husserl, E. (1994d). Briefwechsel. Husserliana Dokumente Band III, IX. Familienbriefe, edited by Schuhmann, E. and Schuhmann, K.. Dordrecht, Boston, London: Kluwer Academic Publishers.Google Scholar
Kanamori, A. (2004). Zermelo and set theory. The Bulletin of Symbolic Logic, 10(4), 487–553.Google Scholar
Kaufmann, F. (1978). The Infinite in Mathematics, Logico-mathematical Writings, edited by McGuinness, B.. Translated by Foulkes, P.. Dordrecht, Boston, London: D. Reidel Publishing Company.Google Scholar
Mancosu, P. (1999). Between Vienna and Berlin: The immediate reception of Gödel’s incompleteness theorems. History and Philosophy of Logic, 20(1), 33–45 Google Scholar
Mancosu, P. (2010). The Adventure of Reason. Interplay between Philosophy of Mathematics and Mathematical Logic 1900–1940. Oxford: Oxford University Press.Google Scholar
Miller, P. J. (1982). Numbers in Presence and Absence: A Study of Husserl’s Philosophy of Mathematics. The Hague, Boston, London: Martinus Nijhoff Publishers.CrossRefGoogle Scholar
Nagel, E. (1978). Introduction. In Kaufmann, F., and McGuiness, B., editors. Translated by Foulkes, P.. The Infinite in Mathematics, Logico-mathematical Writings. Dordrecht, Boston, London: D. Reidel Publishing Company.Google Scholar
Peckhaus, V. (1990). Hilbertprogramm und Kritische Philosophie. Göttingen: Vandenhoeck und Ruprecht.Google Scholar
Schmit, R. (1981). Husserls Philosophie der Mathematik. Platonistisce und konstruktivistische Momente in Husserls Mathematikbegriff. Bonn: Bouvier Verlag Herbert Grundmann.Google Scholar
Waismann, F. (1936/1966). Einführung in das mathematische Denken: die Begriffsbildung der modernen Mathematik. Mit einem Vorwort von Karl Menger.Wien: Gerold. English translation by Benac, Theodore J.; Introduction to Mathematical Thinking. New York: Harper & Row.Google Scholar
Wang, H. (1987). Reflections on Kurt Gödel. Cambridge, Massachusetts, London, England: The MIT Press.Google Scholar