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Gödel's Path from the Incompleteness Theorems (1931) To Phenomenology (1961)

Published online by Cambridge University Press:  15 January 2014

Richard Tieszen
Richard Tieszen*
Affiliation:
Department of Philosophy, San Jose State University, San Jose, CA 95192-0096, USAE-mail: RTieszen@aol.com
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Extract

In a lecture manuscript written around 1961 (Gödel *1961/?), Gödel describes a philosophical path from the incompleteness theorems to Husserl's phenomenology. It is known that Gödel began to study Husserl's work in 1959 and that he continued to do so for many years. During the 1960s, for example, he recommended the sixth investigation of Husserl's Logical Investigations to several logicians for its treatment of categorial intuition (Wang 1997, p. 164). While Gödel may not have been satisfied with what he was able to obtain from philosophy and Husserl's phenomenology, he nonetheless continued to recommend Husserl's work to logicians as late as the 1970s. In this paper I present and discuss the kinds of arguments that led Gödel to the work of Husserl. Among other things, this should help to shed additional light on Gödel's philosophical and scientific ideas and to show to what extent these ideas can be viewed as part of a unified philosophical outlook. Some of the arguments that led Gödel to Husserl's work are only hinted at in Gödel's 1961 paper, but they are developed in much more detail in Gödel's earlier philosophical papers (see especially 1934, *193?, 1944, 1947, *1951, *1953/59). In particular, I focus on arguments concerning Hilbert's program and an early version of Carnap's program.

§1. Some ideas from phenomenology. Since Husserl's work is not generally known to mathematical logicians, it may be helpful to mention briefly a few details about his background.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 4 , Issue 2 , June 1998 , pp. 181 - 203
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

Feferman, S. et al. (editors), 1986/1990/1995: Kurt Gödel: Collected works, Vols. I, II, III. Oxford, Oxford University Press.Google Scholar
Føllesdal, D., 1995: Gödel and Husserl, in Essays on the development of the foundations of mathematics (Hintikka, J., editor). Dordrecht, Kluwer, pp. 427–446.Google Scholar
Gödel, K., 1931: On formally undecidable propositions of Principia Mathematica and related systems I, in Feferman, , et al., 1986, pp. 145–195.Google Scholar
Gödel, K., 1934: On undecidable propositions of formal mathematical systems, in Feferman, , et al., 1986, pp. 346–371.Google Scholar
Gödel, K., *193?: Undecidable Diophantine propositions, in Feferman, , et al., 1995, pp. 164–175.Google Scholar
Gödel, K., 1944: Russell's mathematical logic, in Feferman, , et al., 1990, pp. 119–143.Google Scholar
Gödel, K., 1946: Remarks before the Princeton Bicentennial Conference on problems in mathematics, in Feferman, , et al., 1990, pp. 150–153.Google Scholar
Gödel, K., 1947/64: What is Cantor's continuum problem?, in Feferman, , et al., 1990, pp. 176–187 and 254–270.Google Scholar
Gödel, K., *1951: Some basic theorems on the foundations of mathematics and their implications, in Feferman, , et al., 1995, pp. 304–323.Google Scholar
Gödel, K., *1953/9, III and V: Is mathematics syntax of language?, in Feferman, , et al., 1995, pp. 334–363.Google Scholar
Gödel, K., *1961/?: The modern development of the foundations of mathematics in the light of philosophy, in Feferman, , et al., 1995, pp. 374–387.Google Scholar
Gödel, K., 1972: On an extension of finitary mathematics which has not yet been used, in Feferman, , et al., 1990, pp. 271–280.Google Scholar
Gödel, K., 1972a: Some remarks on the undecidability results, in Feferman, , et al., 1990, pp. 305–306.Google Scholar
Hilbert, D., 1926: Über das Unendliche, Mathematische Annalen, vol. 95, pp. 161–190. English translation by Stefan Bauer-Mengelberg in van Heijenoort, 1967, pp. 367–392.Google Scholar
Hussen, E., 1900: Logische Untersuchungen. Erster Teil: Prolegomena zur reinen Logik. Halle, Max Niemeyer. Reprinted in Husserl 1950-, XVIII.Google Scholar
Hussen, E., 1901: Logische Untersuchungen. Zweiter Teil: Untersuchungen zur Phänomenologie und Theorie der Erkenntnis. Halle, Max Niemeyer. Reprinted in Husserl 1950-, XIX.Google Scholar
Hussen, E., 1911: Philosophie als strenge Wissenschaft, Logos vol. 1, pp. 289–341. English translation by Quentin Lauer in Husserl 1965, pp. 71–147.Google Scholar
Hussen, E., 1913a: Ideenzueiner reinen Phänomenologie undphanomenologischen Philosophie. Erstes Buch: Allgemeine Einfürhung in die reine Phänomenologie. Halle, Max Niemeyer. Reprinted in Husserl 1950-, III. English translation by F. Kersten as Husserl 1982.Google Scholar
Hussen, E., 1913b: Second, revised edition of Husserl 1900 and Investigations I-V of Husserl 1901. Reprinted in Husserl 1950-, XIX, part 1. Translated into English by J. N. Findlay in Husserl 1970b.Google Scholar
Hussen, E., 1921: Second edition of Investigation VI of Husserl 1901. Reprinted in Husserl 1950-, XIX, part 2. Translated into English by J. N. Findlay in Husserl 1970.Google Scholar
Hussen, E., 1929: Formale und transzendentale Logik. Versuch einer Kritik der logischen Vernunft. Halle, Max Niemeyer. Reprinted in Husserl 1950-, XVII. English translation by D. Cairns as Husserl 1969.Google Scholar
Hussen, E., 1950-: Husserliana. Edmund Husserl: Gesammelte Werke, edited by the Achive, Husserl (Leuven) on the basis of the Nachlass. The Hague, Martinus Nijhoff; later Dordrecht, Kluwer.Google Scholar
Hussen, E., 1960: Cartesian Meditations, English translation by Cairns, D. of main text of Kartesische Meditationen, Husserl 1950-, I. The Hague, Martinus Nijhoff.Google Scholar
Hussen, E., 1965: Phenomenology and the crisis of philosophy, English translation, with an introduction by Q. Lauer, of Husserl 1911, along with Die Krisis des europäischen Menschentums und die Philosophie (from Husserl 1950-, VI, 314-348). New York, Harper.Google Scholar
Hussen, E., 1969: Formal and transcendental logic. English translation of Husserl, 1929. Dordrecht, Kluwer.Google Scholar
Hussen, E., 1970a: The crisis of the European sciences and transcendental phenomenology. English translation by Carr, D. of the main text and a selection of additional texts in Husserl 1950-, VI. Evanston, IL, Northwestern University Press.Google Scholar
Hussen, E., 1970b: Logical Investigations, Vols. I, II. English translation of Husserl, 1913b and 1921. London, Routledge and Kegan Paul.Google Scholar
Hussen, E., 1982: Ideas pertaining to a pure phenomenology and to a phenomenological philosophy. First book, General Introduction to a pure phenomenology. English translation of Husserl, 1913a. The Hague, Martinus Nijhoff.Google Scholar
Paris, J. and Harrington, L., 1977: A Mathematical Incompleteness in Peano arithmetic, in Barwise, J. (editor), Handbook of Mathematical Logic, Amsterdam, North Holland, pp. 1133–1142.Google Scholar
Parsons, C. 1995: Platonism and mathematical intuition in Kurt Gödel's thought, This Bulletin, vol. 1, pp. 44–74.Google Scholar
Tieszen, R., 1992: Kurt Gödel and phenomenology, Philosophy of Science, vol. 59, pp. 176–194.Google Scholar
Tieszen, R., 1994: Mathematical realism and GoÜdel's incompleteness theorems, Philosophia Mathematica, vol. 3, pp. 177–201.Google Scholar
Tieszen, R., 1995: Mathematics, in Smith, B. and Smith, D. (editors), Cambridge companion to philosophy: Husserl. Cambridge, Cambridge University Press, pp. 438–462.Google Scholar
Tieszen, R., 1996: Review of: Shadows of the mind: A search for the missing science of consciousness, by Penrose, Roger, Philosophia Mathematica, vol. 4, pp. 281–290.Google Scholar
Tieszen, R., 1997a: Review of: Kurt Gödel: Unpublished philosophical essays, Rodriguez-Consuegra, F. (editor), Annals of Science, vol. 54, pp. 99–101.Google Scholar
Tieszen, R., 1997b: Science Within Reason: Is there a crisis of the modern sciences?, in Otte, M. and Panza, M. (editors), Analysis and synthesis in mathematics: History and philosophy, Boston Studies in the Philosophy of Science. Dordrecht, Kluwer, pp. 243–259.Google Scholar
Tieszen, R., 1998: Gödel's Philosophical remarks on logic and mathematics: Critical notice of: Kurt Gödel: Collected Works, Vols. I, II, III”, Mind, vol. 107, pp. 219–232.Google Scholar
Tieszen, R., 199?: Gödel and Quine on meaning and mathematics, forthcoming in Between logic and intuition: Essays in honor of Charles Parsons, Sher, G. and Tieszen, R. (editors). Cambridge, Cambridge University Press.Google Scholar
van Heijenoort, J. (editor), 1967: From Frege to Gödel. Cambridge, Mass., Harvard University Press.Google Scholar
Wang, H., 1974: From mathematics to philosophy. New York, Humanities Press.Google Scholar
Wang, H., 1987: Reflections on Kurt Gödel. Cambridge, Mass., MIT Press.Google Scholar
Wang, H., 1996: A Logical Journey: From Gödel to philosophy. Cambridge, Mass., MIT Press.Google Scholar