Skip to main content
SpringerLink
Log in

Husserl and Gödel

  • Chapter
  • First Online:
Essays on Husserl's Logic and Philosophy of Mathematics

Part of the book series: Synthese Library ((SYLI,volume 384))

Abstract

Kurt Gödel (1906–1978) began to study the philosophy of Edmund Husserl (1859–1938) in 1959. In this paper I present an overview of central themes in Gödel’s study of Husserl’s phenomenology. Since many of Gödel’s ideas concerning Husserl were never put into a systematic form by Gödel himself, I quote fairly extensively in the paper from several sources in order to inform the reader of the nature of Gödel’s interest in Husserl. Gödel prepared one manuscript specifically on Husserl, as we will see below, and many of Gödel’s comments on Husserl are included in the books of Hao Wang. I will also quote some relevant texts from the Gödel Nachlass. In accordance with these various sources, I provide a brief overview in a later section of the paper of Gödel’s interest in eidetic transcendental phenomenology as a new type of monadology. The relationship of Gödel’s incompleteness theorems to Husserl’s notion of ‘definite’ axiom systems is also discussed briefly.

Professor Richard Tieszen passed away shortly after completing his contribution to this volume. He will be sorely missed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    See also Tieszen 1992, 2005, Part II, 2011, 2012. Perhaps the earliest discussion of Gödel in terms of Husserl’s phenomenology is in Tragesser 1977. Other papers on Husserl and Gödel include Føllesdal 1995, van Atten and Kennedy 2003, da Silva 2005, Hauser 2006, van Atten 2006, and Liu 2010.

  2. 2.

    Wang 1974, 1987, 1996.

  3. 3.

    The items from the Nachlass that I cite are not widely known. I am happy to acknowledge that I have benefitted in a number of ways from being part of the multi-year project Kurt Gödel: Philosopher-Scientist funded by the Agence Nationale de la Recherche (ANR) of France, headed by Professor Gabriella Crocco at Université Aix-Marseille. The project was devoted to transcribing from Gabelsberger shorthand (the shorthand used also by Husserl) Gödel’s philosophical notebooks, known as the Max-Phil notebooks, which are also in the Nachlass. The entries in the notebooks evidently antedate Gödel’s study of Husserl but they should help to shed light on his views on Leibniz, Kant, and other philosophers and on his own philosophical development.

  4. 4.

    I met with and then later corresponded with Wang during this period about Gödel and the philosophy of mathematics. Wang read and commented on Tieszen 1989 and 1992. In our discussions he was especially interested in Gödel’s attraction to Husserl’s philosophy.

  5. 5.

    Reproduced in Wang 1987, 16–21.

  6. 6.

    Menger 1994.

  7. 7.

    Wang 1996, 76.

  8. 8.

    Gödel *1961/?.

  9. 9.

    Wang 1996, 155.

  10. 10.

    In some places in his writings Gödel likens the antinomies to illusions of the senses. They are cases where we have not seen concepts clearly enough, and they lose their grip on us once we have achieved more clarity in our perception of concepts. See, for example, the passages in Wang 1974 on perceiving concepts clearly, 81–86. Also, Gödel *1953/9, 321; 1964, 268, and Tieszen 1992, 1998, 2002.

  11. 11.

    In various places in his writings, going back to the 1930s, Gödel distinguishes the purely formal and relative concept of proof from the ‘abstract’ concept of proof as ‘that which provides evidence’ (see, e.g., 193?, 164, vol. III). To Wang (Wang 1996, 168) he said: “[A proposition or a proof is] a net of symbols associated with a net of concepts. To understand something requires introspection; for instance, the abstract idea of a proof must be seen [the idea ‘behind’ a proof can only be understood] by introspection.” See also the comments in § 2 below on introspection.

  12. 12.

    See also Gödel’s remark in Gödel 1972, vol. II, 271–273.

  13. 13.

    See Gödel, *1953/59.

  14. 14.

    Wang 1996, 166.

  15. 15.

    There are references elsewhere in Gödel’s thinking to meaning clarification and phenomenology. In Wang 1974, 189, for example, Wang says “With regard to setting up the axioms of set theory (including the search for new axioms), we can distinguish two questions, viz., (1) what, roughly speaking, the principles are by which we introduce the axioms, (2) what their precise meaning is and why we accept such principles. The second question is incomparably more difficult. It is my impression that Gödel proposes to answer it by phenomenological investigations.”

    It should be noted that there is virtually no work on higher set theory in Husserl’s writings. The many philosophical issues raised in connection with actual completed infinite totalities, non-denumerable sets, large cardinal axioms, impredicativity, determinateness of power set, reflection principles, forcing, etc., are thus not addressed by Husserl. The philosophy of mathematics literature contains relevant materials but a lot of the work in this direction remains to be pursued.

  16. 16.

    Gödel 1944, 140–141.

  17. 17.

    van Atten and Kennedy 2003, 433.

  18. 18.

    See also Tieszen 1992, 1998, 2002, 2011.

  19. 19.

    See, e.g., Gödel *1951.

  20. 20.

    Cited in van Atten 2006, 257.

  21. 21.

    See the Vienna Lecture, Appendix I in Husserl 1954, 299.

  22. 22.

    Wang 1996, 164–165.

  23. 23.

    Op.cit., 288–289.

  24. 24.

    Op.cit., 327.

  25. 25.

    Tieszen 2011.

  26. 26.

    Wang 1996, 165.

  27. 27.

    Op.cit., 164.

  28. 28.

    Op.cit., 164.

  29. 29.

    Op.cit., 166.

  30. 30.

    Op.cit., 166.

  31. 31.

    Op.cit., 166.

  32. 32.

    Op.cit., 167.

  33. 33.

    Op.cit., 168.

  34. 34.

    Wang 2011, 100.

  35. 35.

    Wang 1996, 173.

  36. 36.

    Gödel *1953/59.

  37. 37.

    Wang 1996, 169.

  38. 38.

    Loc. cit.

  39. 39.

    See, e.g., Husserl 1913, 1923–24.

  40. 40.

    See, e.g., Husserl 1908.

  41. 41.

    Husserl 1910–11.

  42. 42.

    Husserl 1922.

  43. 43.

    Husserl 1923–24.

  44. 44.

    Husserl 1927–28.

  45. 45.

    Husserl 1931.

  46. 46.

    Op.cit., 67.

  47. 47.

    Op.cit., 150.

  48. 48.

    Husserl 1927–28, 175.

  49. 49.

    Husserl 1922, 72.

  50. 50.

    Husserl 1927–28, 191–194.

  51. 51.

    Op.cit., 191–194.

  52. 52.

    The ANR project mentioned in footnote 1 might shed further light on this.

  53. 53.

    Husserl 1913, 133–134.

  54. 54.

    Mahnke 1917.

  55. 55.

    van Atten and Kennedy 2003, 457.

  56. 56.

    Op.cit., 446.

  57. 57.

    See Tieszen 2004.

  58. 58.

    Suzanne Bachelard already distinguishes these properties in her study of Husserl’s FTL (Bachelard 1968). See her discussion on pp. 49–63.

  59. 59.

    Cavaillès 1947, 72.

  60. 60.

    For some of the main sources on these issues see, e.g., Lohmar 1989, Ortiz Hill 1995, 2000, Majer 1997, da Silva 2000, Hartimo 2007, Centrone 2010.

  61. 61.

    Centrone 2010.

  62. 62.

    Bachelard 1968, 54.

  63. 63.

    Op.cit., 55.

  64. 64.

    Husserl 1980, 90.

  65. 65.

    Gödel 1964, 1972a.

  66. 66.

    See also Gödel 1934, 1972a.

  67. 67.

    See, e.g., Husserl 1931, § 41 or Husserl 1929, § 94.

  68. 68.

    See also Tieszen 2010, 2011.

  69. 69.

    See Tieszen 2004.

  70. 70.

    See also Wang 1996, 146; Tieszen 1998.

References

  • In references to Husserl’s works I have used original dates to indicate historical

    Google Scholar 

  • development even though English translations, where available, are cited.

    Google Scholar 

  • S. Bachelard, A Study of Husserl’s Formal and Transcendental Logic (Northwestern University Press, Evanston, 1968)

    Google Scholar 

  • J. Cavaillès, Sur la logique et la théorie de la science (Vrin, Paris, 1947)

    Google Scholar 

  • S. Centrone, Logic and Philosophy of Mathematics in the Early Husserl (Springer, Dordrecht, 2010)

    Book  Google Scholar 

  • J. Da Silva, Husserl’s two notions of completeness: Husserl and Hilbert on completeness and imaginary elements in mathematics. Synthese 125, 417–438 (2000)

    Article  Google Scholar 

  • J. Da Silva, Gödel and transcendental phenomenology. Rev. Int. Philos. 234, 553–574 (2005)

    Google Scholar 

  • S. Feferman et al. (eds.), Kurt Gödel: Collected Works, vol I (Oxford University Press, Oxford, 1986)

    Google Scholar 

  • S. Feferman et al. (eds.), Kurt Gödel: Collected Works, vol II (Oxford University Press, Oxford, 1990)

    Google Scholar 

  • S. Feferman et al. (eds.), Kurt Gödel: Collected Works, vol III (Oxford University Press, Oxford, 1995)

    Google Scholar 

  • D. Føllesdal, Gödel and Husserl, in From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics, ed. by J. Hintikka (Kluwer, Dordrecht, 1995), pp. 427–446

    Google Scholar 

  • K. Gödel, On undecidable propositions of formal mathematical systems (1934), in Feferman et al. (1986), pp. 346–371

    Google Scholar 

  • K. Gödel, Undecidable diophantine propositions (*193?), in Feferman et al. 1995a, pp. 164–175

    Google Scholar 

  • K. Gödel, Russell’s mathematical logic (1944), in Feferman et al. (1990), pp. 119–143

    Google Scholar 

  • K. Gödel, Some basic theorems on the foundations of mathematics and their implications (*1951), in Feferman et al. (1995b), pp. 304–323

    Google Scholar 

  • K. Gödel, Is mathematics a syntax of language? (*1953/9, III and V), in Feferman et al. (1995c), pp. 334–363

    Google Scholar 

  • K. Gödel, The modern development of the foundations of mathematics in the light of philosophy (*1961/?), in Feferman et al. (1995d), pp. 374–387

    Google Scholar 

  • K. Gödel, What is Cantor’s continuum problem? (1964), in Feferman et al. (1990), pp. 254–270. Revised version of Gödel (1947)

    Google Scholar 

  • K. Gödel, On an extension of finitary mathematics which has not yet been used (1972a), in Feferman et al. (1990), pp. 271–280. Revised version of Gödel (1958)

    Google Scholar 

  • K. Gödel, Some remarks on the undecidability results (1972b), in Feferman et al. (1990), pp. 305–306

    Google Scholar 

  • M. Hartimo, Towards completeness: Husserl on theories of manifolds 1890–1901. Synthese 156, 281–310 (2007)

    Article  Google Scholar 

  • K. Hauser, Gödel’s program revisited part I: The turn to phenomenology. Bull. Symb. Log. 12, 529–588 (2006)

    Article  Google Scholar 

  • C. O. Hill, Husserl and Hilbert on completeness, in From Dedekind to Gödel, ed. by J. Hintikka (Ed), (Kluwer, Dordrecht, 1995), pp. 143–163

    Google Scholar 

  • C. O. Hill, Husserl’s Mannigfaltigkeitslehre, in Husserl or Frege? Meaning, Objectivity, and Mathematics, ed. by C.O. Hill, G.E. Rosado Haddock (Open Court, La Salle, 2000) pp. 161–178

    Google Scholar 

  • E. Husserl, Philosophy of Arithmetic: Psychological and Logical Investigations (1891), translated by D. Willard (Kluwer, Dordrecht, 2003)

    Google Scholar 

  • E. Husserl, Logical Investigations, vols. I, II. (1900–01), Translation of the 2nd edition by J. N. Findlay (Routledge and Kegan Paul, London, 1973)

    Google Scholar 

  • E. Husserl, Philosophy as rigorous science (1908), translated by Q. Lauer, in Phenomenology and the Crisis of Philosophy (Harper, New York, 1965), pp. 71–147

    Google Scholar 

  • E. Husserl, Ideas pertaining to a pure phenomenology and to a phenomenological philosophy. in First Book (1913), translated by F. Kersten (Kluwer, Dordrecht, 1982)

    Google Scholar 

  • E. Husserl, The London lectures (Syllabus of a course of four lectures) (1922), in P. McCormick, F. Elliston (eds.), Husserl: Shorter Works (University of Notre Dame Press, Notre Dame, 1981), pp. 68–74

    Google Scholar 

  • E. Husserl, Erste Philosophie. Erster Teil: Kritische Ideengeschichte (1923–24), Husserliana, vol. XII (Nijhoff, The Hague, 1956a)

    Google Scholar 

  • E. Husserl, Erste Philosophie. Zweiter Teil: Theorie der phänomenologischen Reduktion (1923–24), Husserliana, vol. XIII (Nijhoff, The Hague, 1956b)

    Google Scholar 

  • E. Husserl, ‘Phenomenology’ (drafts of the Encyclopedia Britannica article) (1927–28), in Psychological and Transcendental Phenomenology and the Confrontation with Heidegger (1927–1931) (Kluwer, Dordrecht, 1997), pp. 83–194

    Google Scholar 

  • E. Husserl, Formal and Transcendental Logic (1929), translated by D. Cairns (Nijhoff, The Hague, 1969)

    Google Scholar 

  • E. Husserl, Cartesian Meditations. An Introduction to Phenomenology (1931), translated by D. Cairns (Nijhoff, The Hague, 1960)

    Google Scholar 

  • E. Husserl, The Crisis of the European Sciences and Transcendental Phenomenology (1954), translated by D. Carr (Northwestern University Press, Evanston, 1970). Original German manuscripts written 1935–38

    Google Scholar 

  • E. Husserl, Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy. Third Book: Phenomenology and the Foundations of the Sciences, translated by T. Klein, W. Pohl (Nijhoff, The Hague, 1980). Original manuscript dating from 1912

    Google Scholar 

  • I. Kant, Critique of Pure Reason, translated by N.K. Smith (Macmillan, London 1973). First edition originally published in 1781; second edition originally published in 1787

    Google Scholar 

  • X. Liu, Gödel’s Philosophical Program and Husserl’s Phenomenology. Synthese 175, 33–45 (2010)

    Article  Google Scholar 

  • D. Lohmar, Phänomenologie der Mathematik, Elemente einer phänomenologischen Aufklärung der mathematischen Erkenntnis nach Husserl (Kluwer, Dordrecht, 1989)

    Book  Google Scholar 

  • D. Mahnke, Eine neue Monadologie. Kantstudien Ergänzungsheft 39 (Reuther and Reichard, Berlin, 1917)

    Google Scholar 

  • D. Mahnke, Leibnizens Synthese von Universalmathematik und Individualmetaphysik. Erster Teil. Jahrbuch für Philosophie und phänomenologische Forschung VII, 304–611 (1925)

    Google Scholar 

  • U. Majer, Husserl and Hilbert on completeness: A neglected chapter in early twentieth century foundations of mathematics. Synthese 110, 37–56 (1997)

    Article  Google Scholar 

  • K. Menger, Reminiscences of the Vienna Circle and the Mathematical Colloquium, in L. Golland et al. (eds.) (Kluwer, Dordrecht, 1994)

    Google Scholar 

  • R. Tieszen, Mathematical Intuition: Phenomenology and Mathematical Knowledge (Kluwer, Synthese Library series, Dordrecht, 1989)

    Book  Google Scholar 

  • R. Tieszen, Kurt Gödel and phenomenology. Philos. Sci. 59(2), 176–194 (1992). Reprinted in Tieszen (2005)

    Google Scholar 

  • R. Tieszen, Gödel’s path from the incompleteness theorems (1931) to phenomenology (1961). Bull. Symb. Log. 4(2), 181–203 (1998). Reprinted in Tieszen (2005)

    Google Scholar 

  • R. Tieszen, Gödel and the intuition of concepts. Synthese 133(3), 363–391 (2002). Reprinted in Tieszen (2005)

    Google Scholar 

  • R. Tieszen, Husserl’s logic, in Handbook of the History of Logic, ed. by D. Gabbay, J. Woods, vol. III, (Elsevier, Amsterdam, 2004), pp. 207–321

    Google Scholar 

  • R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics (Cambridge University Press, Cambridge, 2005)

    Book  Google Scholar 

  • R. Tieszen, Mathematical Realism and Transcendental Phenomenological Idealism, in Phenomenology and Mathematics, ed. by Hartimo, (Springer, Dordrecht, 2010), pp. 1–22

    Google Scholar 

  • R. Tieszen, After Gödel: Platonism and Rationalism in Mathematics and Logic (Oxford University Press, Oxford, 2011)

    Book  Google Scholar 

  • R. Tieszen, Monads and Mathematics: Gödel and Husserl. Axiomathes 22, 31–52 (2012)

    Article  Google Scholar 

  • R. Tragesser, Phenomenology and Logic (Cornell University Press, Ithaca, 1977)

    Google Scholar 

  • M. van Atten, Two Draft Letters from Gödel on Self-Knowledge of Reason. Philos. Math. 14(2), 255–261 (2006)

    Article  Google Scholar 

  • M. van Atten, J. Kennedy, On the philosophical development of Kurt Gödel. Bull. Symb. Log. 9, 425–476 (2003)

    Article  Google Scholar 

  • H. Wang, From Mathematics to Philosophy (Humanities Press, New York, 1974)

    Google Scholar 

  • H. Wang, Reflections on Kurt Gödel (MIT Press, Cambridge, MA, 1987)

    Google Scholar 

  • H. Wang, A Logical Journey: From Gödel to Philosophy (MIT Press, Cambridge, MA, 1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Philosophie, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Richard Tieszen

Authors
  1. Richard Tieszen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Philosophie, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Stefania Centrone

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Tieszen, R. (2017). Husserl and Gödel. In: Centrone, S. (eds) Essays on Husserl's Logic and Philosophy of Mathematics. Synthese Library, vol 384. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1132-4_16

Download citation

Publish with us

Policies and ethics

Search

Navigation