Abstract
Gödel has argued that we can cultivate the intuition or ‘perception’ of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward ‘objects’ and the meaning of the term ‘abstract’ in the context of a theory of the intentionality of cognition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Benacerraf, P.: 1973, ‘Mathematical Truth’, Journal of Philosophy 70, 661–679.
Dennett, D.: 1971, ‘Intentional Systems’, reprinted in D. Dennett, Brainstorms, Bradford Books, Montgomery, Vermont, 1978, pp. 3-22.
Feferman, S. et al. (eds): 1986/1990/1995, Kurt Gödel: Collected Works, Vols. I, II, III, Oxford University Press, Oxford.
Føllesdal, D.: 1995, ‘Gödel and Husserl’, in J. Hintikka (ed.), Essays on the Development of the Foundations of Mathematics, Kluwer, Dordrecht, pp. 427–446.
Frege, G. 1892, ‘Ñber Sinn und Bedeutung’, translated as ‘On Sense and Reference’, in P. Geachand M. Black (eds.), Translations from the Philosophical Writings of Gottlob Frege, Blackwell, Oxford, 1970, pp. 56–78.
Gödel, K.: 1934, ‘On Undecidable Propositions of Formal Mathematical Systems’, in Feferman et al., 1986, 346–371.
Gödel, K.: 193?, ‘Undecidable Diophantine Propositions’, in Feferman et al., 1995, 164–175.
Gödel, K.: 1944, ‘Russell's Mathematical Logic’, in Feferman et al., 1990, 119–143.
Gödel, K.: 1946, ‘Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics’, in Feferman et al., 1990, 150–153.
Gödel, K.: 1947/64, ‘What is Cantor's Continuum Problem?’, in Feferman et al., 1990, 176-187, 254-270.
Gödel, K.: 1951, ‘Some Basic Theorems on the Foundations of Mathematics and Their Implications’, in Feferman et al., 1995, 304-323.
Gödel, K.: 1953/9, III and V: ‘Is Mathematics Syntax of Language?’, in Feferman et al., 1995, 334–363.
Gödel, K.: 1961/?, ‘The Modern Development of the Foundations of Mathematics in the Light of Philosophy’, in Feferman et al., 1995, 374–387.
Gödel, K.: 1972, ‘On an Extension of Finitary Mathematics Which Has Not Yet Been Used’, in Feferman et al., 1990, 271–280.
Gödel, K.: 1972a, ‘Some Remarks on the Undecidability Results’, in Feferman et al., 1990, 305–306.
Husserl, E.: 1913a, Logische Untersuchungen, 2nd ed. Max Niemeyer, Halle. Reprinted in Husserl 1984. English translation in Husserl 1970.
Husserl, E.: 1913b, Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, Max Niemeyer., Halle. Reprinted in Husserl 1950. English translation in Husserl 1982.
Husserl, E.: 1939, ‘Der Ursprung der Geometrie als intentional-historisches Problem’, translated as ‘The Origin of Geometry’ in E. Husserl, The Crisis of the European Sciences and Transcendental Phenomenology, Northwestern University Press, Evanston, IL, 1970, Appendix VI.
Husserl, E.: 1950, Husserliana III, Nijhoff, The Hague.
Husserl, E.: 1970, Logical Investigations, Vols. I, II. English translation of Husserl 1913b and 1921, Routledge and Kegan Paul, London.
Husserl, E.: 1982, Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy, Nijhoff, The Hague.
Husserl, E.: 1984, Husserliana XIX, Nijhoff, The Hague.
Parsons, C.: 1995, ‘Platonism and Mathematical Intuition in Kurt Gödel's Thought’, The Bulletin of Symbolic Logic 1, 44–74.
Tieszen, R.: 1992, ‘Kurt Gödel and Phenomenology’, Philosophy of Science 59, 176–194.
Tieszen, R.: 1994, ‘Mathematical Realism and Gödel's Incompleteness Theorems’, Philosophia Mathematica 3, 177–201.
Tieszen, R.: 1998a, ‘Gödel's Philosophical Remarks on Logic and Mathematics: Critical Notice of Kurt Gödel: Collected Works, Vols. I, II, III’, Mind 107, 219–232.
Tieszen, R.: 1998b, ‘Gödel's Path from the Incompleteness Theorems (1931) to Phenomenology (1961)’, Bulletin of Symbolic Logic 4, 181–203.
Tieszen, R.: 2000, ‘Gödel and Quine on Meaning and Mathematics’, in G. Sher and R. Tieszen (eds.), Between Logic and Intuition: Essays in Honor of Charles Parsons, Cambridge University Press, Cambridge.
Tieszen, R.: 2003 (forthcoming), ‘Husserl's Logic’, in D. Gabbay and J. Woods (eds.), Handbook of the History and Philosophy of Logic, Springer, Berlin.
Tragesser, R.: 1977, Phenomenology and Logic, Cornell University Press, Ithaca, New York.
Wang, H.: 1974, From Mathematics to Philosophy, Humanities Press, New York.
Wang, H.: 1987, Reflections on Kurt Gödel, MIT Press, Cambridge, MA.
Wang, H.: 1996, A Logical Journey: From Gödel to Philosophy, MIT Press, Cambridge, MA.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tieszen, R. Gödel And The Intuition Of Concepts. Synthese 133, 363–391 (2002). https://doi.org/10.1023/A:1021247624209
Issue Date:
DOI: https://doi.org/10.1023/A:1021247624209