Abstract
What follows is a report on fragments of studies aimed eventually at a thorough phenomenological investigation of Kurt Gödel’s conviction that a form of intuition, not unlike perceptual intuition, plays an essential role in even highly infinitary mathematics. The studies are phenomenological in at least the senses that they attempt to take a microscopically close look at a wide range of purportedly mathematical intuitions, determining on this basis what makes them tick and what they are good for. In them I draw upon and extend Husserl’s studies of the nature of such intuition (which he called ‘categorial intuition’). Indeed, Gödel himself praised them highly, albeit they stand in great need of improvement and development, but decidedly not in the direction of Husserl’s late work, Experience and Judgment 2.
This is an expanded version of a talk given at the conference, Phenomenology and the Formal Sciences, Center for Advanced Research in Phenomenology, Pittsburgh, September 26–29, 1985. I have taken into account some questions from the audience, especially those of Dagfinn Follesdal, as well as some of the very useful considerations by the commentator, Kenneth Manders.
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References
Kurt Gödel, ‘What is Cantor’s continuum Problem?’ in Putnam and Benacerraf, Philosophy of Mathematics, Prentice-Hall, 1964, p. 271.
Charles Parsons, ‘Mathematical Intuition’, Proc. of the Aristotelian Society, 1981.
Gottlob Frege, Foundations of Arithmetic, Northwestern University Press, 1964, § 13.
Edmund Husserl, Logical Investigations, Humanities Press, 1970.
G. Birkhoff, ‘A Set of Postulates for Plane Geometry, Based on Scale and Protractor’, Annals of Math. 33 (1932), 329–345.
J. Hjelmslev, Die Natürliche Geometrie, Hamburg 1923.
In, of course, Hubert’s sense of meaning by implicit definition. 14 Cambridge University Press, 1983.
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© 1991 Springer Science+Business Media Dordrecht
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Tragesser, R.S. (1991). How Mathematical Foundation All But Come About: A Report on Studies Toward a Phenomenological Critique of Gödel’s Views on Mathematical Intuition. In: Seebohm, T.M., Føllesdal, D., Mohanty, J.N. (eds) Phenomenology and the Formal Sciences. Contributions to Phenomenology, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2580-2_13
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