Platonism and mathematical intuition in Kurt Gödel's thought

Received June 6, 1994, and in revised form October 20, 1994. Expanded version of the Retiring Presidential Address presented to the annual meeting of the Association for Symbolic Logic at the University of Florida, Gainesville, March 7, 1994. Material from this paper was also presented in lectures to the Fifteenth Annual Wittgenstein Symposium in Kirchberg am Wechsel, Austria, and at the University of Rochester and the University of California, Berkeley. I wish to thank each of these audiences. I am especially indebted to David Braun, Hans Burkhardt, John Carriero, Cheryl Dawson, Erin Kelly, John Rawls, Gila Sher, Wilfried Sieg, W. W. Tait, Guglielmo Tamburrini, Hao Wang, and the referee for their comments and assistance. Wang and my fellow editors of Gödel’s works, Solomon Feferman, John Dawson, Warren Goldfarb, Robert Solovay, and Sieg have taught me much of what I know about Gödel’s thought. Unpublishedwritings ofGödel are quotedbykindpermissionof the Institute forAdvanced Study. The last revisions of the paper were made when the author was a Fellow of the Center for Advanced Study in the Behavioral Sciences, with the support of the Andrew W. Mellon Foundation. Their support is gratefully acknowledged. Russell [19, page 356].