Repository | Book | Chapter
(2014) Constructivity and computability in historical and philosophical perspective, Dordrecht, Springer.
After a brief survey of Gödel's personal contacts with Brouwer and Heyting, examples are discussed where intuitionistic ideas had a direct influence on Gödel's technical work. Then it is argued that the closest rapprochement of Gödel to intuitionism is seen in the development of the Dialectica Interpretation, during which he came to accept the notion of computable functional of finite type as primitive. It is shown that Gödel already thought of that possibility in the Princeton lectures on intuitionism of Spring 1941, and evidence is presented that he adopted it in the same year or the next, long before the publication of 1958. Draft material for the revision of the Dialectica paper is discussed in which Gödel describes the Dialectica Interpretation as being based on a new intuitionistic insight obtained by applying phenomenology, and also notes that relate the new notion of reductive proof to phenomenology. In an appendix, attention is drawn to notes from the archive according to which Gödel anticipated autonomous transfinite progressions when writing his incompleteness paper.
Publication details
DOI: 10.1007/978-94-017-9217-2_7
Full citation:
Van Atten, M. (2014)., Gödel and intuitionism, in J. Dubucs & M. Bourdeau (eds.), Constructivity and computability in historical and philosophical perspective, Dordrecht, Springer, pp. 169-214.
This document is unfortunately not available for download at the moment.