¹ On November 4,1976, Gödel mentioned some details on this point. At that time (1926 and soon after), he agreed with them that the existing state of philosophy was poor (not necessary but just a historical accident), and, in substance, agreed only with their method of analysis of philosophical and scientific concepts (using mathematical logic). He disagreed with their negation of objective reality and their thesis that metaphysical problems are meaningless. In discussions with them, Gödel took the nonpositivistic position.

In one of their publications before 1930 (a one time publication by H. Hahn and O. Neurath devoted to the Wiener Kreis), Gödel was listed as a member. Of Carnap's Logische Aufbau, Gödel said that it treats only the relation between sense perception and physical objects logically and leaves out psychological aspects. I do not know whether he meant to contrast this with Husserl's writings of which he thought well certainly in the 1970s.

² Gödel had completed his dissertation before showing it to Hahn. This was longer than the published paper and accepted for the degree in its original form. It was in preparing the shorter version for publication that Gödel made use of Hahn's suggestions.

³ Or ‘propositional functions’ according to a prominent tradition at that time.

⁴ At the same meeting F. Waismann also gave a lecture entitled The nature of mathematics: Wittgenstein's standpoint, but the text has not been published (see Erkenntnis, vol. 2, 91 ff. where the other three lectures of the session by Carnap, Heyting, and von Neumann are printed). Compare also Wittgenstein and the Vienna Circle (McGuiness, B., Editor), 1979, pp. 19–21Google Scholar.

Hilbert gave his address Logic and nature at the general session. Gödel went to hear it, and this was the only time when Gödel saw Hilbert.

⁵ Gödel married Adele Pockert on September 20, 1938.

⁶ Professor Wang Sian-jun of Beijing University wrote to me on February 28,1978:

Soon after I arrived at Vienna in February 1937, I went to Gödel's home to see him. During the three terms when I was in Vienna (spring and autumn of 1937, spring of 1938), Gödel gave only one course entitled Axiomatik der Mengenlehre, probably in the autumn of 1937. It was not a seminar. I remember constructible sets being considered in the lectures. Not many people took the course, probably only five or six.

Professor Wang also remembers that Gödel recommended to him Herbrand's Thèse, Fraenkel's and Hausdorff's Mengenlehre, as well as Hilbert and Ackermann's textbook.

Probably in 1937, Gödel told Professor Wang that after the incompleteness theorems more work in the general area of mathematical logic would not make much difference: “Jetzt, Mengenlehre”.

⁷ For an accidental reason, Gödel elaborated the history of these results in May and June of 1977 and I was asked to write up his observations. The result follows:

In this connection his main achievement really is that he first introduced the concept of constructible sets into set theory defining it as in his Proceedings paper of 1939, proved that the axioms of set theory (including the axiom of choice) hold for it, and conjectured that the continuum hypothesis also will hold. He told these things to von Neumann during his stay at Princeton in the autumn of 1935. The discovery of the proof of this conjecture on the basis of his definition is not too difficult. Gödel gave the proof (also for the GCH) not until three years later because he had fallen ill in the meantime. This proof was using a submodel of the constructible sets in the lowest case countable, similar to the one commonly given today.

⁸ On June 9, 1976, Gödel recalled that in 1941 or 1942 he wrote his paper on Russell's mathematical logic. He described the paper as a history of logic with special reference to the work of Russell.

Judging from Russell's reply to his critics (dated July 1943), it seems likely that Gödel wrote the paper mainly in 1942 to 1943. The note says in part: ‘Dr. Gödel's most interesting paper on my mathematical logic came into my hands after my replies had been completed, and at a time when I had no leisure to work on it.… His great ability, as shown by his previous work, makes me think it highly probable that many of his criticisms of me are justified’.

Gödel's paper concludes with some optimistic claims by Leibniz on the future possibilities of mathematical logic. Gödel told me that during the war he was interested in Leibniz but could not get hold of the manuscripts of Leibniz. When these manuscripts finally came in after the war, his interest had shifted to other directions.

⁹ Apparently Gödel continued to work on trying to apply his method to the continuum hypothesis for quite some time. It seems likely that his philosophical paper on the continuum problem (published toward the end of 1947) was meant in part as a sort of conclusion of his own mathematical work on this problem. It could be interpreted as a summary of his thoughts on this problem and an invitation to others to continue where he left off. At any rate, looking back now we may conjecture that between 1943 and 1947 a transition occurred from Gödel's concentration on mathematical logic to other theoretical interests which are primarily philosophical.

In this connection we may also mention Gödel's, 1946 lecture Remarks before the Princeton Bicentennial Conference on problems in mathematics (published in The undecidable (Davis, M., Editor), 1965, pp. 84–88)Google Scholar. Gödel, encouraged by the successful analysis of the invariant concept of computability, suggests looking for invariant notions of definability and provability. From both this lecture and the 1947 paper one gets the clear impression that Gödel was interested only in really basic advances.

Undoubtedly the transition was gradual. The distaste for the work on the independence of CH presumably began in 1944 and grew stronger in the next year or two. The Princeton lecture and the philosophical article on the continuum problem served as an interlude. By Gödel's own account, he began working on relativity theory in 1947.

¹⁰ In fact, Gödel wrote an article (in typescript of 28 pages) entitled: Some observations about the relationship between theory of relativity and Kantian philosophy. Probably this came from this period. It seems likely the paper was written in 1947 or before. The paper published in the volume honoring Einstein was completed before February 1949 but says much less about Kantian philosophy.

¹¹ Since the lecture was given at the end of 1951, this probably means that Gödel essentially spent the year 1951 preparing for it. I have seen a handwritten manuscript of the paper. I attended the lecture and have preserved a printed announcement. The title is Some basic theorems on the foundations of mathematics and their philosophical implications. It was given at Alumnae Hall, Pembrok College in Brown University, December 26, 1951, 8 p.m. I remember Gödel read from a manuscript at high speed, including quotations in French from Hermite. Gödel told me of some of the ideas of the lecture which are reported in my From mathematics to philosophy, 1974.

This hook of mine also contains other contributions by Gödel. Two long letters from him are included which explain how his philosophical view helped him in making his major discoveries in logic. His mature thoughts on objectivism, new axioms of set theory, and the contrast between mind and machine are reported in formulations approved by him.

From 1971 to 1977 I had frequent conversations with Gödel and wrote up some parts of them which were then discussed with him. It is my present intention to try to work over these and other notes from the conversations in order that some of his unpublished views will be known more broadly.

¹² Gödel thought that Husserl probably had a similar experience of revelation some time from 1909 to 1910.

In June 1976 Gödel said that his work at the Institute had been split in three ways: institute work, mathematics, and philosophy. He was very conscientious about his work at the Institute especially with regard to the evaluation of applicants. Hassler Whitney reported on this in his lecture on March 3, 1978.