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Juliette Kennedy: Three Moments in the Philosophical Life of Kurt Gödel


In this talk we will visit three moments in the philosophical life of Kurt Gödel, bearing in mind that Gödel's philosophical work was in a clear sense inseparable from his mathematical work. We consider first the philosophical remarks in the introduction of Gödel's 1929 thesis, in which he presented his proof of the completeness of first order predicate logic. Those remarks concern the use of the law of the excluded middle in his proof of the completeness theorem, and secondly the question whether consistency is a criterion of existence of mathematical objects, the latter being the subject of debate between both Hilbert and Frege, and Hilbert and Brouwer. The second moment concerns Gödel's remarks on meaning in the 1964 supplement to his paper "What is Cantor's Continuum Problem?", an earlier version of which was published in 1947. The last moment concerns his remarks about the life of a philosopher, about phenomenology, and about some other topics, made during a number of conversations with Gödel had with the proof theorist Sue Walker Toledo in 1972. Our remarks are based on the extensive (hitherto unpublished) notes taken by Toledo of those conversations.