Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel’s centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel’s writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible set.

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Part I. General: 1. The Gödel editorial project: a synopsis Solomon Feferman; 2. Future tasks for Gödel scholars John W. Dawson, Jr, and Cheryl A. Dawson; Part II. Proof Theory: 3. Kurt Gödel and the metamathematical tradition Jeremy Avigad; 4. Only two letters: the correspondence between Herbrand and Gödel Wilfried Sieg; 5. Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counter-example interpretation W. W. Tait; 6. Gödel on intuition and on Hilbert's finitism W. W. Tait; 7. The Gödel hierarchy and reverse mathematics Stephen G. Simpson; 8. On the outside looking in: a caution about conservativeness John P. Burgess; Part III. Set Theory: 9. Gödel and set theory Akihiro Kanamori; 10. Generalizations of Gödel's universe of constructible sets Sy-David Friedman; 11. On the question of absolute undecidability Peter Koellner; Part IV. Philosophy of Mathematics: 12. What did Gödel believe and when did he believe it? Martin Davis; 13. On Gödel's way in: the influence of Rudolf Carnap Warren Goldfarb; 14. Gödel and Carnap Steve Awodey and A. W. Carus; 15. On the philosophical development of Kurt Gödel Mark van Atten and Juliette Kennedy; 16. Platonism and mathematical intuition in Kurt Gödel's thought Charles Parsons; 17. Gödel's conceptual realism Donald A. Martin.