紹介
Kurt Godel (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 Godel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Godel'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 sets.
目次
Part I. General: 1. The Godel editorial project: a synopsis Solomon Feferman
2. Future tasks for Godel scholars John W. Dawson, Jr, and Cheryl A. Dawson
Part II. Proof Theory: 3. Kurt Godel and the metamathematical tradition Jeremy Avigad
4. Only two letters: the correspondence between Herbrand and Godel Wilfried Sieg
5. Godel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counter-example interpretation W. W. Tait
6. Godel on intuition and on Hilbert's finitism W. W. Tait
7. The Godel 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. Godel and set theory Akihiro Kanamori
10. Generalizations of Godel'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 Godel believe and when did he believe it? Martin Davis
13. On Godel's way in: the influence of Rudolf Carnap Warren Goldfarb
14. Godel and Carnap Steve Awodey and A. W. Carus
15. On the philosophical development of Kurt Godel Mark van Atten and Juliette Kennedy
16. Platonism and mathematical intuition in Kurt Godel's thought Charles Parsons
17. Godel's conceptual realism Donald A. Martin.
