Kurt Gödel, Essays for His Centennial
Solomon Feferman, Charles Parsons, Steven G. Simpson, editors
Year: 2010
ISBN-13: 9780521115148
384 pages. Hardcover.
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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.
Table of Contents
General:
- Solomon Feferman
The Gödel editorial project: a synopsis - John W. Dawson, Jr., and Cheryl A. Dawson
Future tasks for Gödel scholars
Proof Theory:
- Jeremy Avigad
Gödel and the metamatematical tradition - Wilfied Sieg
Only two letters: The corresondence between Herbrand and Gödel - W.W. Tait
Gödel’s reformulation of Gentzen’s first consistency proof for arithmetic: The no-counterexample interpretation - W.W. Tait
Gödel on intuition and on Hilbert’s finitism - Stephen G. Simpson
The Gödel hierarchy and reverse mathematics - John P. Burgess
On the outside looking in: A caution about conservativeness
Set Theory:
- Akihiro Kanamori
Gödel and set theory - Sy-David Friedman
Generalisations of Gödel’s universe of constructible sets - Peter Koellner
On the question of absolute undecidability
Philosophy of Mathematics:
- Martin Davis
What did Gödel believe and when did he believe it? - Warren Goldfarb
On Gödel’s way in: The influence of Rudolf Carnap - Steve Awodey and A.W. Carus
Gödel and Carnap - Mark van Atten and Juliette Kennedy
On the philosophical development of Kurt Gödel - Charles Parsons
Platonism and mathematical intuition in Kurt Gödel’s thought - Donald A. Martin
Gödel’s conceptual realism