Kurt Gödel: Essays for his Centennial

Front Cover
Solomon Feferman, Charles Parsons, Stephen G. Simpson
Cambridge University Press, Apr 19, 2010 - Mathematics
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 sets.
 

Contents

John W Dawson Jr and Cheryl A Dawson
21
Jeremy Avigad
45
Wilfried Sieg
59
W W Tait
74
Godel on intuition and on Hilberts finitism
88
The Godel hierarchy and reverse mathematics
109
John P Burgess
124
SET THEORY
136
Generalisations of Godels universe of constructible sets
181
Peter Koellner
189
PHILOSOPHY OF MATHEMATICS
224
Warren Goldfarb
242
Steve Awodey and A W Carus
252
Mark van Atten and Juliette Kennedy
275
Platonism and mathematical intuition in Kurt Godels thought
326
Donald A Martin
356

Akihiro Kanamori
145

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About the author (2010)

Solomon Feferman has been a Professor of Mathematics and Philosophy at Stanford University since 1956, from which he retired in 2004. He is a Fellow of the American Academy of Arts and Sciences, was President of the Association for Symbolic Logic in 1980–2, and was the recipient of the Rolf Schock Prize for Logic and Philosophy in 2003. Feferman was editor-in-chief of the Collected Works of Kurt Gödel (1986–2003).

Charles Parsons holds an AB (mathematics) and PhD (philosophy) from Harvard University and studied for a year at King's College, Cambridge. He was on the faculty at Harvard University from 1962–65 and 1989–2005 and at Columbia University from 1965–89. His publications are mainly in logic, philosophy of mathematics, and Kant. He was an editor of the posthumous works of Kurt Gödel (Collected Works, Volumes III–V).

Stephen G. Simpson is a mathematics professor at the Pennsylvania State University. He has lectured and published widely in mathematical logic and the foundations of mathematics. Simpson is the developer of the foundational program known as Reverse Mathematics and the author of Subsystems of Second Order Arithmetic, 2nd Edition.

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