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.
Author(s): Solomon Feferman, Charles Parsons, Stephen G. Simpson (eds.)
Series: Lecture Notes in Logic 33
Publisher: Cambridge University Press
Year: 2010
Language: English
Pages: 385
COVER......Page 1
HALF-TITLE......Page 3
SERIES-TITLE......Page 5
TITLE......Page 7
COPYRIGHT......Page 8
CONTENTS......Page 9
INTRODUCTION......Page 11
GENERAL......Page 13
THE GODEL EDITORIAL PROJECT: A SYNOPSIS......Page 15
REFERENCES......Page 31
FUTURE TASKS FOR GODEL SCHOLARS......Page 33
REFERENCES......Page 54
PROOF THEORY......Page 55
GODEL AND THE METAMATHEMATICAL TRADITION......Page 57
REFERENCES......Page 71
ONLY TWO LETTERS: THE CORRESPONDENCE BETWEEN HERBRAND AND GODEL......Page 73
REFERENCES......Page 84
GODEL’S REFORMULATION OF GENTZEN’S FIRST CONSISTENCY PROOF FOR ARITHMETIC: THE NO-COUNTEREXAMPLE INTERPRETATION......Page 86
REFERENCES......Page 98
GODEL ON INTUITION AND ON HILBERT’S FINITISM......Page 100
REFERENCES......Page 118
THE GODEL HIERARCHY AND REVERSE MATHEMATICS......Page 121
REFERENCES......Page 135
ON THE OUTSIDE LOOKING IN: A CAUTION ABOUT CONSERVATIVENESS......Page 140
REFERENCES......Page 152
SET THEORY......Page 155
GODEL AND SET THEORY......Page 157
REFERENCES......Page 187
GENERALISATIONS OF GODEL’S UNIVERSE OF CONSTRUCTIBLE SETS......Page 193
REFERENCES......Page 199
ON THE QUESTION OF ABSOLUTE UNDECIDABILITY......Page 201
REFERENCES......Page 234
PHILOSOPHY OF MATHEMATICS......Page 239
WHAT DID GODEL BELIEVE AND WHEN DID HE BELIEVE IT?......Page 241
REFERENCES......Page 253
ON GODEL’S WAY IN: THE INFLUENCE OF RUDOLF CARNAP......Page 254
REFERENCES......Page 262
GODEL AND CARNAP......Page 264
REFERENCES......Page 284
ON THE PHILOSOPHICAL DEVELOPMENT OF KURT GODEL......Page 287
REFERENCES......Page 333
PLATONISM AND MATHEMATICAL INTUITION IN KURT GODEL’S THOUGHT......Page 338
Writings of Godel......Page 365
Other Writings......Page 366
GODEL’S CONCEPTUAL REALISM......Page 368
REFERENCES......Page 385
