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[资源] Cambridg2011Kurt Goedel and the Foundations of Mathematics

Contributors page xi
Foreword – Gaisi Takeuti xiii
Preface xv
Acknowledgments xvii
Short Biography of Kurt G¨odel xix
I Historical Context: G¨odel’s Contributions and Accomplishments
Go¨del’s Historical, Philosoph1ical, and Scientific Work
1 The Impact of G¨odel’s Incompleteness Theorems on Mathematics 3
Angus Macintyre
2 Logical Hygiene, Foundations, and Abstractions: Diversity among
Aspects and Options 27
Georg Kreisel
G¨odel’s Legacy: A Historical Perspective
3 The Reception of G¨odel’s 1931 Incompletability Theorems by
Mathematicians, and Some Logicians, to the Early 1960s 57
Ivor Grattan-Guinness
4 “Dozent G¨odel Will Not Lecture” 75
Karl Sigmund
5 G¨odel’s Thesis: An Appreciation 95
Juliette Kennedy
6 Lieber Herr Bernays! Lieber Herr G¨odel! G¨odel on Finitism,
Constructivity, and Hilbert’s Program 111
Solomon Feferman
vii
viii contents
The Past and Future of Computation
7 Computation and Intractability: Echoes of Kurt G¨odel 137
Christos H. Papadimitriou
8 Fromthe Entscheidungsproblem to the Personal Computer –
and Beyond 151
B. Jack Copeland
G¨odelian Cosmology
9 G¨odel, Einstein, Mach, Gamow, and Lanczos: G¨odel’s Remarkable
Excursion into Cosmology 185
Wolfgang Rindler
10 Physical Unknowables 213
Karl Svozil
II A Wider Vision: The Interdisciplinary, Philosophical,
and Theological Implications of G¨odel’sWork
On the Unknowables
11 G¨odel and Physics 255
John D. Barrow
12 G¨odel, Thomas Aquinas, and the Unknowability of God 277
Denys A. Turner
G¨odel and the Mathematics of Philosophy
13 G¨odel’s Mathematics of Philosophy 299
Piergiorgio Odifreddi
G¨odel and Philosophical Theology
14 G¨odel’s Ontological Proof and Its Variants 307
Petr H´ajek
G¨odel and the Human Mind
15 The G¨odel Theorem and Human Nature 325
Hilary W. Putnam
16 G¨odel, the Mind, and the Laws of Physics 339
Roger Penrose
III New Frontiers: Beyond G¨odel’sWork in Mathematics
and Symbolic Logic
Extending G¨odel’s Work
17 G¨odel’s Functional Interpretation and Its Use in
Current Mathematics 361
Ulrich Kohlenbach
contents ix
18 My Forty Years on His Shoulders 399
Harvey M. Friedman
The Realm of Set Theory
19 My Interaction with Kurt G¨odel: The Man and HisWork 435
Paul J. Cohen
G¨odel and the Higher Infinite
20 The Transfinite Universe 449
W. Hugh Woodin
G¨odel and Computer Science
21 The G¨odel Phenomenon in Mathematics: A Modern View 475
Avi Wigderson
Index 509

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