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Cambridg2011Kurt Goedel and the Foundations of Mathematics
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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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