Matthias Baaz, Christos H. Papadimitriou, Hilary W. Putnam e Dana S. Scott
Cambridge University Press | 2011 | páginas | pdf | 3,9 Mb
This volume commemorates the life, work, and foundational views of Kurt Gödel (1906-1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers.
Contents
Contributors page xi
Foreword – Gaisi Takeuti xiii
Preface xv
Acknowledgments xvii
Short Biography of Kurt Gödel xix
I Historical Context: Gödel’s Contributions and Accomplishments Gödel’s Historical, Philosoph1ical, and Scientific Work
1 The Impact of Gödel’s Incompleteness Theorems on Mathematics 3
Angus Macintyre
2 Logical Hygiene, Foundations, and Abstractions: Diversity among Aspects and Options 27
Georg Kreisel
Gödel’s Legacy: A Historical Perspective
3 The Reception of Gödel’s 1931 Incompletability Theorems by Mathematicians, and Some Logicians, to the Early 1960s 57
Ivor Grattan-Guinness
4 “Dozent Gödel Will Not Lecture” 75
Karl Sigmund
5 Gödel’s Thesis: An Appreciation 95
Juliette Kennedy
6 Lieber Herr Bernays! Lieber Herr Gödel! Gödel on Finitism, Constructivity, and Hilbert’s Program 111
Solomon Feferman
7 Computation and Intractability: Echoes of Kurt Gödel37
Christos H. Papadimitriou
8 Fromthe Entscheidungsproblem to the Personal Computer – and Beyond 151
B. Jack Copeland
G¨odelian Cosmology
9 Gödel, Einstein, Mach, Gamow, and Lanczos: Gödel’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 Gödel’s Work
On the Unknowables
11 Gödel and Physics 255
John D. Barrow
12 Gödel, Thomas Aquinas, and the Unknowability of God 277
Denys A. Turner
Gödel and the Mathematics of Philosophy
13 Gödel ’s Mathematics of Philosophy 299
Piergiorgio Odifreddi
Gödel and Philosophical Theology
14 Gödel’s Ontological Proof and Its Variants 307
Petr H´ajek
Gödel and the Human Mind
15 The Gödel Theorem and Human Nature 325
Hilary W. Putnam
16 Gödel , the Mind, and the Laws of Physics 339
Roger Penrose
III New Frontiers: Beyond Gödel ’sWork in Mathematics and Symbolic Logic
Extending G¨odel’s Work
17 Gödel ’s Functional Interpretation and Its Use in Current Mathematics 361
Ulrich Kohlenbach
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
Gödel and the Higher Infinite
20 The Transfinite Universe 449
W. Hugh Woodin
Gödel and Computer Science
21 The Gödel Phenomenon in Mathematics: A Modern View 475
Avi Wigderson
Index 509
