Kurt Gödel and the Foundations of Mathematics: Horizons of Truth

by Edited by Matthias Baaz , Christos H. Papadimitriou , Hilary W. Putnam , Dana S. Scott , Charles L. Harper, Jr

• ISBN13: 9780521761444
• ISBN10: 0521761441
• Format: Hardcover
• Copyright: 2011-06-06
• Publisher: Cambridge University Press

Summary

This volume commemorates the life, work, and foundational views of Kurt Gödel (19061978), 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.

Author Biography

Matthias Baaz is currently University Professor and Head of the Group for Computational Logic at the Institute of Discrete Mathematics and Geometry at the Vienna University of Technology. Christos H. Papadimitriou is C. Lester Hogan Professor of Electrical Engineering and Computer Sciences at the University of California, Berkeley, where he has taught since 1996 and where he is a former Miller Fellow. Hilary w. Putnam is Cogan University Professor Emeritus in the Department of Philosophy at Harvard University. Dana S. Scott is Hillman University Professor Emeritus of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University in Pittsburgh. Charles L. Harper, JR., is Chancellor for International Distance Learning and Senior Vice President of Global Programs at the American University System, as well as President of Vision-Five.com Consulting, in the United States.

Table of Contents

Contributors	p. xi
Foreword	p. xiii
Preface	p. xv
Acknowledgments	p. xvii
Short Biography of Kurt Gödel	p. xix
Historical Context: Gödel's Contributions and Accomplishments
Gödel's Historical, Philosophical, and Scientific Work
The Impact of Gödel's Incompleteness Theorems on Mathematics	p. 3
Logical Hygiene, Foundations, and Abstractions: Diversity among Aspects and Options	p. 27
Gödel's Legacy: A Historical Perspective
The Reception of Gödel's 1931 Incompletability Theorems by Mathematicians, and Some Logicians, to the Early 1960s	p. 57
"Dozent Gödel Will Not Lecture"	p. 75
Gödel's Thesis: An Appreciation	p. 95
Lieber Herr Bernays! Lieber Herr Gödel! Gödel on Finitism, Constructivity, and Hilbert's Program	p. 111
Computation and Intractability: Echoes of Kurt Gödel	p. 137
From the Entscheidungsproblem to the Personal Computer - and Beyond	p. 151
Gödelian Cosmology
Gödel, Einstein, Mach, Gamow, and Lanczos: Gödel's Remarkable Excursion into Cosmology	p. 185
Physical Unknowables	p. 213
A Wider Vision: The Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work
On the Unknowables
Gödel and Physics	p. 225
Gödel, Thomas Aquinas, and the Unknowability of God	p. 277
Gödel and the Mathematics of Philosophy
Gödel's Mathematics of Philosophy	p. 299
Gödel and Philosophical Theology
Gödel's Ontological Proof and Its Variants	p. 307
Gödel and the Human Mind
The Gödel Theorem and Human Nature	p. 325
Gödel, the Mind, and the Laws of Physics	p. 339
New Frontiers: Beyond Gödel's Work in Mathematics and Symbolic Logic
Extending Gödel's Work
Gödel's Functional Interpretation and Its Use in Current Mathematics	p. 361
My Forty Years on His Shoulders	p. 399
The Realm of Set Theory
My Interaction with Kurt Gödel: The Man and His Work	p. 435
Gödel and the Higher Infinite
The Transfinite Universe	p. 449
Gödel and Computer Science
The Gödel Phenomenon in Mathematics: A Modern View	p. 475
Index	p. 509
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