Overview

This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), 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.

Full Product Details

Author:   Matthias Baaz (Technische Universität Wien, Austria) ,  Christos H. Papadimitriou (University of California, Berkeley) ,  Hilary W. Putnam (Harvard University, Massachusetts) ,  Dana S. Scott (Carnegie Mellon University, Pennsylvania)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Dimensions:   Width: 17.80cm , Height: 2.80cm , Length: 25.40cm
Weight:   0.930kg
ISBN:  

9781107677999

ISBN 10:   1107677998
Pages:   540
Publication Date:   27 March 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Part I. Historical Context - Gödel's Contributions and Accomplishments: 1. The impact of Gödel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Gödel's 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Gödel will not lecture' Karl Sigmund; 5. Gödel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity, and Hilbert's program Solomon Feferman; 7. Computation and intractability: echoes of Kurt Gödel Christos H. Papadimitriou; 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland; 9. Gödel, Einstein, Mach, Gamow, and Lanczos: Gödel's remarkable excursion into cosmology Wolfgang Rindler; 10. Physical unknowables Karl Svozil; Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work: 11. Gödel and physics John D. Barrow; 12. Gödel, Thomas Aquinas, and the unknowability of God Denys A. Turner; 13. Gödel's mathematics of philosophy Piergiorgio Odifreddi; 14. Gödel's ontological proof and its variants Petr Hájek; 15. The Gödel theorem and human nature Hilary Putnam; 16. Gödel, the mind, and the laws of physics Roger Penrose; Part III. New Frontiers - Beyond Gödel's Work in Mathematics and Symbolic Logic: 17. Gödel's functional interpretation and its use in current mathematics Ulrich Kohlenbach; 18. My forty years on his shoulders Harvey M. Friedman; 19. My interaction with Kurt Gödel: the man and his work Paul J. Cohen; 20. The transfinite universe W. Hugh Woodin; 21. The Gödel phenomena in mathematics: a modern view Avi Wigderson.

Reviews

'This is a very useful volume that brings together aspects of Goedel's work that relates to logic and mathematics ...' The Mathematical Intelligencer

'This is a very useful volume that brings together aspects of Goedel's work that relates to logic and mathematics ...' The Mathematical Intelligencer This is a very useful volume that brings together aspects of Goedel's work that relates to logic and mathematics ... The Mathematical Intelligencer

'This is a very useful volume that brings together aspects of Godel's work that relates to logic and mathematics ...' The Mathematical Intelligencer

Author Information

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. Dana S. Scott is Hillman University Professor Emeritus of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University in Pittsburgh. Hilary Putnam is Cogan University Professor Emeritus in the Department of Philosophy at Harvard University. 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.

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