Kurt Gödel and the Foundations of Mathematics
Kurt Gödel and the Foundations of Mathematics
Christos H. Papadimitriou, University of California, Berkeley
Hilary W. Putnam, Harvard University, Massachusetts
Dana S. Scott, Carnegie Mellon University, Pennsylvania
Charles L. Harper, Jr, Vision-Five.com Consulting, United States
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.
- Presents an unparalleled breadth of coverage of Gödel's interests and a high level of expertise of the contributors
Reviews & endorsements
'This is a very useful volume that brings together aspects of Gödel's work that relates to logic and mathematics …' The Mathematical Intelligencer
Product details
No date availablePaperback
9781107677999
540 pages
254 × 178 × 28 mm
0.93kg
22 b/w illus. 1 table
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.
