Kurt Goedel and the Foundations of Mathematics : Horizons of Truth
This volume commemorates the life, work and foundational views of Kurt Goedel (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 Goedel 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 Goedel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
- Electronic book text
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 22 b/w illus. 1 table
Table of contents
Part I. Historical Context - Goedel's Contributions and Accomplishments: 1. The impact of Goedel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Goedel's 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Goedel will not lecture' Karl Sigmund; 5. Goedel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Goedel! Goedel on finitism, constructivity, and Hilbert's program Solomon Feferman; 7. Computation and intractability: echoes of Kurt Goedel Christos H. Papadimitriou; 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland; 9. Goedel, Einstein, Mach, Gamow, and Lanczos: Goedel's remarkable excursion into cosmology Wolfgang Rindler; 10. Physical unknowables Karl Svozil; Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Goedel's Work: 11. Goedel and physics John D. Barrow; 12. Goedel, Thomas Aquinas, and the unknowability of God Denys A. Turner; 13. Goedel's mathematics of philosophy Piergiorgio Odifreddi; 14. Goedel's ontological proof and its variants Petr Hajek; 15. The Goedel theorem and human nature Hilary Putnam; 16. Goedel, the mind, and the laws of physics Roger Penrose; Part III. New Frontiers - Beyond Goedel's Work in Mathematics and Symbolic Logic: 17. Goedel'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 Goedel: the man and his work Paul J. Cohen; 20. The transfinite universe W. Hugh Woodin; 21. The Goedel phenomena in mathematics: a modern view Avi Wigderson.
'This is a very useful volume that brings together aspects of Goedel's work that relates to logic and mathematics ...' The Mathematical Intelligencer