Kurt Godel and the Foundations of Mathematics

Kurt Godel and the Foundations of Mathematics : Horizons of Truth

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This volume commemorates the life, work and foundational views of Kurt Godel (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 Godel 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 Godel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.show more

Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 22 b/w illus. 1 table
  • 1139073184
  • 9781139073189

Table of contents

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

Review quote

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