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