Kurt Godel and the Foundations of Mathematics: Horizons of Truth

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Overview

This volume commemorates the life, work, and foundational views of Kurt Gödel (1906–1978), 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.

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Editorial Reviews

From the Publisher
'This is a very useful volume that brings together aspects of Gödel's work that relates to logic and mathematics …' The Mathematical Intelligencer
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Product Details

  • ISBN-13: 9780521761444
  • Publisher: Cambridge University Press
  • Publication date: 6/6/2011
  • Pages: 540
  • Product dimensions: 7.20 (w) x 10.10 (h) x 1.20 (d)

Meet the Author

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.
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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 incompletabilty 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.
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