Kurt Godel and the Foundations of Mathematics

Horizons of Truth
Herausgeber: Baaz, Matthias; Putnam, Hilary W.; Papadimitriou, Christos H.

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 540
• Erscheinungstermin: 17. Oktober 2013
• Englisch
• Abmessung: 254mm x 178mm x 29mm
• Gewicht: 1003g
• ISBN-13: 9781107677999
• ISBN-10: 1107677998
• Artikelnr.: 40557576

Inhaltsangabe

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.