Kurt Gödel and the foundations of mathematics : horizons of truth /

"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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Baaz, Matthias (Editor ), Papadimitriou, Christos H. (Editor ), Putnam, Hilary W. (Editor ), Scott, Dana S. (Editor ), Harper Jr., Charles L. (ditor.)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 2011.
Temas:
Gödel, Kurt.
Gödel, Kurt / Influence.
Gödel's theorem.
Mathematics > Philosophy.
Théorème de Gödel.
Mathématiques > Philosophie.
MATHEMATICS > Infinity.
MATHEMATICS > Logic.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Foreword / Gaisi Takeuti
  • Preface
  • Short Biography of Kurt Godel
  • I. Historical context : Gödel's contributions and accomplishments. Gödel's historical, philosophical, and scientific work. 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
  • Gödel's legacy : a historical perspective. 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 Kennedy ; 6. Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity, and Hilbert's program / Solomon Feferman
  • The past and future of computation. 7. Computation and intractability : echoes of Kurt Gödel / Christos H. Papadimitriou ; 8. From the entscheidungsproblem to the personal computer
  • and beyond / B. Jack Copeland
  • Gödelian cosmology. 9. Gödel, Einstein, Mach, Gamow, and Lanczos : Gödel's remarkable excursion into cosmology / Wolfgang Rindler ; 10. Physical unknowables / Karl Svozil
  • II. A wider vision : the interdisciplinary, philosophical, and theological implications of Gödel's work. On the unknowables. 11. Gödel and physics / John D. Barrow ; 12. Gödel, Thomas Aquinas, and the unknowability of God / Denys A. Turner
  • Gödel and the mathematics of philosophy. 13. Gödel's mathematics of philosophy / Piergiorgio Odifreddi
  • Gödel and philosophical theology. 14. Gödel's ontological proof and its variants / Petr Hájek
  • Gödel and the human mind. 15. The Gödel theorem and human nature / Hilary W. Putnam ; 16. Gödel, the mind, and the laws of physics / Roger Penrose
  • III. New frontiers : beyond Gödel's work in mathematics and symbolic logic. Extending Gödel's work. 17. Gödel's functional interpretation and its use in current mathematics / Ulrich Kohlenbach ; 18. My forty years on his shoulders / Harvey M. Friedman
  • The realm of set theory. 19. My interaction with Kurt Gödel : the man and his work / Paul J. Cohen
  • Gödel and the higher infinite. 20. The transfinite universe / W. Hugh Woodin
  • Gödel and computer science. 21. The Gödel phenomena in mathematics : a modern view / Avi Wigderson.

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