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Kurt Gödel and the Foundations of Mathematics
Horizons of Truth

$129.00 (P)

Angus Macintyre, Georg Kreisel, Ivor Grattan-Guinness, Karl Sigmund, Juliette C. Kennedy, Solomon Feferman, Christos H. Papadimitriou, B. Jack Copeland, Wolfgang Rindler, Karl Svozil, John D. Barrow, Denys A. Turner, Piergiorgio Odifreddi, Petr Hájek, Hilary Putnam, Roger Penrose, Ulrich Kohlenbach, Harvey M. Friedman, Paul J. Cohen, W. Hugh Woodin, Avi Wigderson
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  • Date Published: June 2011
  • availability: Available
  • format: Hardback
  • isbn: 9780521761444

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About the Authors
  • 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.

    • Presents an unparalleled breadth of coverage of Gödel's interests and a high level of expertise of the contributors
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    Reviews & endorsements

    "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

    • Date Published: June 2011
    • format: Hardback
    • isbn: 9780521761444
    • length: 540 pages
    • dimensions: 254 x 178 x 30 mm
    • weight: 1.15kg
    • contains: 22 b/w illus. 1 table
    • availability: Available
  • 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 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.

  • Editors

    Matthias Baaz, Technische Universität Wien, Austria
    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.

    Christos H. Papadimitriou, University of California, Berkeley
    Christos H. Papadimitriou is C. Lester Hogan Professor of Electrical Engineering and Computer Sciences at the University of California, Berkeley, where he has taught since 1996 and where he is a former Miller Fellow.

    Hilary W. Putnam, Harvard University, Massachusetts
    Dana S. Scott is Hillman University Professor Emeritus of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University in Pittsburgh.

    Dana S. Scott, Carnegie Mellon University, Pennsylvania
    Hilary Putnam is Cogan University Professor Emeritus in the Department of Philosophy at Harvard University.

    Charles L. Harper, Jr, Vision-Five.com Consulting, United States
    Charles L. Harper, Jr is Chancellor for International Distance Learning and Senior Vice President of Global Programs at the American University System, as well as President of Vision-Five.com Consulting, in the United States.

    Contributors

    Angus Macintyre, Georg Kreisel, Ivor Grattan-Guinness, Karl Sigmund, Juliette C. Kennedy, Solomon Feferman, Christos H. Papadimitriou, B. Jack Copeland, Wolfgang Rindler, Karl Svozil, John D. Barrow, Denys A. Turner, Piergiorgio Odifreddi, Petr Hájek, Hilary Putnam, Roger Penrose, Ulrich Kohlenbach, Harvey M. Friedman, Paul J. Cohen, W. Hugh Woodin, Avi Wigderson

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