Kurt Godel (eBook, PDF)

Essays for his Centennial
Redaktion: Feferman, Solomon

• Format: PDF

Produktbeschreibung

Kurt Godel (1906-1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Godel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Godel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 19. April 2010
• Englisch
• ISBN-13: 9780511740947
• Artikelnr.: 56689902

Inhaltsangabe

Part I. General: 1. The Gödel editorial project: a synopsis Solomon
Feferman; 2. Future tasks for Gödel scholars John W. Dawson, Jr, and Cheryl
A. Dawson; Part II. Proof Theory: 3. Kurt Gödel and the metamathematical
tradition Jeremy Avigad; 4. Only two letters: the correspondence between
Herbrand and Gödel Wilfried Sieg; 5. Gödel's reformulation of Gentzen's
first consistency proof for arithmetic: the no-counter-example
interpretation W. W. Tait; 6. Gödel on intuition and on Hilbert's finitism
W. W. Tait; 7. The Gödel hierarchy and reverse mathematics Stephen G.
Simpson; 8. On the outside looking in: a caution about conservativeness
John P. Burgess; Part III. Set Theory: 9. Gödel and set theory Akihiro
Kanamori; 10. Generalizations of Gödel's universe of constructible sets
Sy-David Friedman; 11. On the question of absolute undecidability Peter
Koellner; Part IV. Philosophy of Mathematics: 12. What did Gödel believe
and when did he believe it? Martin Davis; 13. On Gödel's way in: the
influence of Rudolf Carnap Warren Goldfarb; 14. Gödel and Carnap Steve
Awodey and A. W. Carus; 15. On the philosophical development of Kurt Gödel
Mark van Atten and Juliette Kennedy; 16. Platonism and mathematical
intuition in Kurt Gödel's thought Charles Parsons; 17. Gödel's conceptual
realism Donald A. Martin.