Kurt Godel

Essays for His Centennial
Erscheinungsjahr 2012
ISBN: 978-1-107-68346-4
Verlag: Cambridge University Press

Buch, Englisch, Band 33, 384 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 555 g

Reihe: Lecture Notes in Logic

Kurt Gödel (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 Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel'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.

Autoren/Hrsg.

Feferman, Solomon

Parsons, Charles

Simpson, Stephen G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

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.

Über Autor(innen)

Simpson, Stephen G.
Stephen G. Simpson is a mathematics professor at the Pennsylvania State University. He has lectured and published widely in mathematical logic and the foundations of mathematics. Simpson is the developer of the foundational program known as Reverse Mathematics and the author of Subsystems of Second Order Arithmetic, 2nd Edition.

Parsons, Charles
Charles Parsons is Edgar Pierce Professor of Philosophy, Emeritus, at Harvard University. He retired in 2005 but has subsequently been a visiting professor at UCLA and the University of Chicago. Parsons is the former longtime editor of the Journal of Philosophy and a former editor for Bulletin of Symbolic Logic. He is the author of Mathematical Thought and Its Objects and a co-editor of Volumes III-V of Kurt Gödel's Collected Works.

Feferman, Solomon
Solomon Feferman has been a professor of mathematics and philosophy at Stanford University since 1956, from which he retired in 2004. He is a Fellow of the American Academy of Arts and Sciences, was President of the Association for Symbolic Logic in 1980-1982, and was the recipient of the Rolf Schock Prize for Logic and Philosophy in 2003. Feferman was editor-in-chief of the Collected Works of Kurt Gödel (1986-2003).