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9780521115148

Kurt Gödel: Essays for his Centennial

by
  • ISBN13:

    9780521115148

  • ISBN10:

    0521115140

  • Format: Hardcover
  • Copyright: 2010-04-19
  • Publisher: Cambridge University Press

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Summary

Kurt Gouml;del (19061978) 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 Gouml;del's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gouml;del'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.

Table of Contents

General:
The Gödel editorial project: a synopsis
Future tasks for Gödel scholars
Proof Theory:
Kurt Gödel and the metamathematical tradition
Only two letters: the correspondence between Herbrand and Gödel
Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counter-example interpretation
Gödel on intuition and on Hilbert's finitism
The Gödel hierarchy and reverse mathematics
On the outside looking in: a caution about conservativeness
Set Theory:
Gödel and set theory
Generalizations of Gödel's universe of constructible sets
On the question of absolute undecidability
Philosophy of Mathematics:
What did Gödel believe and when did he believe it?
On Gödel's way in: the influence of Rudolf Carnap
Gödel and Carnap Steve Awodey
On the philosophical development of Kurt
Platonism and mathematical intuition in Kurt Gödel's thought
Gödel's conceptual realism
Table of Contents provided by Publisher. All Rights Reserved.

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