Kurt Gödel: Essays for his CentennialSolomon Feferman, Charles Parsons, Stephen G. Simpson 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. |
Contents
John W Dawson Jr and Cheryl A Dawson | 21 |
Jeremy Avigad | 45 |
Wilfried Sieg | 59 |
W W Tait | 74 |
Godel on intuition and on Hilberts finitism | 88 |
The Godel hierarchy and reverse mathematics | 109 |
John P Burgess | 124 |
SET THEORY | 136 |
Generalisations of Godels universe of constructible sets | 181 |
Peter Koellner | 189 |
PHILOSOPHY OF MATHEMATICS | 224 |
Warren Goldfarb | 242 |
Steve Awodey and A W Carus | 252 |
Mark van Atten and Juliette Kennedy | 275 |
Platonism and mathematical intuition in Kurt Godels thought | 326 |
Donald A Martin | 356 |
Other editions - View all
Kurt Gödel: Essays for his Centennial Solomon Feferman,Charles Parsons,Stephen G. Simpson No preview available - 2010 |
Kurt Gödel: Essays for his Centennial Solomon Feferman,Charles Parsons,Stephen G. Simpson No preview available - 2013 |
Common terms and phrases
according analysis appears applied argument arithmetic axioms called cardinals Carnap classical clear Collected completeness computable concept concept of set concerning consider consistency consistency proof construction contains continuum correspondence definable defined definition different discussion editors evidence example existence expressed fact finitary finite finitist first formal formula foundations functions further G¨odel give given Herbrand’s Hilbert’s Husserl hypothesis idea idealism implies important incompleteness independence induction interest interpretation intuition intuitionistic logic Kurt G¨odel language large cardinal later lecture letter mathematics means methods natural notes notion objects obtained Oxford University Press particular passage philosophy possible precise present primitive principle problem proof propositions provable prove published question reason recursive reference remarks result seems sense sentences set theory statement suggest Symbolic Logic theorem translation true truth undecidable volume writings