Kurt Gödel (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 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.
Papildus informācija
Papers examining aspects of Godel's work gathered from a symposium celebrating Gödel's centennial and papers from a 2004 ASL symposium.
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The Godel editorial project: A synopsis |
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3 | (18) |
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Future tasks for Godel scholars |
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21 | (24) |
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Godel and the metamathematical tradition |
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45 | (16) |
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Only two letters: The correspondence between Herbrand and Godel |
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61 | (13) |
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Godel's reformulation of Gentzen's first consistency proof for arithmetic: The no-counterexample interpretation |
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74 | (14) |
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Godel on intuition and on Hilbert's finitism |
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88 | (21) |
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The Godel hierarchy and reverse mathematics |
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109 | (19) |
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On the outside looking in: A caution about conservativeness |
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128 | (17) |
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145 | (36) |
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Generalisations of Godel's universe of constructible sets |
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181 | (8) |
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On the question of absolute undecidability |
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189 | (40) |
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Philosophy of Mathematics |
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What did Godel believe and when did he believe it? |
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229 | (13) |
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On Godel's way in: The influence of Rudolf Carnap |
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242 | (10) |
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252 | (23) |
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On the philosophical development of Kurt Godel |
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275 | (51) |
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Platonism and mathematical intuition in Kurt Godel's thought |
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326 | (30) |
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Godel's conceptual realism |
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356 | |
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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 19802, 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 (19862003). Charles Parsons holds an AB (mathematics) and PhD (philosophy) from Harvard University and studied for a year at King's College, Cambridge. He was on the faculty at Harvard University from 196265 and 19892005 and at Columbia University from 196589. His publications are mainly in logic, philosophy of mathematics, and Kant. He was an editor of the posthumous works of Kurt Gödel (Collected Works, Volumes IIIV). 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.
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