Incompleteness: The Proof And Paradox Of Kurt Godel"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven Pinker Probing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness. |
Contents
Introduction | 13 |
A Platonist among the Positivists | 53 |
Hilbert and the Formalists | 121 |
The Proof of Incompleteness | 147 |
Godels Incompleteness | 207 |
Notes | 263 |
Acknowledgments | 279 |
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axiomatic system axioms Carnap cian consistent continuum hypothesis course David Hilbert Dawson defined diagonal lemma example fact Feigl field figure find finitary fiom first first incompleteness theorem Flexner formal system Foundations of Mathematics genius Godel number Godel’s incompleteness theorems Godel’s proof Godel’s result Godel’s theorems Hahn Hans Hahn Hao Wang Hilbert human ideas infinite influence intellectual intuitions Kochen Konigsberg Kurt Godel language liar’s limpid logic logician mathe mathematical logic mathematical truth mathematicians matical meaning Menger metamathematical mind Morgenstern natural numbers Neumann never number theory objective paradox philosopher physicist physics Platonism Platonist positivism positivists precisely Princeton priori problem proposition provable proved question Rebecca Goldstein Rudolf Russell Russell’s Schilpp Schlick scientific second incompleteness theorem seemed sense set theory significance Simon Kochen sort speak specifically statement sufficiently symbols system of arithmetic things thinkers tion Tractatus true Turing University unprovable Vienna Circle Viennese wffs Wittgenstein words wrote