Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries)A masterly introduction to the life and thought of the man who transformed our conception of math forever. Kurt Gödel is considered the greatest logician since Aristotle. His monumental theorem of incompleteness demonstrated that in every formal system of arithmetic there are true statements that nevertheless cannot be proved. The result was an upheaval that spread far beyond mathematics, challenging conceptions of the nature of the mind. 
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LibraryThing Review
User Review  KirkLowery  LibraryThingThis book is an intellectual biography of one of the greatest mathematicians and logicians of the 20th century. Gödel singlehandedly derailed the HilbertRussell program of putting mathematical proof ... Read full review
LibraryThing Review
User Review  jcbrunner  LibraryThingA quick and reasonable explanation about Gödel's monumental proof. The life and personality of Kurt Gödel is not really fleshed out. The Princeton aspect of the book has cut off much of the Viennese ... Read full review
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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Common terms and phrases
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