Incompleteness: The Proof and Paradox of Kurt Gödel

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W. W. Norton & Company, 2005 - Biography & Autobiography - 296 pages
7 Reviews
"The genius behind this discovery was Kurt Godel, himself a man of paradox. He was the greatest logician since Aristotle, as well as Einstein's closest intellectual companion during Einstein's last years. But he was also deeply eccentric and given to paranoiac deductions that ultimately led to his tragic death. Subject to irrationality, he nevertheless put his faith in reason. With the use of an ingenious proof he was able to demonstrate that in any sufficiently complex system - in short, any system a mathematician would want to use - there are true statements that cannot be proven. Some thinkers despaired at this result. Others, like the formidable Wittgenstein, could never accept it. And still others misunderstood it as a torpedo to the hull of rationality itself. For Godel, however, it was evidence of an eternal, objective truth, independent of human thought, that can only be apprehended imperfectly by the human mind."--BOOK JACKET.
 

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excellent book. the author does a great job of describing the intellectual culture of the early 1900s, centred in austria, and the Vienna circle aka the school of logical positivism. Goedel's work was ultimately to throw much of that belief into question. the remarks about the withering academic climate in upper echelons says something about the kind of personalities that endure. it's no wonder that the wittgensteins and russells of the world forebear whereas the goedel's are consigned to the sidelines despite the huge impact of goedel's theorems. sketches of the 1st and 2nd incompleteness theorems are provided and the author does a great job of developing the impact to other figures like alan turing, whose work figures prominently in my field of study (computer science). there is also significant details of the life of goedel and his relationship with einstein which are very enlightening - two giants walking on a grassy path in princeton. we'll never see the like again. 

Review: Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries)

User Review  - Chisho1m - Goodreads

It's always fun to try to wrap my head around watered-down explanations of esoteric math & science, so I was primarily interested in Goldstein's walk through the Incompleteness Theorems. But that's ... Read full review

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Contents

Introduction
13
A Platonist among the Positivists
53
Hilbert and the Formalists
121
The Proof of Incompleteness
147
Gödels Incompleteness
207
Notes
263
Suggested Reading
275
Acknowledgments
279
Index
281
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About the author (2005)

Rebecca Goldstein graduated summa cum laude from Barnard College and received her Ph.D. from Princeton University in the philosophy of science. She has taught philosophy at Barnard. She lives in Cambridge, Massachusetts.

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