Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries Series)

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"The remarkable theorem of incompleteness uncovered an unbridgeable gap in all attempts to systematize mathematical reasoning, a result that appears almost paradoxical." 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. ...
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Overview

"The remarkable theorem of incompleteness uncovered an unbridgeable gap in all attempts to systematize mathematical reasoning, a result that appears almost paradoxical." 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.

"An introduction to the life and thought of Kurt Gèodel, who transformed our conception of math forever"--Provided by publisher.

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Editorial Reviews

Publishers Weekly
Godel's Incompleteness Theorem, which proved that no formal mathematical system can demonstrate every mathematical truth, is a landmark of modern thought. It's a simple but profound statement, but the technicalities of Godel's proof are forbidding. If MacArthur Fellow and Whiting-winning novelist and philosopher Goldstein (The Mind-Body Problem) doesn't quite succeed in explaining the proof's mechanics to lay readers, she does a magnificent job of exploring its rich philosophical implications. Postmodernists have appropriated it to undermine science's claims of certainty, objectivity and rationality, but Godel insisted, to the contrary, that the theorem buttresses a Platonist conception of a transcendent mathematical reality that exists independent of human logic. Goldstein is an excellent choice for this installment of Norton's Great Discoveries series, which seeks to explain the ways of science to humanists. Her philosophical background makes her a sure guide to the underlying ideas, and she brings a novelistic depth of character and atmosphere to her account of the positivist intellectual milieu surrounding Godel (including a caustic portrait of philosopher Ludwig Wittgenstein) and to her sympathetic depiction of the logician's tortured psyche, as his relentless search for logical patterns behind life's contingencies gradually darkened into paranoia. The result is a stimulating exploration of both the power and the limitations of the human intellect. Photos. Agent, Tina Bennett. (Feb.) Copyright 2004 Reed Business Information.
Library Journal
A novelist and professor specializing in philosophy of science, MacArthur Fellow Goldstein reprises the life of mystical mathematician Godel. With a six-city author tour. Copyright 2004 Reed Business Information.
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Product Details

  • ISBN-13: 9780393051698
  • Publisher: Norton, W. W. & Company, Inc.
  • Publication date: 2/28/2005
  • Series: Great Discoveries Series
  • Pages: 288
  • Product dimensions: 5.60 (w) x 8.16 (h) x 1.02 (d)

Meet the Author

Rebecca Goldstein

Rebecca Goldstein is a MacArthur Fellow, a professor of philosophy, and the author of five novels and a collection of short stories. She lives in Cambridge, Massachusetts.

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Table of Contents

I A Platonist among the positivists 53
II Hilbert and the formalists 121
III The proof of incompleteness 147
IV Godel's incompleteness 207
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Customer Reviews

Average Rating 4
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Sort by: Showing all of 2 Customer Reviews
  • Anonymous

    Posted August 12, 2008

    One of the most excellent popular math book I've read

    Most books on esoteric branches of math are either dry works just presenting an overview of the area in technical terms or are 'Gee Whiz!' so superficial they do little to show the true beauty of the topic. Rebecca Goldstein's book is a joyful exception. She does a wonderful job of providing insight into how and why Godel's work changed our understanding of some of the most fundamental concepts of mathematical reality. Her description of Godel's character and personality is very insightful. She is also a master of the English language - This book would be worth reading just for her precise but flowing descriptions, even if the subject matter weren't so fascinating.

    0 out of 1 people found this review helpful.

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  • Anonymous

    Posted December 25, 2008

    No text was provided for this review.

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