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Incompleteness
The Proof and Paradox of Kurt Godel
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by Rebecca Goldstein
W. W. Norton and Co.
Due/Published
February 2005, 288 pages,
cloth
ISBN
0393051692
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 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. |
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