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Incompleteness: The Proof and Paradox of Kurt Godelby Rebecca Goldstein
Synopses & Reviews
Kurt Godel is considered the twentieth century's greatest mathematician. His monumental theorem of Incompleteness overturned the prevailing conviction that the only true statements in math were those that could be proved. Inspired by Plato's philosophy of a higher reality, Godel demonstrated conclusively that there are in every formal system undeniably true statements that nevertheless cannot be proved. The result was an upheaval in mathematics.
From the famous Vienna Circle and sparring with Wittgenstein to Princeton's Institute for Advanced Study, where he was Einstein's constant companion, Godel was both a towering intellect and a deeply mysterious figure, whose strange habits and ever-increasing paranoia led to his sad death by self-starvation. In this lucid and accessible study, Rebecca Goldstein, a philosopher of science and a gifted novelist whose work often focuses on science, explains the significance of Godel's theorems and the remarkable vision behind them, while bringing this eccentric, tortured genius and his world to life.
"Gdel'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 Gdel'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 Gdel 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 Gdel (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.)" Publishers Weekly (Copyright 2004 Reed Business Information, Inc.)
Book News Annotation:
A fiction writer and professor of physics, Goldstein explains for general readers the nature, context, and significant of logician Gödel's (1906-78) incompleteness theorems. She says they belong to a branch of mathematics known as formal logic or mathematical logic, which was considered mathematically suspect until his achievement; and have far reaching implications for the understanding of the nature of truth, knowledge, and certainty.
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
Considered the 20th century's greatest mathematician, Kurt Godel is the subject of this lucid and accessible study, which explains the significance of his theorems and the remarkable vision behind them, while bringing this eccentric, tortured genius and his world to life.
About the Author
MacArthur Fellow and Whiting-Award winner Rebecca Goldstein novels include The Mind-Body Problem and Properties of Light. She lives in New York City.
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