Incompleteness [Hardcover]

Kurt Gödel is often held up as an intellectual revolutionary whose incompleteness theorem helped tear down the notion that there was anything certain about the universe. Philosophy professor, novelist, and MacArthur Fellow Rebecca Goldstein reinterprets the evidence and restores to Gödel's famous idea the meaning he claimed he intended: that there is a mathematical truth--an objective certainty--underlying everything and existing independently of human thought. Gödel, Goldstein maintains, was an intellectual heir to Plato whose sense of alienation from the positivists and postmodernists of the 1940s was only ameliorated by his friendship with another intellectual giant, Albert Einstein. As Goldstein writes, "That his work, like Einstein's, has been interpreted as not only consistent with the revolt against objectivity but also as among its most compelling driving forces is ... more than a little ironic."

This and other paradoxes of Gödel's life are woven throughout Incompleteness, with biographical details taking something of a back seat to the philosophical and mathematical underpinnings of his theories. As an introduction to one of the three most profound scientific insights of the 20th century (the other two being Einstein's relativity and Heisenberg's uncertainty principle), Incompleteness is accessible, yet intellectually rigorous. Goldstein succeeds admirably in retiring inaccurate interpretations of Gödel's ideas. --Therese Littleton

Gödel'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 Gödel'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 Gödel 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 Gödel (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.
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This year is an Einstein anniversary (see Rigden's Einstein 1905 [BKL D 1 04]), but the great physicist would doubtless be pleased by the new attention his last best friend, Austrian logician Kurt Godel (1906-78), has received from philosopher Palle Yourgrau in World without Time [BKL Ja 1&15 05] and now from novelist-philosopher Goldstein. The author opens, as Yourgrau does, with Einstein and Godel strolling and talking together; but she focuses on Godel and says relatively little about Einstein. Her interpretation of the ambitious but diffident, hypochondriac, and paranoiac mathematician's character is much the same as Yourgrau's; but, well acquainted with mathematics herself, she explains Godel's two great proofs more specifically and in greater detail, and readers who understand mathematics well may find her more satisfying on them than Yourgrau. But while she repeatedly, pertinently cites Godel's lifelong Platonism, she makes less of it than Yourgrau, though maybe no more of it than did Godel himself, whose understanding of time in accordance with Einsteinian relativity she characterizes as cyclical, as against the full Platonic idealism Yourgrau wants to extract from Godel. Surely readers excited by the current revolt against materialism, positivism (a leitmotif in this book is comparison of Wittgenstein and Godel), and subjectivism will want to read both Goldstein and Yourgrau. Ray Olson
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"Magnificent.... A stimulating exploration of both the power and the limitations of the human intellect.... Goldstein is an excellent choice for this installment of Norton's Great Discoveries series: Her philosophical background makes her a sure guide to the underlying ideas, and she brings a novelistic depth of character and atmosphere ... to her sympathetic depiction of the logician's tortured psyche, as his relentless search for logical patterns ... gradually darkened into paranoia." --This text refers to the Paperback edition.

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.