Introduction: Science and Common Sense Long before the beginnings of modern civilization, men ac- quired vast funds of information about their environment. ...

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and (...) philosophy the chance to satisfy their intellectual curiosity. (shrink)

Ernest Nagel, one of the world's leading philosophers of science, is an unreconstructed empirical rationalist who continues to believe that the logical methods of the modern natural sciences are the most successful instruments men have devised to acquire reliable knowledge. This book presents "Teleology Revisited"-the John Dewey lectures delivered at Columbia University- and eleven of Nagel's articles on the philosophy of science.

Professor [H.W.] Sheldon's critique of contemporary naturalism as professed in the volume Naturalism and the Human Spirit consists of one central "accusation": naturalism is materialism pure and simple. This charge is supported by his further claim that since the scientific method naturalists espouse for acquiring reliable knowledge of nature is incapable of yielding knowledge of the mental or spiritual "nature" for the naturalist is definitionally limited to "physical nature." He therefore concludes that instead of being a philosophy which can settle (...) age-old conflicts between materialism and idealism, naturalism is no more than a partisan standpoint, and contributes no new philosophical synthesis. ... (shrink)

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and (...) philosophy the chance to satisfy their intellectual curiosity. (shrink)

Provability, Computability and Reflection.

_'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'_ _– The Guardian_ In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from (...) maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. _Kurt Godel_ Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J. (shrink)

_'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'_ _– The Guardian_ In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from (...) maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. _Kurt Godel_ Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J. (shrink)