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)

Provability, Computability and Reflection.

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)

_'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)

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.

_'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)

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)

No account of the development of contemporary empiricism is adequate which neglects the writings and the influence of Charles Peirce. Although he is not easily pigeon-holed and can not be claimed as the exclusive property of any school or movement, it is appropriate that the hundredth anniversary of his birth should be commemorated at this Congress. For the movement of which it is a manifestation is engaged in a coöperative, intensive cultivation of the methods of the sciences with the help (...) of the most advanced tools of modern logic; and Peirce's intellectual career was also a single-minded devotion to that task. It is fitting, also, that his birth-year be celebrated at Harvard by an international congress. For although he was denied the privilege of teaching at this university, much of his influence was propagated by William James and Josiah Royce, two of its great teachers; and however much he may have suffered from neglect during his life-time, his work surely merits recognition from a movement not confined by national bounds. It is characteristic of the best established sciences that though individuals may pursue researches in them independently of one another, the conclusions reached tend to support each other and to converge toward a common stream of sound beliefs; and such convergence is indeed the sole identifiable warrant for the confidence that some measure of the truth has been attained. It is therefore a happy sign that so many of the central ideas of the present movement have been independently developed on both sides of the Atlantic. One is not minimizing the contributions of the Vienna Circle in pointing out that many of its recent views have been taken for granted for some time by American colleagues, largely because the latter have come to intellectual maturity under the influence of Peirce. (shrink)