Godel'S Proof (Routledge Classics)

Description: '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. Table of Contents: Acknowledgments Introduction The Problem of Consistency Absolute Proofs of Consistency The Systematic Codification of Formal Logic An Example of a Successful Absolute Proof of Consistency The Idea of Mapping and its Use in Mathematics Godel's Proof Godel numbering The arithmetization of meta-mathematics The heart of Godel's argument Concluding Reflections Appendix: Notes Brief Bibliography Index