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  An Introduction to Godel's Theorems (Cambridge Introductions to Philosophy) (Paperback) By (author) Peter Smith

  

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  Short Description for An Introduction to Godel's TheoremsPeter Smith examines Godel's Theorems, how they were established and why they matter.
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  • Publisher: CAMBRIDGE UNIVERSITY PRESS
  • Published: 26 July 2007
  • Format: Paperback 376 pages
  • See: Full bibliographic data
  • Categories: Philosophy Of Mathematics | Mathematical Logic | Philosophy: Logic
  • ISBN 13: 9780521674539 ISBN 10: 0521674530
  • Sales rank: 177,345

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Full description for An Introduction to Godel's Theorems

• In 1931, the young Kurt Godel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Godel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.