An Introduction to Gödel's Theorems (Cambridge Introductions to Philosophy) - Softcover

Smith, Peter

Softcover

ISBN 10: 0521674530 ISBN 13: 9780521674539

Publisher: Cambridge University Press, 2007

Synopsis

In 1931, the young Kurt Gödel 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. Gödel 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.

About this title

About the Author

Peter Smith is Lecturer in Philosophy at the University of Cambridge. His books include Explaining Chaos (1998) and An Introduction to Formal Logic (2003), and he is a former editor of the journal Analysis.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2007
• Language: English
• ISBN 10: 0521674530
• ISBN 13: 9780521674539
• Binding: Paperback
• Edition number: 1
• Number of pages: 376