In 1931, the young Kurt Goedel 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. Goedel 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.
- ISBN13 9780521674539
- Publish Date 26 July 2007 (first published 1 January 2007)
- Publish Status Inactive
- Out of Print 31 March 2022
- Publish Country GB
- Imprint Cambridge University Press
- Format Paperback (US Trade)
- Pages 376
- Language English