| An Introduction to Gödel's Theorems Contributor(s): Smith, Peter (Author) |
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ISBN: 0511800967 ISBN-13: 9780511800962 Publisher: Cambridge University Press OUR PRICE: $494.00 Product Type: Open Ebook - Other Formats Published: June 2012 |
| Additional Information |
| BISAC Categories: - Philosophy - Mathematics | Logic |
| Dewey: 511.3 |
| Series: Cambridge Introductions to Philosophy |
| Descriptions, Reviews, Etc. |
| Publisher Description: In 1931, the young Kurt G del 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. G del 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. |
Contributor Bio(s): Smith, Peter: - 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. |