ENGLISH

An Introduction to Godel's Theorems

By Peter Smith

Book information

Publisher
Cambridge University Press
Year
2007
ISBN
9780521857840, 0521857848
Language
english
Format
DJVU
Filesize
3 MB (2920131 bytes)
Series
Cambridge Introductions to Philosophy
Pages
353\353
Topic
Mathematics Logic
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

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.

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