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

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9781107606753: An Introduction to Gödel's Theorems (Cambridge Introductions to Philosophy)

An extensively rewritten second edition of this best-selling standard text for graduates and upper-level undergraduate students of logic, philosophy of mathematics, and pure mathematics. A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems.

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"Smith breathes new life into the work of Kurt Godel in this second edition Recommended. Upper-division undergraduates through professionals." R. L. Pour, Choice"

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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 - extensively rewritten for its second edition - 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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