In 1931, the young Kurt Godel 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. Godel 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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3t written by logician in philosophy, chattier but good for intuition
评分3t written by logician in philosophy, chattier but good for intuition
评分3t written by logician in philosophy, chattier but good for intuition
评分对于介绍godel's incompleteness theorems的书而言 这本是被认为比较权威的 但我觉得这本书的语言实在不敢恭维 运用过多描述性的语言去描述数学/逻辑方面的内容 而且作者个人的感想一类的过多了
评分缺点是废话太多，啰嗦。
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