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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用戶評價
對於介紹godel's incompleteness theorems的書而言 這本是被認為比較權威的 但我覺得這本書的語言實在不敢恭維 運用過多描述性的語言去描述數學/邏輯方麵的內容 而且作者個人的感想一類的過多瞭
评分突然想起來我還讀過這本書。真的十分囉嗦（哲學傢式的囉嗦），當時讓我頭都暈瞭還沒搞明白哥德爾不完全性定理的證明。建議學數學的同學直接讀嚴肅的哥德爾不完全性定理的證明，除非你想鍛煉英語可以讀這本。
评分it does a better job in illustrating the point, but Smullyan's book plays with it
评分對於介紹godel's incompleteness theorems的書而言 這本是被認為比較權威的 但我覺得這本書的語言實在不敢恭維 運用過多描述性的語言去描述數學/邏輯方麵的內容 而且作者個人的感想一類的過多瞭
评分缺點是廢話太多，囉嗦。
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