An Introduction to Gödel's Theorems pdf epub mobi txt 电子书 下载 2026
- 数理逻辑
- 数学
- Logic
- 逻辑
- 哲学
- 哥德尔
- 《数理逻辑》邢滔滔
- to
- Gödel Gödel's Theorems logic mathematics philosophy formal systems computability theory foundations of mathematics
具体描述
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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缺点是废话太多，啰嗦。
评分缺点是废话太多，啰嗦。
评分突然想起来我还读过这本书。真的十分啰嗦（哲学家式的啰嗦），当时让我头都晕了还没搞明白哥德尔不完全性定理的证明。建议学数学的同学直接读严肃的哥德尔不完全性定理的证明，除非你想锻炼英语可以读这本。
评分缺点是废话太多，啰嗦。
评分it does a better job in illustrating the point, but Smullyan's book plays with it
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