…deigns to mention Godel's Second incompleteness theorem, the one about axiomatic systems being unable to prove their own consistency. Now if you were to take up a better book than Manin's, say Smullyan's Godel's Incompleteness Theorems, and study the proof of the second incompleteness theorem, you'd find out that its proof requires a syntactic proof of the first theorem, the proof that Manin says isn't important. This is because proving…
…屈尊提到了哥德尔第二不完备定理，也就是公理系统无法证明自身一致性的那个定理。现在，如果你去看一本比马宁（Manin）那本更好的书，比如斯穆里安（Smullyan）的《Godel's Incompleteness Theorems》，并研读第二不完备定理的证明，你就会发现它的证明需要用到第一定理的句法证明（syntactic proof）——而马宁却说这个证明不重要。这是因为要证明…
…deigns to mention Godel's Second incompleteness theorem, the one about axiomatic systems being unable to prove their own consistency. Now if you were to take up a better book than Manin's, say Smullyan's Godel's Incompleteness Theorems, and study the proof of the second incompleteness theorem, you'd find out that its proof requires a syntactic proof of the first theorem, the proof that Manin says isn't important. This is because proving…
关于不完备性，我最喜欢的一本书是 Raymond Smullyan 的《Godel's Incompleteness Theorems》。
My favorite book about incompleteness is Raymond Smullyan's Godel's Incompleteness Theorems.