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user131753
3:26 AM
@Conifold I see - this interpretation also seems close to Wittgenstein's "Notorious Prargraph". So will it be fair to say that there is a misunderstanding of the system of Principia Mathematica from Gödel's part? There is no doubt that the incompleteness theorems applies to the system that Gödel proposed in his seminal 1931 paper.
 
user131753
But it doesn't apply to the system of Principia Mathematica simply because Gödel's intepretation of the system of PM and the actual system of PM are different.
 
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19 hours later…
Conifold
Conifold
10:18 PM
@user170039 You saw G. Chen arguing that "Gödel misunderstood", but I do not think he did. From his perspective he rather showed PM program to be deficient, he showed that true = provable is not acceptable. Later, a consequence, Tarski's undefinability of truth theorem, explicitly spelled out that certain languages can not talk about truth of their own sentences without inconsistency.
 

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