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user131753
3:34 AM
No problem @user21820. However, I would like to point out (as you yourself also have noticed) that the claim of the author is not that there is a "flaw with the incompleteness theorems". One of his main point (so far as I have understood) is that while Gödel's argument applies well to the system $P$, it doesn't apply to the system of PM that he very briefly sketches in his paper.
 
user131753
Consequently he said that, ""The system of Principia resists Gödel’s technique of arithmetisation and thus provides a viable classical theory of arithmetic."
 
user21820
user21820
5:43 AM
@user170039 Frankly, I'm doubtful that you understand the incompleteness theorems. There are two possibilities: (1) PM is a nebulous imprecise system that cannot be represented by a proof verifier program, and hence it is not viable as a theory of arithmetic, just as Th(N) is not a practical theory of arithmetic; (2) PM is a precise system that has a proof verifier program, and hence it is essentially incomplete (this is a technical and not emphatic term).
Therefore, that quoted statement is false, as I have previously stated.
 

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