I think there's a flaw in Scott's reasoning here because he is mixing and matching statements made in semantic systems of "convincing" and "plausible", but stil

I think there's a flaw in Scott's reasoning here because he is mixing and matching statements made in semantic systems of "convincing" and "plausible", but still using the semantics of true/false to do the reductio ad absurdum step. He initially writes >S(E) = “This sentence has no convincing heuristic explanation accepted by E.” >If S(E) is *true*, then it’s an example of a *true* arithmetical statement without even a convincing heuristic explanation for its *truth* (!). If, on the other hand, S(E) is *false*, then there’s a convincing heuristic explanation of its *truth* The confusion is because the "proof system" isn't supposed to be outputting true/false for E. Its supposed to be an "explanation system" outputting the convincingness of E. So let me try to recast it. >S(E) = “This sentence has no explanation that is accepted by E.” >If S(E) is accepted, then it’s an example of an accepted statement without a convincing explanation. If, on the other hand, S(E) is rejected, then it is a rejected statement that nonetheless has a convincing explanation. Finding a single false statement which a heuristic system erroneously accepts does not invalidate the entirety of the heuristic system. But finding a single false statement which a proof system accepts does invalidate the whole proof system. >S(P) = “This sentence has no argument for it plausible according to P.” >If S(P) is true, then it’s an example of a true arithmetical statement without an argument for why its plausibly true (!). If, on the other hand, S(P) is false, then S(p) is a false statement for which there is nonetheless a plausible argument it is true. Notice that there is no contradiction if this system of formal arguments tells me "A is plausibly true" and later it turns out A is absolutely false. The reductio ad absurdum step of the the incompleteness proof doesn't work when the underlying semantics never asserted anything to be true with certainty. In other words, soundness is not really a necessary or even expected property of these non logic formal reasoning systems. Thus there is no incompleteness problem here because there is no soundness property that contradicts having completeness.