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The Wikipedia article about it mentions using Article V against itself, slowly erroding it and the Constitution. That doesn't seem like the loophole Godel might be concerned about. if he did find something more concerning then given his skills this looks like nearly perfect security by obscurity.

I agree with that. If a logician like Gödel talked about an "inner contradiction", then I'm inclined to believe he really thought he had spotted a contradiction, not just some way of slowly eroding an article.

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