A question about Lob's theorem: assume not provable(X). Then, by rules of If-then statements, if provable(X) then X is provable But then, by Lob's theorem, provable(X), which is a contradiction. What am I missing here?
I'm not sure how you're getting from not provable(X) to provable(provable(X) -> X), and I think you might be mixing meta levels. If you could prove not provable(X), then I think you could prove (provable(X) ->X), which then gives you provable(X). Perhaps the solution is that you can never prove not provable(X)? I'm not sure about this though.
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