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Brian_Jaress2 comments on The Cartoon Guide to Löb's Theorem - Less Wrong

12 Post author: Eliezer_Yudkowsky 17 August 2008 08:35PM

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Comment author: Brian_Jaress2 18 August 2008 12:28:18AM 0 points [-]

I think the error is that you didn't prove it was unprovable -- all provably unprovable statements are also provable, but unprovable statements aren't necessarily true.

In other words, I think what you get from the Deduction Theorem (which I've never seen before, so I may have it wrong) is Provable((Provable(C) -> C) -> C). I think if you want to "reach inside" that outer Provable and negate the provability of C, you have to introduce Provable(not Provable(C)).