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Eliezer_Yudkowsky 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: Eliezer_Yudkowsky 18 August 2008 10:56:52AM 1 point [-]

Larry, interpret the smiley face as saying:

PA + (◻C -> C) |-

Then the steps 1-10 of Lob's proof would seem to take us from:

PA + (◻C -> C) |- (◻C -> C)

to

PA + (◻C -> C) |- C

If this were the case, the deduction theorem would in fact come into play and give us:

PA |- (◻C -> C) -> C

So there must be at least one step of the reasoning 1-10 that does not apply. Which one and why?