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Robert4 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: Robert4 18 August 2008 05:16:48AM 1 point [-]

The problem is that while Lob's theorem says that whenever we have ((◻C)->C), C is provable, it does not mean that there is a proof of C from ((◻C)->C). This means that you're use of the deduction theorem is incorrect. You can only say (((◻C)->C)->(◻C)). It is clear that (X->Y)->X does not imply (not X)->X, so your little trick doesn't work.

Comment author: dlthomas 29 September 2011 04:51:22PM -1 points [-]

(X->Y)->X and (X->Y)->Y have the same truth table.

Comment author: TobyBartels 03 October 2011 03:23:57AM 2 points [-]

Not when X is false and Y is true.

Comment author: dlthomas 03 October 2011 04:29:45PM 3 points [-]

My bad :-\