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Clarity comments on Open Thread, January 11-17, 2016 - Less Wrong Discussion

3 Post author: username2 12 January 2016 10:29AM

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Comment author: Clarity 13 January 2016 03:20:51PM *  3 points [-]

Löb's theorem states that "If it's provable that (if it's provable that p then p), then it's provable that p." In addition to being a theorem of set theory with Peano arithmetic, it's also a theorem of modal logic.

Try this on for size: If I believe that (if I believe that this chocolate chip will cure my headache, then this chocolate chip will cure my headache), then I believe that this chocolate chip will cure my headache.

-Agenty Duck

Comment author: Pfft 15 January 2016 04:08:03PM 1 point [-]

Nitpick: it would be better to write "also a theorem of epistemic logic", since there are other modal logics where it is not provable. (E.g. just modal logic K).

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