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Peter_Woo 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: Peter_Woo 17 August 2008 10:52:32PM 0 points [-]

Tiiba: "(Smoke implies fire, therefore fire) implies (no smoke means fire)?" "therefore fire" should be left out. i)     (Smoke implies fire) implies fire. ii)     No smoke implies fire.

You're confused because i) is false.

Medium puzzle:

"Applying the Deduction Theorem to Löb's Theorem gives us, for all C:

    ((◻C)->C)->C"

Wouldn't it be:     ((?C) -> C) -> ?C     If the provability of C implies C's truth, then C is provable.

In other words, where you write "(X->Y)->Y", it should be "(X -> Y) -> X".