Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

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".