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Comment author: 24 June 2012 07:16:27PM 1 point [-]

I think that this is what the theorem means;

If (X->Y) -> Y, then ~X -> Y (If it's true that "If it's true that 'if X is true, then Y is true,' then Y must be true," then Y must be true, even if X is not true).

This makes sense because the first line, "(X->Y) -> Y," can be true whether or not X is actually true. The fact that ~X -> Y if this is true is an overly specific example of that "The first line being true (regardless of the truth of X)" -> Y. It's actually worded kind of weirdly, unless "imply" means something different in Logicianese than it does in colloquial English; ~X isn't really "implying" Y, it's just irrelevant.

This doesn't mean that "(X -> Y) -> Y" is always true. I actually can't think of any intuitive situations where this could be true. It's not true that the fact that "if Jesus really had come back to life, Christians would be Less Wrong about stuff" implies that Christians would be Less Wrong about stuff even if Jesus really hadn't come back to life.

Also,