From: Eliezer S. Yudkowsky (email@example.com)
Date: Sat Jan 28 2006 - 09:19:12 MST
H C wrote:
> It's funny ... that statement really clicked with me. It reminded me of
> my (day 4... sigh...) symbolic logic class, the teaching assistant spent
> *over an hour* trying to explain to the class why any given set of
> inconsistent premises always preserves truth...
> Fred is taller than Ted. Ted is taller than Ed. Ed is taller than Fred.
> Therefore, God exists.
> is a valid argument.
> *bangs face into table repeatedly at reaction of students*
Perhaps they are confused by the difference between evidential "if",
counterfactual "if", and logical "if".
If Lee Harvey Oswald didn't shoot Kennedy, someone else did. (True.)
If Lee Harvey Oswald hadn't shot Kennedy, someone else would have. (False.)
Lee Harvey Oswald shot Kennedy. Given that Lee Harvey Oswald didn't
shoot Kennedy, Santa Claus exists. (True.)
The way to explain logical "if" to humans is to rephrase "P => Q" as "~P
or Q" which is mathematically equivalent and makes much more human sense:
Either Lee Harvey Oswald shot Kennedy or Santa Claus exists. (True.)
Similarly, now that Fermat's Last Theorem is proved, the Riemann
Hypothesis (or its negation, or any other proposition) implies Fermat's
Last Theorem: RH => FLT. To make this make sense to a human, you
translate the Boolean truth-conditional into:
"Either Riemann's Hypothesis is false or Fermat's Last Theorem is true."
-- Eliezer S. Yudkowsky http://singinst.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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