There is no need for an infinite regress of ever-more-intelligent
demons. Let's say the man, although he doesn't know it yet, will
decide to take the low road.
If the original demon is able to determine this with 100% certainty,
before telling the man its prediction, then why can't the demon also
account for and predict the man's subsequent reversal in response to
learning of the demon's prediction?
The demon can simply lie to the man, saying "you will choose the high
road", when he knew the man was actually going to choose the low road
based only on his original brain state. The man does the opposite of
what the demon predicts, but the demon, although having lied to the
man, still correctly predicted the man's behavior from its own
perspective.
Of course, the man could be aware that the demon is aware that he will
do the opposite of what the demon says, and the demon is aware that
the man is aware that the demon is aware of this... etc. ad infinitum.
But you don't need to invoke anything smarter than the original demon.
The demon's ability to accurately predict the man's apparently free
will is limited only by the superiority of its intellect. If it is
only a bit smarter than the man, an third observer will find the demon
to be consistently lucky, but still only slightly better than random
chance.
This all seems somehow analogous to our understanding of quantum
uncertainty, and also oddly similar to a scene from _The Princess
Bride_. Or maybe I just need to get some sleep.
Bartley Troyan
bt26@andrew.cmu.edu
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