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Anubhav comments on So You Want to Save the World - Less Wrong
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Clearly, if the algorithm concludes that it will certainly not choose the $5, and then does choose the $5, it concluded wrong. But the reasoning seems impeccable, and there don't seem to be any false premises here. It smacks of the unexpected hanging paradox.
Ooh, but wait. Expanding that reasoning a bit, we have...
The assumption "I am an algorithm whose axioms are consistent" is one that we already know leads to a contradiction, by Löb's theorem. If we can avoid the wrath of Löb's theorem, can we also avoid the five-and-ten problem?
(Granted, this probably isn't the best place to say this.)
Very likely yes. Now ask if I know how to avoid the wrath of Löb's theorem.
For someone making a desperate effort to not be a cult leader, you really do enjoy arbitrarily ordering people around, don't you?
</humour possibly subject to Poe's law>