Supertask decision making
December 2, 2008I have a little paper writing up the supertask puzzle I posted recently. I’ve added a second puzzle that demonstrates the same problem, but doesn’t use the axiom of choice (it’s basically just a version of Yablo’s paradox), and I’ve framed the puzzles in terms of failures of the deontic Barcan formulae.
Anyway – if anyone has any comments, I’d be very grateful to hear them!
In the second puzzle, the rule is: choose 1, if you have chosen 0 at every previous round, and chose 0 otherwise (i.e. if you have chosen 1 on at least one other round.)
It seems that these rules determine the following (consistent) sequence:
01000….
Where is the rule violation? What am I missing?
Hi David,
Thanks for reading!
Your sequence is a consistent play of a finite (or well founded) game. Remember that the sequence of rounds that Alice is playing is a backwards omega-sequence: there is no first move (unlike your example.)
Does that make sense?
Yeah, sorry. I came back to correct myself, but was pre-empted! Ha!