## 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!

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Posted in Formal epistemology, Set Theory **|** Tagged Axiom of Choice, Decision theory, Deontic barcan formula, Rational choice, Supertask, Yablo's paradox **|**

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?

by David Horacek December 10, 2008 at 4:08 pmHi 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?

by Andrew December 10, 2008 at 4:22 pmYeah, sorry. I came back to correct myself, but was pre-empted! Ha!

by David Horacek December 10, 2008 at 4:34 pm