What is the “Satan’s apple” reference? I don’t get that, sorry.
I think I agree with you that the version of the example I offered did not fully specify the time dimension. But it’s crucial to the original St Petersburg game that your winnings at stage n are not collected until the game is finished, so that if you lose at stage n+1 you don’t get to enjoy your winnings. So presumably, in Hurka’s variant, the extra world(s) should not be created until after you walk away from the button, so the seconds in-between presses would not be valuable at all. But I take your point that this wasn’t specified well enough in OP.
Satan cuts an apple into a countable infinity of slices and offers it to Eve, one piece at a time. Each slice has positive utility for Eve. If Eve eats only finitely many pieces, there is no difficulty; she simply enjoys her snack. If she eats infinitely many pieces, however, she is banished from Paradise. To keep things simple, we may assume that the pieces are numbered: in each time interval, the choice is Take piece n or Don’t take piece n. Furthermore, Eve can reject piece n, but take later pieces. Taking any countably infinite set leads to the bad outcome (banishment). Finally, regardless of whether or not she is banished, Eve gets to keep (and eat) her pieces of apple. Call this the original version of Satan’s apple.
We shall sometimes discuss a simplified version of Satan’s apple, different from the original version in two respects. First, Eve is banished only if she takes all the pieces. Second, once Eve refuses a piece, she cannot take any more pieces. These restrictions make Satan’s apple a close analogue to the two earlier puzzles.
What is the “Satan’s apple” reference? I don’t get that, sorry.
I think I agree with you that the version of the example I offered did not fully specify the time dimension. But it’s crucial to the original St Petersburg game that your winnings at stage n are not collected until the game is finished, so that if you lose at stage n+1 you don’t get to enjoy your winnings. So presumably, in Hurka’s variant, the extra world(s) should not be created until after you walk away from the button, so the seconds in-between presses would not be valuable at all. But I take your point that this wasn’t specified well enough in OP.
Source: Satan, Saint Peter and Saint Petersburg