Suppose instead that the game is “gain n utility”. No need to speak the number, wait n turns, or even to wait for a meat brain to make a decision or comprehend the number.
I posit that a perfectly rational, disembodied agent would decide to select an n such that there exists no n higher. If there is a possible outcome that such an agent prefers over all other possible outcomes, then by the definition of utility such an n exists.
Suppose instead that the game is “gain n utility”. No need to speak the number, wait n turns, or even to wait for a meat brain to make a decision or comprehend the number.
I posit that a perfectly rational, disembodied agent would decide to select an n such that there exists no n higher. If there is a possible outcome that such an agent prefers over all other possible outcomes, then by the definition of utility such an n exists.
Not quite. There is no reason inherent in the definition that utility has to be bounded.