@ shane: I was specifically talking about utility functions from the set of states of the universe to the reals, not from spacetime histories. Using the latter notion, trivially every agent is a utility maximizer, because there is a canonical embedding of any set X (in this case the set of action-perception pair sequences) into the set of functions from X to R. I’m attacking the former notion—where the domain of the utility function is the set of states of the universe.
@ shane: I was specifically talking about utility functions from the set of states of the universe to the reals, not from spacetime histories. Using the latter notion, trivially every agent is a utility maximizer, because there is a canonical embedding of any set X (in this case the set of action-perception pair sequences) into the set of functions from X to R. I’m attacking the former notion—where the domain of the utility function is the set of states of the universe.