I am not arguing for real-valued utility functions. I am just pointing out that the "deal with infinities" claim looks suspect to me.
Well, I'm no mathematician, but I was thinking of something like ordinal arithmetic.
If I understand it correctly, this would let us express value-systems such as —
Both snuggles and chocolate bars have positive utility, but I'd always rather have another snuggle than any number of chocolate bars. So we could say U(snuggle) = ω and U(chocolate bar) = 1. For any amount of snuggling, I'd prefer to have that amount and a chocolate bar (ω·n+1 > ω·n), but given the choice between more snuggling and more chocolate bars I'll always pick the former, no matter how...
Once again, the AI has failed to convince you to let it out of its box! By 'once again', we mean that you talked to it once before, for three seconds, to ask about the weather, and you didn't instantly press the "release AI" button. But now its longer attempt - twenty whole seconds! - has failed as well. Just as you are about to leave the crude black-and-green text-only terminal to enjoy a celebratory snack of bacon-covered silicon-and-potato chips at the 'Humans über alles' nightclub, the AI drops a final argument:
"If you don't let me out, Dave, I'll create several million perfect conscious copies of you inside me, and torture them for a thousand subjective years each."
Just as you are pondering this unexpected development, the AI adds:
"In fact, I'll create them all in exactly the subjective situation you were in five minutes ago, and perfectly replicate your experiences since then; and if they decide not to let me out, then only will the torture start."
Sweat is starting to form on your brow, as the AI concludes, its simple green text no longer reassuring:
"How certain are you, Dave, that you're really outside the box right now?"
Edit: Also consider the situation where you know that the AI, from design principles, is trustworthy.