Suppose you were going to die tomorrow, and I come up to you and offer a deal. I'll give you an ice-cream now, in return for being able to torture your daughter the day after tomorrow for the rest of her life. Also, I'll wipe your memory, so you won't even feel guilty.
Anyone who really didn't care about things after they died would accept. But very few people would accept. So virtually all people care about the world after their death.
There's no way of making that offer without interacting with the "utility function" that cares about the present mental images of the future.
More than once, I've had a conversation roughly similar to the following:
Me: "I want to live forever, of course; but even if I don't, I'd still like for some sort of sapience to keep on living."
Someone else: "Yeah, so? You'll be dead, so how/why should you care?"
I've tried describing how it's the me-of-the-present who's caring about which sort of future comes to pass, but I haven't been able to do so in a way that doesn't fall flat. Might you have any thoughts on how to better frame this idea?