Indeed, already figured that out here.

Can't make an omelette without breaking some eggs. Videotape the whole thing so the next one has even more evidence.

I think that's mostly because money is too abstract, and as long as you get by you don't even realize what you've lost. Survival is much more real.

You don't "judge" a book by its cover; you use the cover as additional evidence to more accurately predict what's in the book. Knowing what the publisher wants you to assume about the book is preferable to not knowing.

You can't calculate utilites anyway; there's no reason to assume that u(n days) should be 0.5 * (u(n+m days) + u(n-m days)) for any n or m. If you want to include immortality, you can't assign utilities linearly, although you can get arbitrarily close by picking a higher factor than 0.5 as long as it's < 1.

Put them in a situation where they need to use logic and evidence to understand their environment and where understanding their environment is crucial for their survival, and they'll figure it out by themselves. No one really believes God will protect them from harm...

A really smart 'shoot lasers at "blue" things' robot will shoot at blue things if there are any, and will move in a programmed way if there aren't. All its actions are triggered by the situation it is in; and if you want to make it smarter by giving it an ability to better distinguish actually-blue from blue-looking things, then any such activity must be triggered as well. If you program it to shoot at projectors that project blue things it won't become smarter, it will just shoot at some non-blue things. If you paint it blue and put a mirror in front of it it will shoot at itself, and if you program it to not shoot at blue things that look like itself it won't become smarter, it will just shoot at fewer blue things. If anything it shoots at doesn't cease to be blue or you give it a blue laser or camera lens, it will just continue shooting because it doesn't care about blue things or shooting; it just shoots when it sees blue. It certainly won't create blue things to shoot at.

A really dumb 'minimize blue' robot with a laser will shoot at anything blue it sees, but if shooting at something doesn't make it stop being blue, it will stop shooting at it. If there's nothing blue around it will search for blue things. If you paint it blue and put a mirror in front of it it will shoot at itself. If you give it a blue camera lens it will shoot at something, stop shooting, shoot at something different, stop shooting, move around, shoot at something, stop shooting, etc, and eventually stop moving and shooting altogether and weep. If instead of the camera lens you give it a blue laser it will become terribly confused.

Actually, it seems you can solve the immortality problem in ℝ after all, you just need to do it counterintuitively: 1 day is 1, 2 days is 1.5, 3 days is 1.75, etc, immortality is 2, and then you can add quality. Not very surprising in fact, considering immortality is effectively infinity and |ℕ| < |ℝ|.

This isn't a paradox about unbounded utility functions but a paradox about how to do decision theory if you expect to have to make infinitely many decisions.

I believe it's actually a problem about how to do utility-maximising when there's no maximum utility, like the other problems. It's easy to find examples for problems in which there are infinitely many decisions as well as a maximum utility, and none of those I came up with are in any way paradoxical or even difficult.