Rebutting radical scientific skepticism
Suppose you distrusted everything you had ever read about science. How much of modern scientific knowledge could you verify for yourself, using only your own senses and the sort of equipment you could easily obtain? How about if you accept third-party evidence when many thousands of people can easily check...
It's a tempting thought. But I think it's hard to make the math work that way.
I have a lovely laptop here that I am going to give you. Suppose you assign some utility U to it. Now instead of giving you the laptop, I give you a lottery ticket or the like. With probability P I give you the laptop, and with probability 1 - P you get nothing. (The lottery drawing will happen immediately, so there's no time-preference aspect here.) What utility do you attach to the lottery ticket? The natural answer is P * U, and if you accept some reasonable assumptions about preferences, you are in fact forced to that answer. (This is the basic intuition behind the von Neumann-Morgenstern Expected Utility Theorem.)
Given that probabilities are real numbers, it's hard to avoid utilities being real numbers too.