This is an argument from absurdity against infinite utility functions, but not quite against unbounded ones.
Can you elaborate on the practical distinction? My impression is that if your utility function is unbounded, then you should always be able to devise paths that lead to infinite utility—even by just infinite amounts of finite utility gains. So I don’t know if the difference matters that much.
Infinite utility functions mean that there is a concrete input such that the output is “infinity”, such as “you go to heaven in the Wager scenario”. Unbounded utility functions do not necessarily output “infinity” for a particular value.f(x)=x or “count the number of paper clips” is unbounded but at no concrete input does it tell you “infinity”.
Can you elaborate on the practical distinction? My impression is that if your utility function is unbounded, then you should always be able to devise paths that lead to infinite utility—even by just infinite amounts of finite utility gains. So I don’t know if the difference matters that much.
Infinite utility functions mean that there is a concrete input such that the output is “infinity”, such as “you go to heaven in the Wager scenario”. Unbounded utility functions do not necessarily output “infinity” for a particular value.f(x)=x or “count the number of paper clips” is unbounded but at no concrete input does it tell you “infinity”.