What they said about the U(-)=0 problem. But the way I think about it resolves more contradictions, more easily, IMO.

• Utility is no more than a mathematical artifact, do not phrase questions in terms of utility

Utility functions are equivalent under positive affine transforms. This is a huge clue that thinking about utility will lead to major intuition problems. Instead, use quantities that are not ambiguous. You're gonna have to get rid of the a and b in au(x)+b, so you're going to need three states of the world, always, before you're allowed to use intuition. You can combine them in different ways, but I like

r = [U(x)-U(z)] / [U(y)-U(z)]

Mere differences in utility are not pinned down, because of scale. Ratios of differences in utility are great, though. It's 2.67x as good to go from nothing to chocolate as to go from nothing to vanilla. 0 and 3 and 8, or 4 and 7 and 12, those are just there for computational convenience in some circumstances and can be ignored.