Bentham

The notion that interests can in some way be summed is common across most of right-wing thought and across all of left-wing thought. This assumption is mathematic, though almost no one who makes it recognizes it as such.

For a property to be subject across persons, it must have some common measure across persons. (This is what is meant by “commensurable”.) A necessary (though not sufficient) condition for things to have a common measure is that they should correspond to quantities.

A necessary (though not sufficient) condition for a property to correspond to a quantity is that the property be fully orderable — that every two things with that property must such that one has more of the property than the other or that one has the property just as much as does the other. If some two things have the property but such no relative ordering prevails, then the property does not correspond to a quantification, because quantifications are always fully ordered.

So, if, for example, you prefer X to Z and Y to Z but are undecided about the relative desirability of X to Y, then your preferences cannot be quantified. If, given some information, X is more plausible than Z and Y is more plausible than Z but the relative plausibility of X and Y cannot be determined, then plausibility cannot be quantified.

Finding cases in which preferences or plausibilities cannot be quantified explodes the assumption that interested are measurable, are commensurable, are summable. All of left-wing thought and most of right-wing thought is invalidated.

We must look elsewhere to found our ethics.