The formal machinery behind the discussion above traces back to ideas of Carnap. In this tradition possible worlds are central, and sense or intension is a function from possible worlds to denotations. Senses determine denotations, but detailed machinery accounting for how this happens is not made concrete (except for definite descriptions). One need not do things this way. If the Church approach is followed, one can simply say that “Hesperus” and “Phosphorus” have the same designation rigidly, hence necessarily, but even so they do not have the same sense. This is possible because senses are, in effect, independent and not derived things. Senses can determine the same extension across possible worlds without being identical.