Thus, on this analysis, a proposition p is true in a world w just in case w ∈ p and an individual a has a property P just in case a ∈ P. (Note that propositions are thus simply properties of worlds on these definitions.) a has P accidentally just in case a ∈ P but b ∉ P for some other-worldly counterpart of b of a; and a has P essentially if b ∈ P for every counterpart b of a.