Full Idea
We can't take a property as sets of this-worldly instances, because two properties may be coextensive. Some say it is just as bad in all possible worlds, if the property is necessary, as when all triangles are trilateral, which seem different.
Gist of Idea
Trilateral and triangular seem to be coextensive sets in all possible worlds
Source
David Lewis (On the Plurality of Worlds [1986], 1.5)
Book Reference
Lewis,David: 'On the Plurality of Worlds' [Blackwell 2001], p.55
A Reaction
[compressed] Renate/cordate is the standard example of the first problem. Lewis seems to equivocate over exactly what is meant by a property. I take the example to be a powerful objection to treating properties as sets.