Full Idea
Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept.
Gist of Idea
Vague membership of sets is possible if the set is defined by its concept, not its members
Source
Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5)
A Reaction
I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy.