Full Idea
In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it.
Gist of Idea
The null set is a structural position which has no other position in membership relation
Source
Charles Chihara (A Structural Account of Mathematics [2004], 11.6)
Book Reference
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.343
A Reaction
It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set.