Full Idea
The null set is a denotation of last resort for class-terms that fail to denote classes, an intersection of x and y where they have no members in common, the class of all self-members, and the real numbers such that x^2+1=0. This is all mere convenience.
Gist of Idea
There are four main reasons for asserting that there is an empty set
Source
David Lewis (Parts of Classes [1991], 1.4)
Book Reference
Lewis,David: 'Parts of Classes' [Blackwell 1991], p.11
A Reaction
A helpful catalogue of main motivations for the existence of the null set in set theory. Lewis aims to undermine these reasons, and dispense with the wretched thing.