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Full Idea
Without the assumption of the empty set, one would often have to take special precautions for the case where a set happened to contain no elements.
Gist of Idea
The empty set avoids having to take special precautions in case members vanish
Source
Michal Walicki (Introduction to Mathematical Logic [2012], 1.1)
Book Ref
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.45
A Reaction
Compare the introduction of the concept 'zero', where special precautions are therefore required. ...But other special precautions are needed without zero. Either he pays us, or we pay him, or ...er. Intersecting sets need the empty set.