Full Idea
If even non-existent things are still counted as self-identical, then all non-existent things must be counted as identical with one another, so there is at most one non-existent thing. We might arbitrarily choose zero, or invent 'the null object'.
Gist of Idea
If non-existent things are self-identical, they are just one thing - so call it the 'null object'
Source
David Bostock (Intermediate Logic [1997], 8.6)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.362