Full Idea
The main technical problem with counterpart theory is that the being-a-counterpart relation is, in general, neither symmetric nor transitive, so no natural logic of equality is forthcoming.
Gist of Idea
Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.5)
Book Reference
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.93
A Reaction
That is, nothing is equal to a counterpart, either directly or indirectly.