 If we do wish to view identity as a non-logical notion, then the phenomenon of language relativity suggests that it is best not to formalize identity using a single identity predicate ‘=’. Instead, we have the following picture: We begin with a language \(L\) and define an L-theory with identity to be a theory whose logical axioms are those of FOL and which is such that \(L\) contains a two-place predicate \(E_L\) satisfying the non-logical axiom \(\textrm{Ref}\,'\) and the non-logical axiom schema \(\textrm{LL}'\)