Full Idea
Surely it is true of Socrates that he is Socrates and he is identical with Socrates. If these are true of him, then 'being Socrates' and 'being identical with Socrates' characterize him; they are among his properties or attributes.
Gist of Idea
'Being Socrates' and 'being identical with Socrates' characterise Socrates, so they are among his properties
Source
Alvin Plantinga (World and Essence [1970], II)
Book Reference
Plantinga,Alvin: 'Essays in the Metaphysics of Modality' [OUP 2003], p.58
A Reaction
As far as I can see (if you insist on accepting self-identity as meaningful) the most you get here is that these are predicates that can attach to Socrates. If you identify predicates with properties you are in deep metaphysical trouble.