Full Idea
'Cicero=Cicero' and 'Cicero=Tully' are both dyadic predications. It is unnatural to suppose that the use of the same name converts a dyadic predicate into a reflexive predicate, or that there is one reference to Cicero in the first and two in the second.
Gist of Idea
If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well?
Source
Kit Fine (Semantic Relationism [2007], 3.A)
Book Reference
Fine,Kit: 'Semantic Relationism' [OUP 2007], p.69
A Reaction
I am deeply suspicious of the supposed 'property' of being self-identical, but that may not deny that it could be a genuine truth (shorthand for 'the C you saw is the same as the C I saw'). Having an identity makes equality with self possible.