Ontology of a universe
"Existence in the most general sense means being identical to oneself and different from others."
I agree that: x exists <-> x=x
x exists <-> Ey(x=y)
Names and descriptions refer or not.
1. (x=x, for all x) is an axiom in FOPL=.
Leibnitz/Russell: x=y =def AF(Fx <-> Fy).
In which case x=x <-> AF(Fx <-> Fx),
ie. x=x is tautologous for any x.
AF(F(Vulcan) <-> F(Vulcan)) is tautologous.
Therefore, Vulcan exists ???
Note that: AF(F(The present King of France) = F(The present King of France)), is also tautologous.
Therefore (The present King of France exists) ???
A better definition of Identity...
x=y =def (EF(Fx) & EF(Fy) & AF(Fx <-> Fy)).
x=x <-> (EF(Fx) & EF(Fx) & AF(Fx <-> Fx)).
x=x <-> EF(Fx).
x=x <-> x exists.
If x or y do not exist then x=y is false.