If existence is not a property then doesn't it follow that necessary existence is also not a property? If it is then why?
If it is then why?
My dog exists.
The Unicorn doesn't.
So, existence is a property of my dog, but it is not of the Unicorn.
doesn't it follow that necessary existence is also not a property?
The only necessity is logical necessity: To say that ψ → ξ is true is to say that if ψ is true, then ξ is true.
That is to say, ξ is necessarily true when ψ is true.
Which is why we say that ξ is the necessary condition of the implication ψ → ξ.
Existence is necessary if the existence of y follows from some assumption. For example:
Horses exist and they are mammals, therefore mammals exist
Once you recognise that horses exist and that they are mammals, you have to recognise that necessarily mammals exist. The existence of mammals is necessary if horses exist and are mammals.