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Full Idea
In the quantification '(∃)(x=a)', it is the existential quantifier, not the 'a' itself, which carries the existential import.
Gist of Idea
Existence is implied by the quantifiers, not by the constants
Source
Willard Quine (Existence and Quantification [1966], p.94)
Book Ref
Quine,Willard: 'Ontological Relativity and Other Essays' [Columbia 1969], p.94
A Reaction
The Fregean idea seems to be that the criterion of existence is participation in an equality, but here the equality seems not more than assigning a name. Why can't I quantify over 'sakes', in 'for the sake of the children'?