What do the existential quantifier and existence have in common?

Recent extensional logic considers a formula containing existential quantifier as an adequate way of rewriting a statement about the existence of something. Quine even claims that "to be is to be the value of a variable". That means that if we consider a theory to be true, we have to treat all members of an appropriate universe as existing. This article intends to point out a difficulty in this conception: The primary task of an existential quantifier is only to claim that something can be found in a universe, whatever the universe is.