When we stipulate that the universe of discourse is some smaller set of things, e.g. the set of all human beings, then the quantifiers refer only to that set of things. These conventions are modern, due to George Boole. Aristotle held that both forms of quantification possess existential import. In predicate logic, there are also statements all of whose substitution instances are true. All tautologies are logical truths, but not all logical truths are tautologies.
Quantifiers have scope , namely, the first whole proposition, simple or compound, to their right.
In this sense, they have the same scope as the negation sign. Hence it is imprecise to speak merely of free and bound variables. We must speak of free and bound occurrences of variables. A variable may also occur freely with respect to one quantifier and bound with respect to another. So we must speak of free and bound occurrences of variables with respect to a given quantifier.