Although our way of analyzing multiple generalizations forces us to assign differences in relative scope to the quantifier phrases, these differences do not always affect the propositions expressed. One example of this is a sentence containing two affirmative direct quantifier phrases. We can analyze these in either order, and the result of either analysis can be thought of as a generalization concerning pairs of values. Such generalizations are sometimes restricted to pairs whose members stand in a certain relation. In this case, we may leave the quantifier with widest scope unrestricted, using the relation to restrict the quantifier with narrower scope.
In many other cases, the scope assigned to quantifier phrases makes a difference. This is usually true in cases where there are negative generalizations. Subject-predicate expansion can be used to see which quantifier phrase should be given widest scope, but there are other signs. For example, any can be used in contrast to every to indicate that an affirmative generalization has wider scope than a negative generalization. It also can be used to show that one quantifier phrase that appears in the class indicator of another nevertheless has wider scope. Uses of every that contrast with any have the opposite significance.