English sentences that involve both generalization and claims of exemplification are often ambiguous, and the differences between interpretations can be expressed in analyses of them by the relative scope of universal and existential quantifiers. We will refer to a sentence that mixes generalization and with a claim of exemplification as a claim of general exemplification. One in which the existential has wider scope than the universal can be thought of as a claim of uniformly general exemplification because it asserts that a single example can be given that suffices for all instances of the generalization.

When more than two quantifier phrases are present, an existential may be classified as making or not making a claim of uniformity with respect to each universal, giving rise to a variety of uniformity claims that a sentence may be understood to make. The issue of quantifier scope can thus be addressed by asking, for each of the dimensions of generality with which a claim of exemplification is asserted, whether the exemplification is claimed to uniform in that dimension; this settles the relative scope of each existential with respect to each universal, and the relative scope of contiguous universals and contiguous existentials does not matter.

The ambiguity in sentences involving both existentials and universals is hard to eliminate, but syntax and word choice can help. The first quantifier phrase is usually understood to have widest scope, and a quantifier phrase in a relative clause usually has its scope limited to that clause (a fact that makes the there-is form useful). The choice of quantifier words can counteract the effect of word order to some extent, and the use of the special quantifier phrases a certain X and some X or other will strongly tend, respectively, to advance or to renounce a claim of uniformity.