8.2. Uniform generality

8.2.0. Overview

The ambiguity of sentences containing both existentials and universals was an important motivation in the development of logic, and we are now in a position to consider it directly.

8.2.1. General and uniformly general exemplification
The key distinction marked by the relative scope of a universal and an existential quantifier is the difference between the general existence of examples and the existence of an example that serves generally.

8.2.2. Quantifier scope ambiguities
When there are more than two quantifiers, scope ambiguities multiply and we must ask, for each existential quantifier phrase and each universal, whether or not an example is claimed to serve generally.

8.2.3. Controlling ambiguity
While scope ambiguities are hard to avoid entirely, English has some devices for minimizing them.