7.3. Quantifiers and connectives

7.3.0. Overview

Many of the logical properties of quantifiers come from their interactions with other logical constants, both connectives and quantifiers; in this section, we will look at their interaction with connectives.

7.3.1. Generalizations and counterexamples
Although denials of conditionals are rare, denials of generalizations are common and have the effect of claiming the existence of counterexamples.

7.3.2. Generalizations as components
The analysis of combinations of generalization with other connectives can be less straightforward.

7.3.3. Any and every
In contexts where it is an alternative to every, the word any can interpreted as indicating a generalization with wide scope.