8.3. Numerical quantification

8.3.0. Overview

Claims of exemplification speak of quantity in a very limited way; but, when combined with identity, the existential quantifier can be used to express quite a variety of clearly numerical claims.

8.3.1. Else
The key device we will use appears in the English word else, which can be used to claim the existence of a new example.

8.3.2. Numerical quantifier phrases
The phrase something else provides a way to claim the existence of ever more new examples, allowing us to express phrases of the form at least n symbolically, and a variety of specific numerical claims can be captured by considering truth-functional compounds employing these phrases.

8.3.3. Exactly n
A simpler analysis of exactly n is possible by using a device that is captured in English by the phrase nothing else.