8. Numerations

8.1. The existential quantifier

8.1.0. Overview

A generalization quantifies only by claiming the absence of counterexamples. We will now turn claims that are more explicitly quantificational; the first are claims of the existence of examples, each of which asserts that there is at least one object of a certain sort.

8.1.1. Exemplification
Most of the ideas used in analyzing English generalizations apply also to claims of exemplification; but, instead of three forms, we have only one.

8.1.2. Obversion
As was noted in 7.3.1, every claim of existence amounts to the denial of a generalization.

8.1.3. Conversion
The quantifier phrase and quantified predicate of an existential claim are interchangeable, a feature that is associated with the use of the phrase there is.

8.1.4. Existentials exemplified
Most analyses of existential claims are straightforward, but there is often a great variety of ways of expressing the same content in English.

8.1.5. Existential commitment
The impact of the way undefined terms are being handled is clearest when we consider the content of existential claims.