Page "First-order logic" Paragraph 24

The range of the quantifiers is the set of objects that can be used to satisfy them.

( In the informal examples in this section, the range of the quantifiers was left unspecified.

) In addition to specifying the meaning of predicate symbols such as Person and Time, an interpretation must specify a nonempty set, known as the domain of discourse or universe, as a range for the quantifiers.

Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.