 The existential quantifier, \(\exists\), is, for Frege, a second-level predicate, which expresses a second-level concept under which a first-level concept such as square root of 4 falls if and only if it has some instances. Likewise, the universal quantifier, \(\forall\), is a second-level predicate, which expresses a second-level concept under which a first-level concept such as self-identical falls if and only if it has all objects as instances.