 According to Hintikka, our pretheoretical idea of the truth of a quantified sentence \(\phi\) (in negation normal form) is that there exist ‘witness individuals’ for the existential quantifiers, usually depending on values corresponding to the preceding universal  quantifiers.[75]  It is the existence of such witnesses that constitutes the truth of \(\phi\). Providing witnesses is precisely what Skolem functions for \(\phi\)  do.[76]  The truth of a quantified sentence \(\phi\) amounts to the existence of a full set of Skolem functions for \(\phi\). In Hintikka’s view, then, our ordinary notion of first-order truth is conceptualized in terms of (existential) second-order logic. What happens when this idea is applied to axiomatic set theory, say Zermelo-Fraenkel set theory with the Axiom of Choice \((\mathbf{ZFC})\)? It should be borne in mind that the very idea of axiomatic set theory is to dispense with higher-order logic; its underlying logic is taken to be \(\mathbf{FO}\). Hintikka argues as  follows.[77]