 This reasoning shows that \(\mathbf{ZFC}\) does not fully capture the idea of truth according to which the truth of a sentence \(\phi\) means that the Skolem functions for \(\phi\) exist. Furthermore, it also shows that the standard interpretation of higher-order logic is not fully captured by \(\mathbf{ZFC}\). To see this, observe that for every sentence \(\phi\) there is a logically equivalent second-order sentence \(\phi^{**} = (\exists F_1)\ldots(\exists F_n)\psi^{**}\) actually asserting the existence of Skolem functions for \(\phi\). The first-order sentence \(\phi^* = (\exists f_1)\ldots(\exists f_n)\psi^*\) must not be confused with the second-order sentence \(\phi^{**} = (\exists F_1)\ldots(\exists F_n)\psi^{**}\). The Skolem functions \(F_i\) of which the sentence \(\phi^{**}\) speaks are sets built out of individuals of the set-theoretical universe, while the ‘Skolem functions’ \(f_i\) spoken of by \(\phi^*\) are  individuals.[79]