 The question arises, why do we not use second-order set theory \(\ZFC^2\) as the metatheory of second-order logic, as recommended in Shapiro (1991). In fact we could use it. However, the question might rise, what is the semantics of our metatheory? In principle such questions can lead to an infinite regress. By using first order set theory as the metatheory, the question about the semantics of the metatheory would simply be the question about the semantics of first order logic. We have pointed out in  §6  that semantics of first order logic is absolute relative to ZFC. This gives some assurance that we need not continue asking, what the metatheory is.