 Many existential assertions—e.g., \(\exists x(x=x),\) \(\exists x(Px \rightarrow Px),\) \(\exists x(Px \rightarrow \forall yPy)\)—are true in all nonempty domains and hence are valid in both classical logic and non-inclusive free logic. But since all existentially quantified formulas are false in the empty domain, none are valid in inclusive logic. Correlatively, since all universally quantified formulas are true in the empty domain, none are self-contradictory in inclusive logic. Even vacuously universally quantified formulas (formulas of the form \(\forall xA\), where \(x\) is not free in \(A)\) are true in the empty domain. Hence the schema: