The logical formalisms that have dominated in the analytic tradition ever since Frege do not allow for plural quantification.
But the existence of two or more objects may not be semantically required; for instance, “The students who register for this class will learn a lot” seems capable of being true even if only one student registers.
It is therefore both reasonable and convenient to demand only that there be at least one object satisfying \(\phi(x)\).
We see this by distinguishing between two kinds of plural predication.
A predicate \(P\) taking plural arguments is said to be For instance, the predicate “is on the table” is distributive, since it is analytic that some things \(xx\) are on the table just in case each of \(xx\) is on the table.