 However, the language \(L_{\textrm{PFO}}\) has one severe limitation. We see this by distinguishing between two kinds of plural predication. A predicate \(P\) taking plural arguments is said to be distributive just in case it is analytic that: \(P\) holds of some things \(xx\) if and only if \(P\) holds of each \(u\) such that \(u\prec  xx\).[5]  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. A predicate \(P\) that isn’t distributive is said to be non-distributive or  collective.[6]  For instance, the predicate “form a circle” is non-distributive, since it is not analytic that whenever some things \(xx\) form a circle, each of \(xx\) forms a circle. Another example of non-distributive plural predication is the second argument-place of the logical predicate \(\prec\): for it is not true (let alone analytic) that whenever \(u\) is one of \(xx, u\) is one of each of \(xx\). It is therefore both natural and useful to consider a slightly richer language: