 If C = triangle and P = red, P would be, following this definition, a real predicate, since it is possible that there exists an x which is a triangle and is not red. By contrast, if P = three-sidedness, then we do not, by this definition, have a real predicate of C, since there are no triangles that are not three-sided. In other words, where C = triangle and P = three-sidedness, since \(\forall x (Cx \supset Px)\), P fails to meet the test for conceptual enlargement of C. Likewise, existence will fail to meet the definition above since for any concept C, \(\exists x (Cx \supset \langle\textrm{exists}\rangle x)\). That is, if there exists some x such that x is a C, then x exists. Hence, Van Cleve treats existence as not an enlarging concept since, per his analysis, he is “letting the existential quantifier express existence” (Van Cleve 1999: 188).