 In particular, there is some reason to think that the Gödelian ontological argument goes through just as well—or just as badly—with respect to other sets of properties (and in ways which are damaging to the original argument). Suppose that there is some set of independent properties {I, G1, G2, …} which can be used to generate the set of positive properties by closure under entailment and “necessitation”. (“Independence” means: no one of the properties in the set is entailed by all the rest. “Necessitation” means: if P is in the set, then so is necessarily having P. I is the property of having as essential properties just those properties which are in the set. G1, G2, … are further properties, of which we require at least two.) Consider any proper subset of the set {G1, G2, …}—{H1, H2, …}, say—and define a new generating set {I*, H1, H2, …}, where I* is the property of having as essential properties just those properties which are in the newly generated set. A “proof” parallel to that offered by Gödel “establishes” that there is a being which has as essential properties just those properties in this new set. If there are as few as 7 independent properties in the original generating set, then we shall be able to establish the existence of 720 distinct“God-like” creatures by the kind of argument which Gödel offers. (The creatures are distinct because each has a different set of essential properties.)