The modal entailment criterion, however, appears to be inadequate with respect to the vast majority of philosophical applications, at least as metaphysical necessity is standardly interpreted (but see §2.2 for possible lines of defense). This is because many philosophically controversial kinds of entity are taken to exist necessarily if they exist at all, for example, numbers, or universals. But necessarily existing kinds of entity make trouble for the criterion: for any theory T, any world at which T is true is a world whose domain contains numbers. So any theory T is ontologically committed to numbers, whether or not the content of T, intuitively, has anything to do with numbers. This suggests that we return to a Quinean criterion that ties ontological commitment directly to the values of the variables; numbers need not be values of the variables for a theory T that has nothing to do with numbers. To make the variable assignments relevant, we can quantify doubly over worlds and sub-domains of worlds. This leads to the modal quantifier criterion: