On this criterion, every theory is ontologically committed to every necessarily existing kind of entity, what was called above (§1.5) the problem of irrelevant necessary existents. The problem can be ignored when comparing the ontological costs of theories that disagree only over contingently existing kinds: the irrelevant commitments are the same for both theories, and cancel one another out. But many traditional ontological disputes are over the existence of necessarily existing kinds of entity, such as mathematical entities or intensional entities. Consider, for example two theories that disagree only over whether numbers exist. On the modal entailment criterion, these theories have the same ontological commitments; moreover, supposing numbers do exist, the theory that explicitly denies the existence of numbers is nonetheless committed to numbers. Clearly, the modal entailment criterion fails to capture the intuitive notion of ontological commitment.  Applying the criterion in this case will do nothing to further the ontological enterprise.