But some less pressing objections remain that suggest that metaphysical necessity is too blunt an instrument to capture the notion of ontological commitment. Three will be mentioned here. First, just as extensional criteria could not distinguish between ontological commitments to co-extensional kinds, the modal criteria cannot distinguish between ontological commitments to co-intensional kinds. A theory that is committed to triangular polygons will also be committed to trilateral polygons, and vice versa, because, necessarily, a polygon is triangular if and only if it is trilateral. A theory that is committed to round squares will also be committed to even prime numbers greater than two, and vice versa, because, necessarily, (it is vacuously true that) something is a round square if and only if it is an even prime number greater than two. Second, metaphysically impossible theories, theories that are true at no world, will be (vacuously) committed to every kind of entity. But that seems wrong: naïve set theory is committed to sets, but not to angels that dance on the head of a pin. Third, the modal criteria may introduce spurious commitment if there are metaphysically necessary connections between distinct kinds of entity. For example, if whales are necessarily mammals, then a theory committed to whales would automatically be committed to mammals, even if the theory explicitly claims that there are no mammals and that whales are fish. A theory committed to Hesperus would automatically be committed to Phosphorus, assuming the necessity of identity, even if the theory explicitly claims that Hesperus exists and that Phosphorus doesn't.