All of these objections to modal criteria for ontological commitment have a common source: ontological commitment appears to be sensitive to distinctions that metaphysical necessity cannot accommodate. One solution, then, would be to seek a more discriminating entailment relation. Thus, the third objection suggests that a priori entailment should replace metaphysically modal entailment. In the modal quantifier criterion, one could quantify over domains and sub-domains of worlds that are conceptually, rather than metaphysically, possible.[14] That won't help with the first two objections, however, since the existence of triangular polygons is a priori entailed by the existence of trilateral polygons, and, assuming classical logic is a priori, the existence of angels (and everything else) is a priori entailed by naïve set theory (or any inconsistent theory). For these, we can retreat further to some sort of relevant entailment relation within a paraconsistent logic. The quantifier criterion could be expressed by quantifying over domains and sub-domains of worlds that are both conceptually and metaphysically  impossible.[15]  Alternatively, one could revert to an entailment account, since relevant entailment by itself can handle the problem of irrelevant necessary existents. It is not the case that any theory relevantly entails that numbers exist. 