Metaphysicalnecessity is too coarse-grained to track these distinctions (e.g., it cannot distinguish triangular polygons from trilateral polygons, or relevant from irrelevant necessary existents).
A shape defined by having three sides; here it's being described based on its side-based properties.
coarse-grained(Ontology of properties and criteria of individuation)
Descriptive of individuation criteria or entities that make fewer distinctions; extensional criteria are paradigmatically coarse-grained relative to intensional or hyperintensional ones
metaphysical necessity(Distinguishing types of necessity)
A property of things that must be the case but not purely by logical form — true in all possible worlds without being logical tautologies
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 conceptu