If entity X cannot exist without entity Y existing, then a theory asserting X's existence is ontologically committed to Y's existence.

The problem of extrinsic properties arises because there are analytic connections between one predicate holding of a thing and another predicate holding of some other thing. Similar problems arise for quantifier criteria if there are metaphysically necessary connections between non-identical things. Thus, if a set cannot exist without its members existing, then it appears that a theory that contains ‘∃x x = {a, b}’ is ontologically committed to the existence of a. But a need not be assigned as