 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 a value to the variable ‘x’ in order for the theory to be true.  Similarly, if a whole cannot exist without one of its parts existing, then there appears to be implicit commitment. Suppose, for example, that a human cannot exist without his head. Then a theory that contains ‘∃x x = Obama’ is ontologically committed to Obama's head. But, again, Obama's head need not be assigned as a value to the variable ‘x’ in order for the theory to be true.