For the proponent of second-order theories, no such transformation is needed: the quantifier criterion can be applied directly to the values of the second-order variables. The ontological commitments of second-order theories will then depend on how the second-order variables are interpreted. If the second-order variables range over properties (“attributes”), then second-order theories are committed to properties; if instead they range over sets, then second-order theories are committed to sets. On either interpretation, any world at which a second-order theory is true will have either properties or sets in its domain, and so the modal quantifier criterion (from §1.5) can be applied without amendment. Extending the quantifier criterion to second-order theories, then, would seem to be within the spirit, if not the letter, of Quine's account of ontological commitment.