This section and the next provide an evaluation of quantifier accounts of ontological commitment. It is still assumed, following Quine, that the target theory is couched within first-order predicate logic. (For discussion of ontological commitment in ordinary language, see §4.) The critique is divided into two parts: in this section, it is asked whether the quantifier criterion is sufficient for ontological commitment; in the next section, it is asked whether it is necessary. Objections that were considered above in presenting specific versions of the quantifier criterion will not be repeated.