 Some philosophers emphasize the ontological economies possible by using schemas rather than second-order axioms (e.g., Quine 1970/1986). But rarely if ever do these philosophers present a full and objective discussion of the “ontological commitments” entailed by the use of schemas. For example, number theory per se presupposes the existence of numbers, and perhaps numerical functions and numerical properties, but it does not presuppose the existence of mathematical notation and it a fortiori does not presuppose the existence of the vast, intricate notational system that we call the language of number theory. Sometimes the use of schemas may decrease the ontological commitments of the object language while increasing those of the metalanguage, or at least not achieving any net savings.