The logic behind Quine's criterion of ontological commitment

This article first explains why Quine took first-order classical logic to be the only language in which we should formulate a theory or declarative statement to determine its ontological commitments. I then argue that Quineans cannot relax Quine's restriction to classical logic such thatanynonclassical logic may be used to uncover a theory's ontological commitments. The reason is that this leads to radical ontological relativism according to which the ontological commitments of a theory are relative to a logic. This is not a Quinean picture of ontology, but a Carnapian one. Finally, I consider whether Quineans can go beyond Quine by allowing for classical and plural logic, but no other logics. I claim that this is not possible because plural logic is not transparent: it allows for ontologically nonequivalent theories to be formulated such that they come out as ontologically equivalent.