  Quine’s choice of first-order logic, rather than second-order logic, has been more controversial than his adoption of bivalence. One reason he gives for the decision is that every formalization of second-order logic (unlike first-order logic) is incomplete, relative to the standard semantics. A further reason is that one purpose of the canonical framework is to enable us to assess the ontology of a theory. From this point of view it is an advantage that first-order logic has no ontological presuppositions of its own. (By adopting that logic we do commit ourselves to there being some object or other, but not to the existence of any particular entity.) Here again there is a clear contrast with second-order logic, which does have ontological presuppositions. Exactly what those presuppositions are is unclear, and has been debated; for Quine, this unclarity is a further reason to avoid the subject entirely.