David Wallace's `Dennett's Criterion' plays a key part in establishing realist claims about the existence of a multiverse emerging from the mathematical formalism of quantum physics, even after decoherence is fully appreciated. Although the philosophical preconditions of this criterion are not neutral, they are rarely explicitly addressed conceptually. I tease apart three: (I) a rejection of conceptual bridge laws even in cases of inhomogeneous reduction; (II) a reliance on the pragmatic notion of usefulness to highlight quasi-classical patterns, as seen in (...) a decoherence basis, over others; and (III) a structural realist or `functional realist' point of view that leads to individuating those patterns as real macroscopic objects at the coarse-grained level, as they are seen from the Classical Stance (analogous to Dennett's Intentional Stance). I conclude that the justification of Dennett's Criterion will be intimately tied up with the fate of strong forms of naturalism, and in particular that Wallacian quantum mechanics is a key case study for concretely evaluating his `math-first' structural realism (Wallace 2022). (shrink)