 Commendably, Goodman and Quine do not shy away from the metatheory problem, the difficulty that syntax and metamathematics itself seems as ontologically rich and committed to abstract objects as arithmetic. On the contrary, they face it squarely and attempt to make do entirely with an ontology of concrete objects, finitely many such objects in fact. (However they do assume fairly powerful mereological principles, essentially universal composition: they assume that any fusion of objects, however scattered or diffuse, is also an object in good standing.)