 If we take the mathematics that is involved in our best scientific theories at face value, then we appear to be committed to a form of platonism. But it is a more modest form of platonism than Gödel’s platonism. For it appears that the natural sciences can get by with (roughly) function spaces on the real numbers. The higher regions of transfinite set theory appear to be largely irrelevant to even our most advanced theories in the natural sciences. Nevertheless, Quine thought (at some point) that the sets that are postulated by ZFC are acceptable from a naturalistic point of view; they can be regarded as a generous rounding off of the mathematics that is involved in our scientific theories. Quine’s judgement on this matter is not universally accepted. Feferman, for instance, argues that all the mathematical theories that are essentially used in our currently best scientific theories are predicatively reducible (Feferman 2005). Maddy even argues that naturalism in the philosophy of mathematics is perfectly compatible with a non-realist view about sets (Maddy 2007, part IV).