Corresponding to every physical object, there are infinitely many distinct sets (e.g., the set containing the ball, the set containing that set, and so on)

Let us move on now to immanent-realist, or physicalist, views of mathematics, and let us concentrate first on views like Mill's (1843, book II, chapters 5 and 6), i.e., views that maintain that sentences about numbers are really just general claims about bunches of ordinary objects. On this view, the sentence ‘2 + 1 = 3’, for instance, isn't really about specific objects (the numbers 1, 2, and 3). Rather, it says that whenever we add one object to a pile of two objects, we will get a pile of thr