 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 three objects. Now, in order to account for contemporary mathematics in this way, a contemporary Millian would have to take set theory to be about ordinary objects as well. This, however, is untenable. One argument here is that set theory could not be about bunches of ordinary objects, or piles of physical stuff, because corresponding to every physical pile, there are many, many sets. Corresponding to a ball, for instance, is the set containing the ball, the set containing its molecules, the set containing its atoms, and so on. (And we know that these are different sets, because they have different members, and it follows from set theory that if set A and set B have different members, then A is not identical to B.) Indeed, the principles of set theory entail that corresponding to every physical object, there is a huge infinity of sets. Corresponding to our ball, for instance, there is the set containing the ball, the set containing that set, the set containing that set, and so on; and there is the set containing the ball and the set containing the set containing the ball; and so on and on and on. Clearly, these sets are not just piles of physical stuff, because (a) there are infinitely many of them (again, this follows from the principles of set theory) and (b) all of these infinitely many sets share the same physical base. Thus, it seems that claims about sets are not claims about bunches of ordinary objects, or even generalized claims about such bunches. They are claims about sets, which are objects of a different kind.