 In connection with numbers, one strategy is to take numbers to be universals of some sort — e.g., one might take them to be properties of piles of physical objects, so that, for instance, the number 3 would be a property of, e.g., a pile of three books — and to take an immanent realist view of universals. (This sort of view has been defended by Armstrong (1978).) But views of this kind have not been very influential in the philosophy of mathematics. A more prominent strategy for taking number talk to be about the physical world is to take it to be about actual piles of physical objects, rather than properties of piles. Thus, for instance, one might maintain that to say that 2 + 3 = 5 is not really to say something about specific entities (numbers); rather, it is to say that whenever we push a pile of two objects together with a pile of three objects, we will wind up with a pile of five objects — or something along these lines. Thus, on this view, arithmetic is just a very general natural science. A view of this sort was developed by Mill (1843) and, more recently, a similar view has been defended by Philip Kitcher (1984). It should be noted, however, that while there are certainly physicalist themes running through the views of Mill and Kitcher, it is not clear that either of them should be interpreted as an immanent realist. Kitcher is probably best classified as a kind of anti-realist (I'll say a bit more about this in  section 4.1),  and it's not entirely clear how Mill ought to be classified, relative to our taxonomy, because it's not clear how he would answer the question, “Are there numbers, and if so, what are they?”