 There are numerous problems with physicalistic views of mathematics. To mention just one of these problems, physicalism seems completely incapable of accounting for various kinds of claims about infinities that we find in mathematics. For instance, it is a theorem of set theory that there are infinitely many transfinite cardinal numbers that keep getting bigger and bigger without end. Thus, set theory is committed to the existence of infinite sets that are so huge that they simply dwarf garden variety infinite sets, like the set of all the natural numbers. There is just no plausible way to interpret this talk of gigantic infinite sets as being about physical objects.