 Another problem with physicalistic views along the lines of Mill's is that they seem incapable of accounting for the sheer size of the infinities involved in set theory. Standard set theory entails not just that there are infinitely large sets, but that there are infinitely many sizes of infinity, which get larger and larger with no end, and that there actually exist sets of all of these different sizes of infinity. There is simply no plausible way to take this theory to be about physical stuff.