If a domain as well-established as mathematics can span multiple ontological categories, then spanning multiple categories is not a mark against pluralism about that domain.

There is an obvious rebuttal on behalf of pluralism, namely that “the linguistic” is a complex phenomenon with parts that belong to distinct ontological categories. This shouldn’t surprise, since even “the mathematical” is like this: Two wholly physical dogs plus two other wholly physical dogs yields four dogs; there certainly is the mental operation of multiplying 26 by 84, the mental state of thinking about the square root of 7, and so on. (2014: 5)