  Other apparent problems for reductionist ontological naturalism include the problem of arbitrariness and the fact that it goes profoundly against mathematical method. Suppose arithmetic is the study of some particular spatiotemporal entities. Very well; but which ones? Surely it is arbitrary which spatiotemporal entity is chosen as the number zero. This criticism is a version of a general anti-reductionist argument presented in Benacerraf (1965). The response to it is usually that reductionism does not seek to uncover the meaning of number terms but instead proposes a theoretical identification (Paseau 2009).  The charge of contradicting mathematical method is a serious one too. If mathematical objects are spatiotemporal, why do mathematicians not perform experiments to discover their properties? If mathematics were genuinely concerned with the spatiotemporal, surely its methodology would be more empirical.