Mathematical relativism: logic, grammar, and arithmetic in cultural comparison

Cultural relativism is supposed to be a bold and provocative thesis. In this paper we challenge the idea that it is an empirical thesis, i.e., one that is supported through anthropological and historical examples. We focus on mathematical relativism, the view that a mathematics from another culture or time might be so radically divergent from our mathematics that ‘theirs’ would stand in direct conflict with ‘ours’ (and in that sense constitute an alternative mathematics). We question in what sense the examples given to support the general thesis are relativistic about mathematics and argue that on close inspection they are not, and certainly not in any radical sense. We do not contest the fact that there can be great mathematical diversity between cultures, but wonder whether it makes sense to talk of ‘the same’ mathematical forms in heterogeneous mathematical environments. Finally, while relativists see the later Wittgenstein as providing support for their own thesis, we claim that Wittgenstein argues against both realism and relativism.