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

Cultural relativism is supposed to be a bold and provocative thesis. In this paper wechallenge the idea that it is an empirical thesis, i.e., one that is supported throughanthropological and historical examples. We focus on mathematical relativism, theview that a mathematics from another culture or time might be so radically divergentfrom our mathematics that ‘theirs’ would stand in direct conflict with ‘ours’ (and inthat sense constitute an alternative mathematics).We question in what sense the examples given to support the general thesis arerelativistic about mathematics and argue that on close inspection they are not, andcertainly not in any radical sense. We do not contest the fact that there can be greatmathematical 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.