I think the role of mathematics in various culture war arguments is regrettable. It often seems to me that team SJ are treated as peddling the most absurd and laughable relativistic position for suggesting that there could be cultural difference in theorems (2+2=4 often used)...
... whereas I think this is a perfectly comprehensible position and would be fascinating to think about. For instance, it seems to me a total contingency, something actually true but which evidently could have been otherwise, that we never encountered the following situation...
... Three civilisations developed mathematics to a high level in relative isolation from one another. One of them developed constructive mathematics, one of them developed classical mathematics, and the other actually developed a dialethic mathematics based on naive set theory...
... when commerce between them starts their mathematicians find they disagree re theorems. Perhaps nothing so immediate as 2+2, but still disagreements arise. Indeed imagine differences in approach to mathematics correspond to moral or religious differences and are felt keenly...
... it doesn't seem in this scenario we'd do well to dismiss any one involved as irrationalists who hate Truth or whatever. In this scenario the mathematical disagreements are susceptible of further study and fruitful dialogue, and maybe even a higher unity may be achieved...
... Now this is not a realistic case. This is not the sort of inter-cultural mathematical disagreement we have observed. I draw attention to it partly because there's actual disagreement over theorems, which is what is always suggested as the absurd possibility...
... and partly because such disagreements did arise within actual professional logic or mathematics, and while they could get rancorous at times, in the end far from leading to the downfall of the enterprise they were constructive and mutually enlightening. As to more realism...
... it seems that where there's been cultural difference in mathematics it has often related to units of measurement or number base (people sometimes take paraconsistency as an India::rest of the world cultural difference, but are forgetting that syllogistic is paraconsistent)...
... so it's around such differences that more SJ-ish pieces on mathematics build their case. See, for instance, the linked paper which I recently enjoyed reading...
journals.sagepub.com/doi/abs/10.117…
journals.sagepub.com/doi/abs/10.117…
... (side note: one sees such mathematical claims, and sometimes inter-cultural logical pluralism claims. But I have never seen anyone argue that different cultures made different decisions at Lakatosian choice points as discussed in Proofs & Refutations. Worth exploring!)...
... but I think this, if anything, strengthens the point about potential cooperation here. There's not even purported substantial disagreement about theorems at stake here! It's instead focussed on the representation of mathematical facts and the way in which focus is directed...
... surely these are matters that we can discuss in a reasonable manner? Just dismissing this misses out on fascinating opportunities to learn. Don't let the culture war rob you of your curiosity or of the true cosmopolitan heritage of our mathematical culture in all its variety.
