Mason  🏃‍♂️ ✂️

For my part (being non-mathsy), David Deutsch has gotten me interested in Popper & I like Popper's take (what we call math can be logical *or* descriptive claims). A layer up, I think relabeling "useful math conventions" as "social constructs" isn't helpful for understanding them

You can go another layer up and talk about whether any society (necessarily biased & systemically ignorant, as they all are) that funds maths research for its own purposes will output distorted math. I'm certain this does output some amount of bad work and less useful conventions

I'm not a mathematician and have low confidence in all of these positions, and tbh at each layer I don't think "Is this socially constructed?" is a particularly useful question — though I think it's a more useful question at the top of the stack (re: institutions).

But I wouldn't bemoan anyone asking or answering it at any layer **as long as they're clear about the layer they're working on.** When Matt relies on a "philosophy of math" motte & then follows up by tweeting about trans athletes, I feel very https://twitter.com/mattyglesias/status/1126228807273336833 …

Why is that? I don't see the Motte and Bailey here. Both are socially constructed, neither of which confers a moral value on the construction. Indeed, in the case of both gender and math, it invites criticism that long held beliefs that are held to be may not be true

Math and gender are frameworks on entirely different layers. Even "sex" isn't near the layer where ground truths in math reside, bc despite being highly bimodal, phenotype + genotype do not consistently cut cleanly. If you think logic behaves similarly, I do think you're confused

Mathematics has become vastly more rigorous over the past century, but perhaps this is where your "not being a mathematician" weakness is showing? What form of logic are you talking about? Which topos? Which set of axioms do you adopt?

Possibly, I really can't claim a lot of content knowledge re: maths. But I don't think that a field becoming more rigorous over time indicates that the content it has always concerned itself with is itself socially constructed (if that's what you're suggesting)