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so you're saying that any math that can't be used to build stuff is invalid?
I think it becomes more like any other language in that case: it conveys information but doesn't necessarily correspond to anything in the world or have ontological significance for the world we actually live in. Modal logic is sort of like this: it's a sieve for intuitions.
then I guess I'm not exactly sure what your original point was? All math is valid, just some math is useful for building things, but the math that is useful for building things is not social?
Maybe all math is valid but only some math is sound
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