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Annoyance comments on The Least Convenient Possible World - Less Wrong
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Euclidean geometry isn't a theory about the world, and therefore cannot be falsified by evidence from the world. The primitives (e.g. "line" and "point") do not have unambiguous referents in the world.
You can associate real-world things (e.g. patterns of graphite, or wooden rods) to those primitives, and to the extent that they satisfy the axioms, they will also satisfy the conclusions.
Math is not physics.
"Math is not physics."
It's made out of physics. I think perhaps you mean that math isn't about physics.
To the degree that axioms aren't being used to talk about potential worlds, I would say that they're meaningless.