The idea that there is some "real" mathematical structure, and statements about other structures are nonsensical because "numbers don't work like that!"
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The people who, when shown something like the surreal numbers, exclaim "Wow! I can't believe numbers work like that!"
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Replying to @CurlOfGradient
What kind of evidence should we use to know which structures are real?
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Replying to @ObjectOfObjects
I was watching an interview with a model theorist about monads in the hyperreals, and the interviewer kept going “now hang on; there aren’t *really* all these infinitesimals hanging around every number, are there?” Hence my tweet.
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Replying to @CurlOfGradient @ObjectOfObjects
I think mathematics is about asserting a set of axioms and then seeing what facts are true about the resulting structure. We could ask whether there exists a physical system that mimics the structure, but that tells us more about our universe than the math.
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I suppose that makes me a formalist
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