i wrote a mathoverflow answer about godel's incompleteness theorem and nonstandard models of arithmetic that believe arithmetic is inconsistent that some of you might be interested in:
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thinking about the incompleteness theorem is good mental exercise i think. forces you to get really clear about the difference between believing something and something being true 🤔
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it's very striking that the incompleteness theorem, relativity, and quantum mechanics all emerged in the same few decades around WWI and you have to wonder how much of that had to do with people losing faith in the universe making sense in a general sort of way
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Relevant Twitter thread: twitter.com/Meaningness/st and my Web log take: ansuz.sooke.bc.ca/entry/346
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If you are unfamiliar with the unsolved foundational crisis, my favorite account—informal, entertaining, eccentric: arxiv.org/html/nlin/0004