Mathematicians and scientists have vague folk theories of what math and science are that both are blurred ancestral memories of pre-WWII logical positivism.
These theories are totally wrong, but do little *direct* harm because they are mainly ignored in practice.
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Comfortable folk theories of technical work do harm by filling the space where a better understanding could go, making its absence invisible. “Yes of course we know how to do science! We are scientists!” But clearly you didn’t, because you go so much of it wrong.
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Some sciences are upgrading their understanding, which I am optimistic will lead to better science.https://meaningness.com/metablog/upgrade-your-cargo-cult …
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Does the folk theory of mathematics also cause trouble? Here I am less confident, because math rarely has replication crises. However, this paper suggests to me that more and better math might get done if it were upgraded: https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/XSbDWXhDpz
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"Of course we know how to do mathematics! We are mathematicians!" But there's good evidence you don't, and so you can't teach it clearly, and you can't reflect on whether you are doing it well or badly. https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/YsL16YdGVe
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Replying to @Meaningness
This essay is satirical. Many mathematicians can give quite reasonable discussions of the ambiguity of the term 'exist', most others just don't find the issue worth considering one way or another. Platonists/intuitionists/etc. are considered somewhat cranky.
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Replying to @St_Rev @Meaningness
I think in physics the analogous stance is called 'shut up and calculate'. Worry about that stuff (not challenge it, but take a stance at all) is for when you're old and your research days are mostly over.
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Yes and I would agree that philosophy of mathematics is a waste of time, because it doesn’t come to grips with the empirical phenomena at all. A quite different sort of theory that looks at what mathematicians actually do might be more useful
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