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
yeah, I suspect that for many students who find they're "no good at" a subject (even when they're good at other similarly difficult subjects), it's because they can't catch on to the pattern of which things that discipline includes in its models and which are "irrelevant details"
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Replying to @s_r_constantin @Meaningness
I managed to "get" which steps in a proof are supposed to be "obvious" and which need to be worked out explicitly. But I never managed to figure out what parts of a hypothetical physical situation go into the diagram & physics equations and which "we can neglect".
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Replying to @s_r_constantin @Meaningness
"Where do the assumptions of Econ 101 come from, and to what extent are they realistic?" is an *advanced* econ question; if you get hung up on doubting axioms before your teachers are willing to discuss them, you will not do well in economics classes
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"what counts as a valid argument for the purpose of academic philosophy" is just...not a fun question to ask at all, is it.
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