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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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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"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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My copy of that Ideal Mathematician essay has this Wittgenstein story at the start. "If a child does not respond to the suggestive gesture, it is separated from the others and treated as a lunatic."pic.twitter.com/lFMVTXqAux
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(the book is Tymoczko's 'New Directions in the Philosophy of Mathematics: An Anthology')
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