Rationalism/empiricism is one possible stage 4 structure.
Working scientists mostly don’t understand the math. But that’s less of a problem than not understanding how the math relates to reality, imo.
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This article is not ideal, but it lists many common misconceptions about how (frequentist) stats relate to reality. These aren’t math misunderstandings, they are real-world interpretation misunderstandings. https://link.springer.com/article/10.1007/s10654-016-0149-3 …
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There are corresponding (fatal) misunderstandings about how Bayesian methods relate to reality.
End of conversation
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