A lot of the questions you pose, including the definition of the Level 2 formalism, are addressed in the article I linked (and wrote).
I classify those who can do something well but not explain or understand the connections from the inputs and outputs to the rest of the world, to be at a Level 1 understanding. It's certainly an accomplishment, but I agree with you that it's missing something: the ability to recognize where it fits in with the rest of reality (Level 2) and the command of a reliable truth-detecting procedure that can "repair" gaps in knowledge as they arise (Level 3).
"Level 1 savants" are certainly doing something very well, but that something is not a deep understanding. Rather, they are in the position of a computer that can transform inputs into the right outputs, but do nothing more with them. Or a cat, which can fall from great heights without injury, but not know why its method works.
(Yes, this comment seems a bit internally repetitive.)
Ah, OK, I read your article. I think that's an admirable task to try to classify or identify the levels of understanding. However, I'm not sure I am convinced by your categorization. It seems to me that many of these "Level 1 savants" as you call them are quite capable of fitting their understanding with the rest of reality. Actually it seems like the claim of "Level 1 understanding" basically trivializes that understanding. Yet many of these people who are bad teachers have a very nontrivial understanding -- else I don't think this wou...
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