Comments on “Aspects of reasonableness”
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Some thoughtful reccomendations
Still enjoying your writing. Nice!
I think there are a couple of things worth reccomending, that would interest you, considering the work you are currently doing. If you have a couple of minutes - probably worth your time.
Catafalque, by Peter Kingsley
Catafalque would be a great book for you to read that would probably deeply interest you in particular.
That reasonable/rational/meta-rational table reminds me of Terence Tao’s pre-rigorous/rigorous/post-rigorous progression in learning mathematics, which shows up in many other domains as well. (And which could be a way of characterizing the K3/K4/K5 progression as well.)
It is of course vitally important that you know how to think rigorously, as this gives you the discipline to avoid many common errors and purge many misconceptions. Unfortunately, this has the unintended consequence that “fuzzier” or “intuitive” thinking (such as heuristic reasoning, judicious extrapolation from examples, or analogies with other contexts such as physics) gets deprecated as “non-rigorous”. All too often, one ends up discarding one’s initial intuition and is only able to process mathematics at a formal level, thus getting stalled at the second stage of one’s mathematical education. (Among other things, this can impact one’s ability to read mathematical papers; an overly literal mindset can lead to “compilation errors” when one encounters even a single typo or ambiguity in such a paper.)
The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Without one or the other, you will spend a lot of time blundering around in the dark (which can be instructive, but is highly inefficient). So once you are fully comfortable with rigorous mathematical thinking, you should revisit your intuitions on the subject and use your new thinking skills to test and refine these intuitions rather than discard them.
Alignment with Kegan stages?
How well does reasonable, rational, meta-rational align with the Kegan stages? For example, could stages 0-2 align with the development of reasonableness, 3-4 (i.e. formal operations) of rationality, and 5 of meta-rationality? Stage 3 would perhaps be the less systematic precursors to stage 4’s systematic rationality.