Comments on “Aspects of reasonableness”
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Stages of development of rationality
Yes, you’ve got that pretty much right! I’m taking 3=reasonable, 4=rational, 5=meta-rational. Kegan stage 3 isn’t capable of dealing with complex formal systems.
In Piagetian terms, pretty much all rich-country teens have achieved his “formal operations,” but the Neo-Piagetian adult cognitive development researchers have consistently found that this is inadequate to actually think rationally in the sense of “systematic, formal, technical rationality.” Only about a third of American adults are capable of that. (As is pretty obvious if you look at unfiltered twitter, which is mostly stage 3.) William Perry’s work founded this lineage of research, which has been done mostly at the Harvard Ed School, including by Kegan.
Part III will tell a story about the gradual development of this formal rationality during ages roughly 15-30, because I find that understanding how you get to be more rational helps understand what rationality is and how it works.
To the extent possible, I want to base this on empirical studies of how people learn college-level STEM. Unfortunately, in my literature search so far, startlingly little research seems to have been done on that. You’d think universities (and the people who fund them) would want to know… Or, maybe, to be more cynical, maybe it’s unsurprising, because they don’t want to know!
Some thoughtful reccomendations
Hi David,
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.
Take care,
Will
That reasonable/rational/meta
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.
Pre-rigorous/rigorous/post-rigorous
Yes, very relevant, and I had already intended to discuss this in Part Three!
My recollection is that Tao explicitly cites cognitive-developmental stage theory as the inspiration for this.
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.