AnnaSalamon comments on Raising the Sanity Waterline - Less Wrong
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It seems to me that the principal issue is that, even if you know all those things... that doesn't guarantee that you're actually applying them to your own beliefs or thought processes. There is no "view source" button for the brain, nor even a way to get a stack trace of how you arrived at a particular conclusion... and even if there were, most of us, most of the time, would not push the button or look at the trace, if we were happy with our existing/expected results.
In addition, most people are astonishingly bad at reasoning from the general to the specific... which means that if you don't mention religion explicitly in your hypothetical course, very few people will actually apply the skills in a religious context... especially if that part of their life is working out just fine, from their point of view.
It may be fictional evidence, but I think S.P. Somtow's idea that "The breaking of joy is the beginning of wisdom" has some applicability here... as even highly-motivated individuals have trouble learning to see their beliefs, as beliefs -- and therefore subject to the skills of rationality.
That is, if you think something is part of the territory, you're not going to apply something you think of as map-reading skills.
Hm, in fact, here's an interesting example. One of my students in the Mind Hackers' Guild just posted to our forum, complaining that by eliminating all his negative motivation regarding work, he now had no positive motivation either. But it was not apparent to him that the very fact he considered this a problem, was also an example of negative motivation.
That's because even though I teach people that ALL negative motivation is counterproductive for achieving long-term, directional goals (as opposed to very short-term or avoidance goals), people still assume that "negative motivation" means "motivations I don't like, or already know are irrational"... and so they make exceptions for all the things they think are "just the way it is". (Like in this man's case, an irrational fear linked to his need to "pay the bills".)
And this happens routinely with people, no matter how explicitly and repeatedly I state that, "no, you have to include those too". It seems like people still have to go through the process at least once or twice with someone pointing one of these out, before they "get it" that those other motivations also "count".
Heck, truth be told, I still sometimes take a while to find what hidden assumption in my thinking is leading to interference... even at times when I'd happily push the "view source" button or look at the stack trace... if only that were possible.
But since I routinely and trivially notice these map-territory confusions when my students do them, even without a view-source button -- heck, I can spot them from just a few words in the middle of their forum posts! -- I have to conclude that there is something innate at issue, besides me just not being a good enough teacher. After all, if I can spot these things in them, but not me, there must be some sort of bias at work.
I suspect you are right; the issue isn't that these people haven't "learned" relevant abstractions or tools. They just don't have enough incentives to apply those tools in these context. I'm not sure you "teach" incentives, so I'm not sure there is anything you can teach which will achieve the goal stated. So I'd ask the question: how can we give people incentives to apply their tools to cases like religion?
I'd say there're two problems: one is incentives, as you say; the other is making "apply these tools to your own beliefs" a natural affordance for people -- something that just springs to mind as a possibility, the way drinking a glass of liquid springs to mind on seeing it (even when you're not thirsty, or when the glass contains laundry detergent).
Regarding incentives: good question. If rationality does make peoples' lives better, but it makes their lives better in ways that aren't obvious in prospect, we may be able to "teach" incentives by making the potential benefits of rationality more obvious to the person's "near"-thinking system, so that the potential benefits can actually pull their behavior. (Humans are bad enough at getting to the gym, switching to more satisfying jobs in cases where this requires a bit of initial effort, etc., that peoples' lack of acted-on motivation to apply rationality to religion does not strongly imply a lack of inventives to do so.)
Regarding building a "try this on your own beliefs" affordance (so that The Bottom Line or other techniques just naturally spring to mind): Cognitive-Behavioral Therapy people explicitly teach the "now apply this method to your own beliefs, as they come up" steps, and then have people practice those steps as homework. We should do this with rationality as well (even in Eliezer's scenario where we skip mention of religion). The evidence for CBT's effectiveness is fairly good AFAICT; it's worth studying their teaching techniques.