which seem like sensible English descriptions if for some bizarre reason you can't use the shorter names
The motivation of Kahnmann to use system I and system II isn't to have shorter names. It's that there are existing conceptions among people about words describing mental concepts and he doesn't want to use them.
Wikipedia list from Kahnmann:
In the book's first section, Kahneman describes two different ways the brain forms thoughts:
System 1: Fast, automatic, frequent, emotional, stereotypic, subconscious
System 2: Slow, effortful, infrequent, logical, calculating, conscious
Emotional/logical is a different distinction then intentional/autopilot. Trained people can shut on and off emotions via their intentions and the process has little to do with being logical or calculating.
But even given them new names that scientists don't give them might be a valid move. If you how even do that then you should be open about the fact that you invented new names. Given science public nature I also think that you should be open about why you choose certain terms and choosing new terms should come with an explanation of why you prefer them over alternatives.
The reason shouldn't be that your organisation is named "intentional insights" and that's why you call it the "intentional system". Again that pattern leads to the rationality is about using system II instead of system I position with differ from the CFAR position.
In Gleb's own summary of Thinking Fast and slow he writes:
System 1 runs automatically and System 2 is normally in a comfortable low-effort mode, in which only a fraction of its capacity is engaged. System 1 continuously generates suggestions for System 2: impressions, intuitions, intentions, and feelings.
Given that in Kahnmann's framework intentions are generated by system I, calling system II the "intentional system" produces problems.
What is your credence for the explanation you give,
Explanations don't have credence, predictions do. If you specify a prediction I can give you my credence for it.
What is your opinion on rationality-promoting articles by Gleb Tsipursky / Intentional Insights? Here is what I think:
Trying to teach someone to think rationally is a long process -- maybe even impossible for some people. It's about explaining many biases that people do naturally, demonstrating the futility of "mysterious answers" on gut level; while the student needs the desire to become stronger, the humility of admitting "I don't know" together with the courage to give a probabilistic answer anyway; resisting the temptation to use the new skills to cleverly shoot themselves in the foot, keeping the focus on the "nameless virtue" instead of signalling (even towards the fellow rationalists). It is a LW lesson that being a half-rationalist can hurt you, and being a 3/4-rationalist can fuck you up horribly. And the online clickbait articles seem like one of the worst choices for a medium to teach rationality. (The only worse choice that comes to my mind would be Twitter.)
On the other hand, imagine that you have a magical button, and if you press it, all not-sufficiently-correct-by-LW-standards mentions of rationality (or logic, or science) would disappear from the world. Not to be replaced by something more lesswrongish, but simply by anything else that usually appears in the given medium. Would pressing that button make the world a more sane place? What would have happened if someone had pressed that button hundred years ago? In other words, I'm trying to avoid the "nirvana fallacy" -- I am not asking whether those articles are the perfect vehicle for x-rationality, but rather, whether they are a net benefit or a net harm. Because if they are a net benefit, then it's better having them, isn't it?
Assuming that the articles are not merely ignored (where "ignoring" includes "thousands of people with microscopic attention spans read them and then forget them immediately), the obvious failure mode is people getting wrong ideas, or adopting "rationality" as an attire. Is it really that wrong? Aren't people already having absurdly wrong ideas about rationality? Remember all the "straw Vulcans" produced by the movie industry; Terminator, The Big Bang Theory... Rationality already is associated with being a sociopathic villain, or a pathetic nerd. This is where we are now; and the "rationality" clickbait, however sketchy, cannot make it worse. Actually, it can make a few people interested to learn more. At least, it can show people that there is more than one possible meaning of the word.
To me it seems that Gleb is picking the low-hanging fruit that most rationalists wouldn't even touch for... let's admit it... status reasons. He talks to the outgroup, using the language of the outgroup. But if we look at the larger picture, that specific outgroup (people who procrastinate by reading clickbaity self-improvement articles) actually aren't that different from us. They may actually be our nearest neighbors in the human intellectual space. So what some of us (including myself) feel here is the uncanny valley. Looking at someone so similar to ourselves, and yet so dramatically different in some small details which matter to us strongly, that it feels creepy.
Yes, this whole idea of marketing rationality feels wrong. Marketing is like almost the very opposite of epistemic rationality ("the bottom line" et cetera). On the other hand, any attempt to bring rationality to the masses will inevitably bring some distortion; which hopefully can be fixed later when we already have their attention. So why not accept the imperfection of the world, and just do what we can.
As a sidenote, I don't believe we are at risk of having an "Eternal September" on LessWrong (more than we already have). More people interested in rationality (or "rationality") will also mean more places to debate it; not everyone will come here. People have their own blogs, social network accounts, et cetera. If rationality becomes the cool thing, they will prefer to debate it with their friends.
EDIT: See this comment for Gleb's description of his goals.