Let's start with a false statement from one of Gleb's articles:

Intuitively, we feel our mind to be a cohesive whole, and perceive ourselves as intentional and rational thinkers. Yet cognitive science research shows that in reality, the intentional part of our mind is like a little rider on top of a huge elephant of emotions and intuitions. This is why researchers frequently divide our mental processes into two different systems of dealing with information, the intentional system and the autopilot system.

What's false? Researchers don't use the terms "intentional system" and "autopilot system".

Why is that the problem? Aren't the terms near enough to system I and system II? A person who's interested might want to read additional literature on the subject. The fact that the terms Gleb invented don't match with the existing literature means that it's harder for a person to go from reading Gleb articles to reading higher level material.

If the person digs deeper they will sooner or later run into trouble. The might have a conversation with a genuine neuroscientist and talk about the "intentional system" and "autopilot system" and find that the neuroscientist hasn't heard of making the distinction in those terms. It might take a while till they understand that deception happened but it might hinder them from propressing.

I think talking about system I and system II in the way Gleb does raises the risk of readers coming a way with believing that reflective thinking is superior to intuitive thinking. It suggests that it's about using system II for important issues instead of focusing on aligning system I and system II with each other the way CFAR proposes. The stereotype of people who categorically prefer system II to system I is straw-vulcan's. Level 2 of rationality is not "being a straw-vulcan".

In the article on his website Gleb says:

The intentional system reflects our rational thinking, and centers around the prefrontal cortex, the part of the brain that evolved more recently.

That sounds to me like neurobabble. Kahnmann doesn't say that system II is about a specific part of the brain. Even if it would be completely true, having that knowledge doesn't help a person to be more rational. If you want to make a message as simple as possible you could drop that piece of information without any problem.

Why doesn't he drop it and make the article simpler? Because it helps with pushing an ideology. What other people in this thread called rationality as religion. The rationality that fills someone sense of belong to a group.

I don't see that people rationality get's raised in the process of that. That leads to the question of "what are the basics of rationality?"

I think the facebook group provides sometimes a good venue to understand what new people get wrong. Yesterday one person accused another of being a fake account. I asked the accuser for his credence but he replied that he can't give a probability for something like that. The accuser didn't thought in terms of Cromwell's rule. Making that step from thinking "you are a fake account" to having a mental category of "80% certainty: you are a fake account" is progress. No neuroscience is needed to make that progress.

Rationality for beginners could attempt to teach Cromwell's rule while keeping it as simple as possible. I'm even okay if the term Cromwell's rule doesn't appear. The article can have pretty pictures, but it shouldn't make any false claims.

I admit that "What are the basics of rationality?" isn't an easy question. This community often complicates things. Scott recently wrote what developmental milestones are you missing. That article list 4 milestones with one of them being Cromwell's rule (Scott doesn't name it).

In my current view of rationality other basics might be TAPs, noticing, tiny habits, "how not to be a straw-vulcan" and "have conversation with the goal of learning something new yourself, instead of having the goal of just effecting the other person".

A good way to searching for basics might also be to notice events where you yourself go: "Why doesn't this other person get how the world works, X is obvious to people at LW, why to I have to suffer from living in a world where people don't get X?". I don't think the answer to that question will be that people think that the prefrontal cortex is about system II thinking.