Because we may be unaware of our ignorance we may feel very confident of our untrue beliefs. The confidence we feel about the truth of our beliefs is a rather unreliable indicator of their truthfulness. When we have no other means of determining the validity of our beliefs than our own subjective confidence that they are true, we may become arrogant while we are also ignorant.
Some psychological mechanisms may keep us trapped in the arrogant-yet-ignorant box. One is the Dunning-Kruger effect which is that ignorant or incompetent people do not, and cannot know to some extent, know how ignorant or incompetent they are. To be able to know how knowledgeable/ competent you are at something you need to have some knowledge about that competence domain. People who know very little about a topic do not realize how much there is to know about that topic and therefore how much knowledge they lack.
There are other factors which may keeps us trapped in box 1. One example of such a factor is that many people are brought up with certain beliefs about reality, such as religious beliefs, which they are thought to never question. These beliefs may become so attached to one's identity and one's sense of security that any questioning of criticizing of them may feel very threatening. Someone I spoke to several years ago was brought up religiously. This person, roughly of my age, had picked up an academic study which he had now been doing for several years. He worked hard and enjoyed it a lot, at least it had seemed that way. Now he told me that, while he had enjoyed studying a lot, he was intending to stop. I asked why and he responded that learning all these things had raised many questions in his head. He was afraid that further studying would raise even more questions and that he might gradually start to lose his religious beliefs. He was very scared of what that might lead to fearing he might lose his sense of meaning and his moarality.
Tying one's beliefs to one's identity and being taught that some beliefs may never be questioned are two things which can keep you trapped in box 1 (or 2).
I would propose that, in the 2x2 model described above, the least sophisticated and desirable box for someone to be in is box 1, arrogant-yet-ignorant and the most sophisticated and desirable is box 3. Box 3 seems to be more desirable than box 1 not only for oneself but also for other people. As human civilization has progressed, we have begun to wonder and to ask questions about the world which was a sign of us becoming more aware of our own ignorance and more modest. Then, as the tools and methods of the scientific approach, bit by bit began to become more available to us, we also systematically began to build more knowledge about the world (two great books about this gradual development of science are To explain the world and The upright thinkers).
In the same way as humanity as a whole seems to be doing, we can also, as individuals develop both modesty and knowledge. As we develop knowledge, it seems wise to avoid falling into box 4. Is that a realistic challenge? Can 'great minds' remain modest? It certainly seems to. Some of the most educated and sophisticated people in history seem to have done exactly this. Some quotes mentioned in this post illustrate this.The most probable explanation for this can be found, again, in the Dunning-Kruger effect. As one gathers more knowledge, one also becomes more aware of the vastness of what there further is to know. In other words, of one's own ignorance.
At the same time, it is also true that, with respect to certrain topics, you can never be sure that you yourself are not also in box 1. An extra reason to try to remain modest.
When a person in a box 1 state of mind meets a person with a box 3 state of mind meet, something paradoxical may happen. While box 3 people are more knowledgeable they act more modestly while box 1 people are less knowledgeable yet more confident. Also, box 1 people are unlikely to be appreciative of the greater knowledge of box 3 people (because of the Dunning-Kruger effect). Recent research suggests that, in collaborations, more competent people tend to to go along with the confident ignorance of less competent partners by giving judgments of these less knowledgeable people equal weight (this is called equality bias).
When dealing with people who are in a box 1 state of mind, direct and confrontational approaches may backfire. When people feel their cherished beliefs, about which they so confident, are criticized they may become even less open minded and the strength of their (misplaced) belief may even become stronger.
While I am not sure what works best to help people escape box 1, I do have some hunches, which I will share. Strategies that may work better than confrontational methods are more subtle. Creating a conversational context which seems safe is a good beginning. Listening and asking questions are good way to proceed. Next, providing information and sharing one's own views, is good way to continue. Being clear about the other person's right to either question of hold on to his or her beliefs may also be a prerequisite for a fruitful conversation.
What do you think?