Nicolo Machiavelli in his oft-followed and imitated work The Prince, stated that there were three classes of intellects. Using those three classes we can tell what kind of thinker a person is and in using that we can come to an understanding of whether the person speaking or writing is worth listening to.
The Three Classes of Intellects are:
"One which comprehends by itself.
The other appreciates, what another comprehends.
And the last doesn't comprehend by itself nor by the showing of others."
The first is said to be the best and rightfully so. If one can truly read or listen and understand without further explanation should he not be considered an intellectual? Now I believe that in order to fully understand many ideas such deep theories stemming from the scientific, mathematic or otherwise, it requires much study and much explanation. So then this first class is not saying that one has to pick up on an ideology or theory and understand it with perfection in a short time but that one dedicates themselves to understanding it on their own to the point where they can comprehend the concept on their own because they are familiar with it.
One such example of this first class would be a college professor. A professor that lectures on a topic, has done the necessary research on the topic, they have become fluid on the topic, the have mastered it. Now there are "student-professors" meaning professors who don't have the paper diploma necessary to prove their mastery but if they are given an opportunity to teach then surely they have some mastery over the information.
The first class, as far as I am concerned, is the most interesting. The reason being it is the class that all people strive, it is their plan to master a position, a craft and be considered a leader in that field. That term, "leader" is exactly what Machiavelli is writing about. He is writing a manual on leadership and what an effective leader needs. Surely an effective leader needs to be able to comprehend situations and make the best decisions possible on their own. They need to have an intellect on a higher plane so than those they lead or they cannot truly call themselves a leader. A leader that has mastery over information and can understand and problem-solve on their own will eventually gain the favor of many followers, in the same way all the good professors have full classes.
The second class is considered by Machiavelli to be only "good". I consider it a useful skill. Knowing that you cannot fully comprehend a situation or understand a problem is useful because it doesn't create a false sense of self. This is one thing people do all the time as well. We quote people (as I am doing with Machiavelli) because we understand that they know more than we do. We come to grips with our own limitations but we know who does have the knowledge that is needed to solve this problem.
Have you ever encountered an issue and needed to ask someone else for clarification? Of course you have and there is intelligence in not knowing how to solve an issue because you do know who to turn to.
I liken this class to being an understudy or a tutor to keep with the academic theme. A tutor has some of the answers and can help a lot if your low on understanding but they know their weaknesses. If an issue arises where they become perplexed they know where to go (and I don't mean simply going to the professor) they could be familiar with a higher level writer or thinker they can look to for advice or clarification. Remember many tutors are still students themselves but they have the experience to point you in the right direction. A tutor or an understudy definitely appreciates one who has mastery on a subject.
Going back to Machiavelli's book which, like I mentioned before, is on leadership, leaders also need to have an understanding of their own limitations. A leader needs to have full control over their flaws as they do their strengths, it is a requirement. If you have followers or employees that need to understand when they are over their heads on an issue and need to contact someone with more experience, you should be able to do that as well. So Machiavelli is perhaps saying that there is strength in understanding your own weaknesses.
The last class of intellect is said to be "useless" by Machiavelli and I fully agree. These are possibly the stubborn, prideful folks who know they don't have the knowledge but refuse to seek someone who does out of their own selfishness but it is not just those people.
As the class is written it looks to say that it is a person that cannot grasp the answers on their own or with the help of others. And that is somewhat true, "by the showing of others" is saying that they have been shown, the answers have been explained yet they still cannot grasp it. This happens a lot too. In academia we all face a course where no matter how simplistic it is, no matter the tutors, the amount of time studying we just don't get it (for me it was Geology..ugh).
What do you do then? While you have noticed your own weakness and have asked for help and after the help you still don't understand frustration usually kicks in. The more frustrated you become the more you would want to quit and just do something else. However I would say, that if you don't quit and you keep trying then you don't belong in this class after all. Think about it you are able to appreciate what another knows still, even if you still can't comprehend it yourself.
I have discussed here Machiavelli's three classes of intellects as written in his book The Prince. The first class, the "excellent" class are of masters and strong leaders who have the knowledge and problem-solving skills within themselves necessary to be effective. The second class, the "good/useful" class are the ones who may not hold full mastery but have a good handle on it and know where to find helpful information when the problem is beyond their skill set. The final, "useless", class are a mixture of the stubborn, selfish and the somewhat hapless. They can't get it. No matter how many times they try they can't get a handle on it. However by continuously trying they perhaps can jump to the second class.
Of course all these classes would vary depending on the field. The aforementioned professor is a master of his field, not all fields. A tutor may only be useful for a particular course. So perhaps in reality we are all apart of all three classes at some point in time because we are fallible and we can't possibly know everything, even those with high levels of knowledge (mastery) can't know it all. But when it comes to the concept of leadership the first two classes are the best and that's what Machiavelli was putting out there.