Can I understand how your mind works? The object of cognition, although of the same kind, isn't the same thing as the instrument of cognition (my mind isn't your mind).

... we employ the same mind as the subject of cognition as well. (The MIND tries to understand how the mind works). — Dmitri

This is a misplaced concreteness (i.e. reification) fallacy. "The mind" is only a concept. We use our minds in order to attain some understanding of the 'concept of mind' (which can be elaborated from a conjecture (from experimental observation of others AND their reports of the subjectivity of cognition) into an explanatory model, that, if it survives falsifying tests, is then accepted as a scientific (rather than merely intuitive) 'theory of mind'). The argument fails on this account alone.

I mean 'the human mind' and this should be obvious. I don't dig as deep as 'the concept of mind', which would be too much for me.

In this instance, the human mind that you are thinking about is a concept itself.
You are reflecting on a concept, in my opinion, it just so happens to be your mind.

Can you think about one of your thoughts? Can you use your own body to move your own body? Seems easy. Why? Because these things -- your mind, your thoughts, your body -- are not undifferentiated atomic objects. You can use parts of them of them on other parts of them. You can use your current state of mind to think about what was your state of mind a minute ago, much like you can use your leg muscles to lift your foot. If you couldn't think about other parts/states of your mind, you couldn't be said to have self-awareness -- you'd be some lower animal only able to react to experience without reflection.

And you can also use your mind to ponder a generalized notion of "the human mind" by abstracting from your own experiences. First you abstract from your current mind to a generalized concept of your mind as it generally is across time, and then outward from that to the things all human minds in general seem to have in common. That gets you into the whole other problem of how we know whether other minds exist and dualism vs. monism, and issues of conveying internal states with language, of course.

The question that I have is: what do you mean by ‘understand’? As a human, I can have some understanding about how my brain works. Cognitive science has come a long way in figuring out how people perceive and think. Psychology and sociology comes up with some pretty good rules that can predict how a person will likely act in a given situation. So, yes, I think a human can ‘understand’ how a human mind works. At least to some level.

Well, Munchausen trilemma didn’t stop the search for truth even if it should have. If you cannot offer anything but a sophistical refutation of my argument, it means that epistemology (gnoseology) is pointless and ‘philosophy of mind’ is an oxymoron. Common, go ahead and refute me!

Argument: If we try to understand how the human mind works, it means that we have the mind as the object of cognition. However, we employ the same mind as the subject of cognition as well. (The MIND tries to understand how the mind works). Besides, we use the mind as the instrument of cognition while cognizing how the mind works. (No other instrument is available to us to perform this task.)
Conclusion: These dialectical conditions make it impossible for us to understand how the human mind works. — Dmitri

Your conclusion does not seem to follow from your Argument. You need to actually justify your conclusion and its connection to your argument. Why does it make it impossible?

I know it does't follow. In logical terms. But nothing valuable follows in logical terms, does it?

I don't how much sense this makes but I'm, in a sense, deeply disturbed by how dogs can't scratch every itch they experience. They mostly use their hind legs, sometimes their front paws, and their teeth to scratch but there are certain zones - directly over their spines close to their hind quarters , the area where the tail attaches to the body, inside their ears, and probably other places I can't think of right now - that are simply going to itch without any possibility of relief.

Primates, especially humans, are a different story. I remember my back itching so much one day and not being able to get the nails on my hand to the spot. I simply went to my sister's room and used one of her back-scratchers - you know those longish things with claws at the end. Another time, there were no back-scracthers near at hand so, I simply bent down, loosened my collar and asked a friend to scracth my itchy back.

To study and understand minds, does it require a cooperative effort (this is ongoing I believe) or do we need to design and build a specific tool for it (this I have no idea about)? Both perhaps?

If you think it is impossible to understand how the human mind works, you already have a concept of how it works. If you believe that something is impossible to be true, that is already true. If you only know that you know nothing, you already know something...

There are more irrefutable things in this world. For example, marriage is the only known physical case in which two bodies that no longer attract each other stay together. This is beyond your understanding until you are married. Fifteen days after the wedding, the party will be over. Einstein didn't see it coming either.

It depends what you mean by "mind"...

Certainly, if you mean the patterns of thought, they are observable by awareness... indeed, this awareness is the psyche. I would go so far as to suggest this is actually the very purpose of philosophy, to analyze the thought processes and see if they are valid.

If you mean something else, please clarify.