The Mind- Body Problem is a meta-physical argument concerning the intellect and how that relates to the body. In short, it asks the following question
Is there an immaterial soul (for lack of a better term) that gives credence to our unique ability of conceptual thought?
There are two different sides to this argument of course, the side of dualism and the side of monism.
Dualism says to the question I postulated above, "Yes, there must be an immaterial soul or something alone those lines that allows us conceptual thought. Though, this soul must be dependent on the brain, but the brain itself cannot conceptually think."
Monism says, "No. Our brain is enough to conceptually think."
Dualism
I had written a post a while back in a thread concerning reality about Descartes' view on this argument, here's a quote of that post.
Rene Descartes invented a new way of learning, called methodological skepticism. He literally threw out every single piece of knowledge that came before him, and started from scratch. He doubted everything that he could not be sure of. There were only a few facts that Descartes could not doubt:
Statements such as "There is no such thing as a round square"
"Cogito ergo sum", latin for "I think therefore I am."
Probably a few other things which I cba to read up on again.
This is not a reality argument. This is a dualistic argument. He is giving credence to the existence of another self, a soul. He was able to doubt the existence of the world and of his body because we only experience those two things with our senses, which are fallible. He went on to say that everything one thought they knew were just various levels of belief, none of which can be said with actual truth as you can with the facts I listed.
This argument was touched upon by Plato and Aristotle, and then made modern by Rene Descartes.
Plato and Aristotle used the argument concerning universals and particulars, as opposed to Descartes' Cogito Ergo Sum. In a nutshell, they said that ideas are universal, while the material world is only particular. By universal, I mean there is an essence to an object that makes that object, well, that object.
For example, if you try to imagine a triangle, you can imagine a scalene triangle, an equilateral triangle, a blue triangle, an obtuse triangle, or a red triangle. These are all particular types of triangles. This means that the concept (note: conceptual thought being demonstrated) of a triangle is universal, capable of being imagined as so many particular things that the concept itself cannot be a particular thing.
Our ability of conceptual thought as being demonstrated above shows us that our intellect is capable of dealing with said universal concepts, but that our imagination is not, because imagination derives from memory, and memory is all particular. We can then go on to say that as we have studied our brains, it is an organ of memory, perception, and imagination; but not of conceptual thought. You may ask that imagination would create conceptual thoughts, but we can only imagine particular thoughts, as I said above. We can't imagine triangle as such, we need to imagine a scalene... etc particular type of triangle.
Thomas Aquinas said that the brain and mind are like a rower and a rowboat. The rower works in accord with his rowboat, but the two do not necessarily require each other to work.
Mortimer J Adler stated that the mind requires the brain, but the brain cannot conceptually think on its own; in the same way that an eye cannot see on its own.
Personally, I am a subscriber to dualism. I do indeed think that the brain is only capable of perception, imagination, and memorization. I feel that if monism is true, neurology and psychology would be one and the same. If we could not use universals, then we wouldn't be able to use common nouns. When we talk about a triangle, we refer to anything to which the name triangle is capable of applying to. Triangle is thus a common noun and a universal. When we say triangle A, we talk about a particular triangle we have labeled with the letter A.
Monism
To counter the argument of universals, David Hume stepped forth. He invented Bundle Theory. He stated that when something is thought about without its particular qualities, it ceases to exist. Here was his famous thought experiment:
Try to think of a triangle without any of its particular qualities. Try not think of the triangle as having any size, any color, or any measures. You will then realize that you cannot because universals do not exist.
That leads us to the Monist's argument about universals in general. They do not exist. Common nouns and so called universals are only so because we assign particular qualities to them.
A Duelist's reply to this is that we cannot comprehend universals as such, just as we cannot comprehend triangles as such without properties, but we use triangles as such to name the three-sided, three-angled conceptual objects we have invented. We can't imagine universals. That's the point.
As for Aquinas' argument, there is one objection which I think nullifies it. When someone suffer's brain damage, the mind should be able to per se, swim away. If a row boat is damaged, the rower is able to swim away.
So, that's really all I've to say about it right now. Feel free to reply and rebut.