What philosophers call the mind body problem originated with Descartes. In Descartes' philosophy the mind is essentially a thinking thing, while the body is essentially an extended thing - something which occupies space. Descartes held that there is two way causal interaction between these two quite different kinds of substances. So, the body effects the mind in perception, and the mind effects the body in action. But how is this possible? How can an unextended thing effect something in space. How can something in space effect and unextended thing?
Cartesian dualism, and the general problem of the relation of the mind to the body, is a subject which aroused considerable controversy as soon as Descartes' Meditations started to be circulated. There are really many issues here, and as a consequence focus is a particularly difficult problem. One place to start is to read the article on "The Mind Body Problem" in the Encyclopedia of Philosophy, editor, Paul Edwards. I offer a Philosophical Problem connected with this issue in the Descartes file.
Here are some possible ways to narrow the scope of your
paper should you wish to pursue this issue:
(a) Focus your attention on Descartes' arguments in the sixth Meditation for the real distinction between the mind and the body. Go to the Philosopher's Index and look for articles which focus on just those arguments. With a little research you will find problems aplenty to occupy you just with one or the other of these two arguments.
(b) Focus your attention on the problem of substances of different kinds causally interacting with one another. The issue in this sense might be put this way: Can the mind and the body causally interact with one another if the mind is not part of the physical system of the world?
Defenders of the view that the mind can interact with the body include, of course, Descartes himself, as well as the contemporary English philosopher C.D. Broad, in "The Traditional Problem of Body and Mind" in his book Mind and its Place in Nature. There is a reply to Broad by James Cornman "A Nonreductive Identity Thesis about Mind and Body" in J. Fineberg's Reason and Responsibility 4th ed. (see me for a copy).
An author who gives a fairly good overview of dualism and its problems, as well as alternative theories and their problems, is Jerome Shaffer, in Philosophy of Mind, Prentice Hall, 1968. Shaffer presents particular problems with dualism such as:
(c) The problem of individuating immaterial substances. How can you tell one immaterial substance from another?
(d) Descartes held that the body is basically a machine, which is fundamentally different from the mind. He had various tests which show that machines cannot think. This, of course, raises interesting questions about artificial intelligence and computers.
Many philosophers after Descartes proposed alternative systems to avoid the difficulties of Cartesian dualism, including Spinoza, Leibniz and others. You might wish to explore Spinoza's criticisms of Descartes on substance, and the alternative he proposed. You might start with Cottingham's book The Rationalists. Then there is Roger Scruton's book Spinoza and the Encyclopedia of Philosophy article on Spinoza and the Philosophers Index. There are good comentaries on Spinoza by Wolfson, Curley and Bennett. I would follow the analogous procedure for Leibniz.