For a very interesting article on "the problem of the soul" see Calvin College philosophy professor Kevin Corcoran's "A New Way to Be Human" in Books and Culture.
Today there is a philosophical and scientific battle going on over the nature of humanity, or the nature of "persons." Atheists such as Steven Pinker, Owen Flanagan, and Daniel Dennett deny the existence of a "soul" and reduce all human behavior to neurophysiological determinism and/or indeterminism.
The philosophical legacy of Descartes divided the person into two metaphysically unrelated "substances," which he called res extensa (extended substance) and res cogitans (thinking substance). Thus, for Cartesians, the "soul" is ontologically unrelated to the physical body. The theological problem with Cartesian mind-body dualism is that it is non-Hebraic.
Corcoran proposes another "materialistic alternative to dualism."
Corcoran writes: "We are animals in the sense that we are wholly constituted by our bodies; every material part of me is a part of the biological body that constitutes me and I have no immaterial parts—just like the statue and the copper. We human beings are wholly physical creatures constituted by our bodies without being identical with them. To borrow words U2's Bono used for more poetic ends, "We are one, but we're not the same."
The materialist view of human persons I am proposing is compatible with every important Christian belief related to human nature, including beliefs about the afterlife and the claim that human beings have been created in the image of God. Indeed the Christian doctrines of creation and incarnation are actually more hospitable to a materialist view of human nature than they are to the more extreme versions of dualism.
For example, since dualism identifies us with immaterial souls capable of disembodied existence (or attributes to us such souls as parts), dualism is quite obviously compatible with belief in an afterlife. But for Christians it is important to recognize that the relevant Christian doctrine with respect to an afterlife is that of resurrection of the body. None of the ecumenical creeds of the Church confesses belief in a doctrine of soul survival. It is curious, then, that contemporary dualists seem to have forgotten this in a way that our Christian ancestors did not. While most, if not all, orthodox Christian theologians of the early church were anthropological dualists, they nevertheless struggled in systematic ways to make sense of the Christian doctrine of bodily resurrection."
The statement "we are wholly physical creatures constituted by our bodies without being identical with them" is, or course, the point. But this is just a statement, and must be argued for. I think it has greater biblical/theological consistency than does Cartesian dualism. Note: it's one thing, and a good thing, for Christian theologians to define personhood in relation to Christian scriptures. It's another thing to argue scientifically and philosophically for the nature of humans.
And, for me, when Pinker et. al. try to explain free will on their sheer materialism it is awkward and, to me, ultimately nonsensical. (See my thoughts on this in the archives.)
Finally, I am sure Corcoran, should he continue to develop his proposal, will be challenged by J.P.Moreland's substance and property dualism. For an excellent introduction to the "mind-body problem" see Moreland and Craig, Philosophical Foundations for a Christian Worldview, chapters 11 and 12.