Descartes without Dualism
There is something right about Descartes’ metaphysics of mind and body and something wrong. He is right in supposing there is a kind of symmetrical duality with respect to mind and body, but wrong in supposing there is a corresponding dualism of substances. A body is an extended thing that moves; a mind is a conscious thing that thinks. The essence of body is extension and the essential activity of body is motion (we might think of these as passive and active essence). The essence of mind is consciousness and the essential activity of mind is thinking (again, passive and active essence). Matter is something and does something; mind is something and does something: the former is extended and moves, while the latter is conscious and thinks. Thus we have the ontological categories of extended mobile things and conscious thinking things. The attributes differ, but the abstract structure is much the same.
There are questions of creation or emergence in both cases. What is the origin of extended body and what confers motion on things? What is the origin of consciousness and what confers thinking on things? Both questions raise difficult explanatory problems: How could extension arise from the absence of extension, and what is the ultimate origin of motion? And how could consciousness arise from the absence of consciousness, and what is the origin of thought? Descartes postulated God (i.e. miracles) in both cases, because these creation questions seemed to him insurmountable otherwise. We still have these questions, only now we talk about the big bang and kinetic energy, or about the brain and neural activity. In both cases we have explanatory gaps and the appearance of creation ex nihilo. Both problems are “hard”. We are told that space (extension) itself emerged at the moment of the big bang, but it is far from clear how; and we are also told that consciousness arose at some point during evolution by means of genetic mutation, but it is far from clear how.
A further symmetry concerns laws: the activity of motion is subject to law, described first by Newton and then by Einstein; the activity of thinking should also be subject to law, though we have yet to find our Newton or Einstein. Still, thinking should be subject to law, since it is a dynamic process; and maybe we have glimmerings of what the laws would look like (logic gives a clue).
Perhaps, too, we can apply the innate-acquired distinction in both cases. A body has a shape that belongs to it by its original nature, but the shape can be changed during its history: there is original extension and acquired extension (though of course all extension has a history). A planet has a certain extension in space as part of its “initial endowment”, but it may be subject to external bombardment and lose that shape, acquiring a new shape. An object has a certain size and shape at the time of its creation (at the moment of its “birth”), but these can be modified over time (“by experience”). This mirrors the traditional distinction between innate and acquired ideas: those we are born with and those we acquire.
Thus there are clear symmetries between the dual attributes of mind and body: we have structural parities within differences. So Descartes was right to erect a system of distinct elements that nevertheless exhibit a parallel structure. The world consists of (a) extended bodies that move and (b) conscious minds that think—so far so good. But he took another step that was not so good: he claimed that this duality is underpinned by a dualism of substances. Not content with claiming that consciousness and thought are not modes of extension and motion, he also claimed that these attributes could not be attributes of the same thing: nothing could be both extended and mobile and conscious and thinking. Thus consciousness and thought had to exist in a substance lacking extension and mobility, ontologically separate from the body.  I won’t go over the standard arguments against this picture, except to note that it is no more intelligible how an immobile entity without extension could be a conscious thinking thing than how an extended mobile body could be one—rather less so. Substance dualism gets us nowhere. The reason we always find conscious thinkers conjoined with extended moving bodies is simply that these are aspects of the same thing—they don’t float free of one another. The mental substance is the material substance (the mind is the brain). But that does not imply that mental and physical attributes are the same. Descartes has interpreted a lack of intelligible connection between the attributes as an actual incompatibility in their possibilities of instantiation—inferring that they cannot be attributes of the same thing. What we really have is co-instantiation of attributes in a single substance, combined with an absence of explanatory connection between the attributes: extension does not explain consciousness, and motion does not explain thinking. Still, extension may well be a necessary condition of consciousness, and motion may be a necessary condition of thinking: you need an extended brain to be conscious, and there have to be motions in that brain for thinking to be possible. Not that we can understand these dependencies; it is just that we have good reason to believe that they obtain.
So I take it Descartes was wrong to deny that a conscious thinking thing is an extended moving thing—that is precisely what a person is. There is no dualism of substances and no possibility of separation of mind and body. Yet he was quite right to distinguish mind and body in the way he did: he was right to see a difference of essence, and he was right to see deep parities in the abstract form of both sides of the dichotomy. In fact, the abstract parities are at least as important, metaphysically, as the difference of essence—though less often noted. From a metaphysical point of view, mind and body are on a par—both of them being substances with defining essences (both passive and active), and raising similar questions of origin and laws, as well as exhibiting an innate-acquired distinction. There is no “category mistake” in remarking these symmetries. Metaphysically, Descartes’ duality is perfectly reasonable and useful; he erred simply in supposing that it requires a dualism of substances. But that dualism is easily detachable from the basic picture, leaving what we can describe as Cartesian monism. It is monism because there is only one substance, and it is Cartesian because it agrees with Descartes’ account of the difference between mind and body. It also recognizes the broad structural similarities between mind and body that Descartes identified. To repeat: mind is essentially a substance that is conscious (passive) and thinks (active), while body is essentially a substance that is extended (passive) and moves (active). Mind is thinking consciousness, while matter is moving extension. A person or self has both mind and body. 
 I don’t know if Descartes ever explicitly claimed that the soul cannot move, but if it is without extension and does not exist in space it is difficult to see how it could move. The question is clearly awkward for him, since we do go on as if people move about, not just their bodies.
 To put the point in more modern terms, the mind is identical to the brain but the brain has two sorts of attribute: (a) extension and motion, and (b) consciousness and thought—with neither pair of attributes being reducible to the other pair.