Cartesian dualism is false, yes, but to my knowledge the Church puts forth what basically amounts to Aristotle’s hylemorphic dualism theory which is different from Descartes’ theory in that it posits that all substances are unions of form and matter. The form of a human being is a rational soul which is immaterial. Instead of it being like a ball and a “ghost” ball that fits inside the real ball and controls it, the relationship between soul and body is like that of the shape of a triangle with the ink in which the triangle is written.
Balto is right.
The Church does not endorse any particular philosophy, but its tendency is definitely in the direction of Aristotelian-Thomistic hylemorphism in which the soul is the form of the body. (Such a position is visible in certain encyclicals, like Veritatis Splendor.) Aristotle argued that the intellect had no bodily organ, which sounds odd to us, but what he meant was that intellectual operations (particularly the abstraction of universal forms from particular substances in the world) was a necessarily immaterial operation. He believed that such an operation, though, relied on humans’ material bodies and the physical world since such operations depend on sense data.
This is a point on which Aquinas had to modify Aristotle. Aristotle was focused on the form-matter distinction, while Aquinas made a more general essence-existence distinction (in addition to the form-matter distinction). The relevance of that is that Aristotle did not see the possibility of a form existing apart from a body, while Aquinas did believe that there could be such subsistent forms just in case that they were essentially immaterial. Aquinas argued that human souls are essentially immaterial (his basis for this was that humans’ intellectual operations entailed their vegetative and appetitive operations, but the opposite is not true, ie. there are animals which have appetitive powers but not intellectual powers), which means that the persevere after the death of the body (though, since they rely on the body for their operation, in a reduced state).
These are certainly points on which a Catholic could disagree.(
Here is an example of a Catholic substance dualist.) Feser’s book
Philosophy of Mind is a good introduction to the subject of philosophy of mind and will spell out the major arguments for materialism and dualism. His book
Aquinas, I think, spells out the arguments for hylemorphic dualism in more specificity and with more relation to Aquinas’s thinking.
It’s hard to find full treatments of the subject.
Mind, Matter, Nature by Jim Madden and
Philosophy of Mind by William Jaworski are both introductions to philosophy of mind that introduce hylemorphism as a “third way” between substance dualism and materialism toward the end; but the treatments are therefore necessarily a bit limited. (They are also not too cheap and probably are not worth buying unless you are serious about the subject. If you’re fortunate enough to have access to an academic library, then you could probably find them there.)