The brain will never fully explain experience, because consciousness is not its product: it is a reality of another nature, the soul, which could in principle exist apart. This is the spontaneous view of many, and that of many religions.
What thinks cannot be of the same nature as what is thought from without: the soul knows the immaterial Forms, it moves itself and outlasts the body's states, traits no arrangement of matter could produce. Consciousness thus belongs to an order other than the sensible, prior to and independent of it, not to a bodily configuration that would generate it. Platonism thereby refuses in advance any reduction of mind to matter, where the Stoics will make the soul a corporeal breath.
The argument rests on a principle: what I clearly and distinctly conceive as able to exist apart really exists apart, since God could create it so. Now I can conceive my mind, pure thinking thing (res cogitans), with nothing corporeal attributed to it, and body, pure extension (res extensa), with no thought. My essence is therefore to think, and the mind is really distinct from the body, a substance of another nature than the brain. This substance dualism breaks with the Aristotelian soul, form of a body, and at one stroke frees matter for a purely mechanistic physics; yet it bequeaths the problem, which Descartes will struggle to solve, of their union and interaction.
Meditations on First Philosophy, VI
Foundations and implications
↑ What grounds it↓ What it implies
↑ What grounds it
Nature of reality
If reality comprises two irreducible substances, extended matter and thought, then my consciousness belongs to the second: it is not the brain but a reality of another nature. Metaphysical dualism directly grounds substance dualism in the philosophy of mind, of which Descartes gives the classic formulation.
↓ What it implies
Moral circle
If only the rational soul confers genuine inwardness, animals, lacking this thinking substance, are nothing but mechanisms without worth of their own. Substance dualism supports moral anthropocentrism: for Descartes, the "animal-machine" does not enter the circle of our direct duties. The link is looser, however, among anthropocentrists who, like Kant, ground dignity in reason rather than in a soul-substance.
Being or having a body
If I am essentially a mind distinct from matter, my body becomes an instrument I use, even a prison I set myself apart from. Substance dualism supports the body-as-instrument conception, from Plato to Descartes, even though the latter eventually insisted on the union of soul and body.
Freedom of the will
If the mind does not belong to the mechanical order of matter, the will escapes the determinism of physical causes and can determine itself. Substance dualism thus supports free will, by removing decision from the chain of natural causes.
After death
If the mind is a substance distinct from the body, its survival becomes conceivable: substance dualism is the metaphysical ground of the immortal soul, from Plato to Descartes.
Nature of the self
If the mind is a substance distinct from the body, the self that says "I" is this thinking thing, identical to itself beneath the flow of experiences. Substance dualism grounds substantialism: personal identity rests on the permanence of the soul, not on memory or narrative. This is Descartes' position.