Dualism
Dualism says the mental and the physical are not the same kind of thing.[1] Descartes' version is substance dualism: a body is extended in space and divisible, a mind is neither, so they cannot be one thing. A weaker property dualism keeps a single substance but holds that it has mental properties not captured by any physical description — one stuff, two irreducible sets of facts.
The case for it is the difficulty materialism has with experience, and the case against it is one objection that has never been answered well: interaction. A decision moves an arm; a pin moves a mind. If the mental is genuinely non-physical, where does it touch the physical, and what happens to the conservation laws at that point? Descartes' pineal gland is a location, not an explanation. The alternatives — that mind and body run in parallel without touching, or that mental events are effects of physical ones that cause nothing themselves (epiphenomenalism) — each buy consistency by giving up something people are reluctant to give up, namely that our thoughts do anything.
This is why the mind-body problem stays open rather than being settled by evidence: every position pays somewhere, and the disagreement is largely about which bill is worth paying.