Does this help?

By far the best definition I've ever heard of the supernatural is Richard Carrier's: A "supernatural" explanation appeals to ontologically basic mental things, mental entities that cannot be reduced to nonmental entities.

This is the difference, for example, between saying that water rolls downhill because it wants to be lower, and setting forth differential equations that claim to describe only motions, not desires. It's the difference between saying that a tree puts forth leaves because of a tree spirit, versus examining plant biochemistry. Cognitive science takes the fight against supernaturalism into the realm of the mind.

Why is this an excellent definition of the supernatural? I refer you to Richard Carrier for the full argument. But consider: Suppose that you discover what seems to be a spirit, inhabiting a tree: a dryad who can materialize outside or inside the tree, who speaks in English about the need to protect her tree, et cetera. And then suppose that we turn a microscope on this tree spirit, and she turns out to be made of parts—not inherently spiritual and ineffable parts, like fabric of desireness and cloth of belief; but rather the same sort of parts as quarks and electrons, parts whose behavior is defined in motions rather than minds. Wouldn't the dryad immediately be demoted to the dull catalogue of common things?

-Eliezer Yudkowsky, Excluding the supernatural