For all my talk of defending naturalism, unfortunately I, like many before me, haven’t made much of an effort to explain the difference between supernaturalism and naturalism. What exactly is the difference between the supernatural and the natural? One of the most useful distinctions I’ve come across, primarily due to aligning with how people use the terms in practice, was made by Richard Carrier who claimed it is between entities which are fundamentally mental and those which are reducible in principle.* That is to say the reason something would be supernatural is not because of the particular powers it exhibits, or because it is currently considered paranormal, but because it would not be reducible to nonmental entities.
Take the competing efforts to explain human consciousness as an example. If naturalism is correct, as I believe it is, then our mental properties are the result of the interaction of nonmental particles, namely the interaction between a vast number of neurons. However, if our mind is not dependent on the brain (or any other sub-component parts) then our mind is supernatural as it is irreducibly mental. The mind would simply possesses mental traits as an innate property.
Under this framework if we were to examine Slimer from Ghostbusters and it turned out that he was able to traverse through walls, and dimensions, completely due to the motion of component parts he would be natural. Similarly, even if a being could examine and alter all of our universe so long as it was reducible to the mindless interactions of particles and fields, as opposed to irreducible mental desires, it would be natural. These creatures still could have a supernatural origin, they could have been “willed” into existence by a supernatural being, but their bodies would still be natural. Conversely, a ghost or god would be supernatural only if upon examination it can’t be reduced, there are no parts underlying their desires and they can simply “will” events into happening.
Not surprisingly, even with this clarification supernatural claims are still contain many fatal flaws. What does such a non-reductionist entity look like?** It is not enough to assert that we inhabit a universe with such entities without making testable observations as to what we would expect to find in one. The problem is, as has been repeated by many before, even if we were to find, say, demonstrable effects of wizardry it would demonstrate only that we have found such effects not that they were due to supernatural entities. After eliminating all possible currently understood natural phenomena we wouldn’t then be justified in concluding the result was supernatural because it could also be a natural phenomena we don’t yet understand.
Of course in practice with any allegedly supernatural claim, like witchcraft, we can test whether or not the effects on the universe claimed really arise. Simply to check whether or not incantation spells are effective doesn’t require a distinction to be made between irreducibly mental entities and some type complex machine of nano-robots as the root cause, all that matters is whether or not the stones really do come to life on command. As I’m sure you are aware, thus far all such tests have come back negative for the alleged effects of supernatural powers but there is no test, even in principle, which takes the currently unknown and eliminates all but irreducible mental entities as the cause. Ultimately, I think this is because supernaturalism and the underlying idea of non-reductionism are fundamentally just confused ideas. It’s not just that they are wrong and reality could have been that way but as an explanation for reality they are incoherent.
*I encourage you to read Carrier’s entire post though I ultimately disagree with it on whether or not a supernatural explanation can be made probable.
**More specifically what happens when you subject these irreducible entities to examination? Does your microscope just explode? The response I suspect to get to such a question, that supernatural entities cannot be examined, completely undermines any standing for supernatural claims. It is a confession that ultimately means we can’t know they exist.