But how is it better than a prankster alien? Or a prankster god? Or a universal field of energy that is activated by a certain keyword? Or that it is prayer that has the magic power itself, without a god?
Maybe these aren't good hypothesis; maybe someone can suggest better ones. My point is that your hypothesis needs to be tested against rival ones.
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If praying to FSM would work, would you really think that FSM exists???
How would we "prove" that prankster aliens weren't reducing our pain every time we took an aspirin?
The problem here is that people are appealing to different meanings of the word "prove." From an empirical scientific perspective, nothing is proved
absolutely, such that no possible future discovery could overturn the weight of that proof. What had better "proofs" to support it than Newtonian physics? In the late C18th you'd have been considered a madman to doubt the universal validity of Newtonian laws. Then Einstein comes along and, whoops, we can prove that there are limits to the explanatory power of Newtonian physics.
On an empirical basis, proof can only ever rise to the level of "best evidence" and never to the level of "it could not possibly be otherwise." The existence of a supernatural being of some kind can never be proven "beyond all possible future doubt" by empirical evidence (although an actually
omnipotent being can establish its existence beyond all possible doubt simply by willing that this be the case). But it's fair to say that the existence of such a being could be "proven" to the same degree of confidence as, to use DrKitten's example, the efficacy of any given medical procedure.
So, if a guy floats up to you on a cloud and says "I'm the great hoodly doodly FlumWump and have magical powers!" and then proceeds to perform a series of magical acts for you under controlled circumstances and before competent and impartial witnesses, it is fair to say that that being has proven it's capacity to perform paranormal acts. It is also fair to say that this does not mean that at some future occasion these acts may be proven
not to be paranormal, but merely the products of a technological capacity beyond our current understanding.