The paranormal is not superstition. It's something that is outside what science and our current knowledge considers normal, hence paranormal. If evidence of precognition, or mind-reading, or whatever becomes proven, then it simply becomes a "normalized", accepted part our knowledge. At one point in history, flying through the air would be consider demonic. Today, people fly through the air all the time via planes, helicopters, hot air balloons, etc. We can now send messages to each other through the "ether" via wireless internet connections. Even mentioning such a possibility in the Middle Ages might get you tied to a stake.
Heck, even if God could be proven, then it would no longer be religion but a scientific fact. Miracles would no longer be supernatural but natural occurrences. I don't believe in God or precognition, but that's beside the point. Whether you or I want God, or the Devil, or telekinesis, or levitation, or precognition to exist is irrelevant to whether in fact they do exist. They either are true or not, and may even someday be proven, or not. The question is, does one base their beliefs on observations of what is or faith/intuition of what might be? In the context of the film, there is some body of evidence to conjecture Puri may have some "paranormal" skills, as well as being emotionally disturbed, but none that she is actually possessed. Spider-walking proves nothing other than being exceptionally limber.
If you watch the film again, she does seem to have some odd predictive power, which could, of course, also just be coincidence. The point, however, is that her method of dealing with this possible power (whether real or imagined) was conditioned by the fundamentalist culture in which she was surrounded. The culture in which she was surrounded might even be the cause of her belief in such "powers" in the first place. Anyway, her "embrace of Witchcraft" seems rather muddled and confused to me, and I believe was conditioned by the way she was treated by her co-villagers and also by a sense of rejection she was feeling.
Flying through the air unaided would probably still be considered demonic today, but it doesn't happen, just like things such as mind reading haven't been proven to happen when placed under scientific scrutiny. It's not a question of what we understand, merely what we can observe. The flying machines we operate now are built courtesy of an increased understanding and application of empirical scientific principles, they're not a vindication of superstitions from a prior age.
The paranormal is not superstition. It's something that is outside what science and our current knowledge considers normal, hence paranormal.
... hence superstition. The two terms are equally remote from science. You can't operate on the assumption that something may one day be proven, thus it deserves the (apparently more prestigious) categorisation of 'paranormal'. You could do the same for all superstitions. It may one day be proven that touching wood wards off bad luck, that doesn't mean we shouldn't be free to call it a superstition. Similarly, the distinction between paranormal powers and demonic possession seems only a semantic one.
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The fact would still remain that Puri was experiencing something other than demonic possession if some other force was at work. The film doesn't answer whether anything strange was going on, rather focusing on how a particular community chose to react to such perceived events and the mental state this created in a specific individual. For those people, the only possible explanation for anything they couldn't understand was witchcraft and possession...there was no third, fourth, or fifth option in there minds. Maybe they were completely right, and she was possessed. On the other hand, maybe nothing at all was going on at all. Please note again I didn't say I believed in the supernatural or paranormal, only that the film was clearly attempting to make the events in the film ambiguous for us, which The Exorcist, for instance, really didn't do.
Further, I think there is a distinction between the paranormal and superstition. A particular phenomenon may simply be a force of nature so rare it's never been properly observed or verified. Still, I can speculate about spontaneous human combustion without claiming that God hurled a thunderbolt as a judgement at someone. Balled lightning is a very rare event in purpose, yet has no meaning or purpose other than the fact that it occurs. To assume that there is some "purpose" or "meaning" or "intelligence" operating behind a phenomenon to me is where superstition comes into play, especially those that are perceived as detrimental or beneficial. Just suppose, for the sake of argument Puri did have some strange mental skill in the fictional world of the film. While there no evidence a person can be aware of an event (the death of the young boy in the film) that's happening somewhere else, it does appear to happen in the film. Whether such things actually exist or not isn't really what I'm driving at, nor is it what the film was driving at, I think. It's the attempt to give it some "meaning" or "purpose" to such possibilities, and how certain communities attempt to do this, that is being discussed in the film.