The existence or not of supernatural phenomena, is a question which lies just outside of the scientific method of inquiry, which requires a certain rigour, when it comes to methodology, for example establishing laboratory conditions, which are required, so any experimentation is independently reproducible and therefore verifiable, as is required.
A few videos and photos of your pots and pans flying about of their own accord, is interesting, and is evidence, but it is not by itself nearly enough. To form any kind of scientific theory on the phenomena, no starting points, and so, science ignores the paranormal. Having more pressing concerns, of things which are testable. Like fusion power.
The philosophy of science limits itself to only things outside us, that can be sensed by the five senses, that we all share. This allows us to see to believe, as a group. The philosophy does not take into account the inner reality, that is not easy to share via the five externally tuned senses. For example, dreams are real. We have all had a dreams at one time. But another person cannot reproduce my dream in the lab. It is real output from the brain, but it needs to be seen from within, which is beyond the philosophy of science. Consciousness can perceive both outside and inside, with science limited itself to the outside. The inside still is real.
If you look at the concepts of dark energy and dark matter, these have never been seen in the lab to make sure they are real. Why does this get a pass in terms of the philosophy? Shouldn't there by reproducible lab proof before we celebrate? What is used as collective proof is circumstantial evidence. There appears to be something impacting secondary things, that can seen. I could just as well use fairies as the casual placeholder, since we cannot see them in the lab either. This is an example of inner reality projected to fill in the gaps.
The theory of life on other planets or in other solvents has never been demonstrated and then reproduced in the lab, so why is that still allowed in science? Why is it not lumped as superstition? It involves intellect and intuition that feel agreeable, within.
If we include applied science and the science burden of reproducible lab proof, one can refute many dogma of science. For example diamonds, which are girl's best friend, are assumed to be formed by carbon subjected to heat and pressure over millions of years. Has anyone done any million year experiments, in the lab to confirm this theory? I can build an apparatus like an anvil hot press and make diamonds in weeks. This has been reproduced in the lab and are for sale at
Chatham Lab Grown Diamonds and Lab Grown Gemstones . Why hasn't the theory changed due to my latter theory playing by the book? Are politics involved?
In all cases, dark energy/matter, diamonds, life on other planets or in other solvents, etc., we sneak in some inner synthesis; logic and imagination, and gut feelings, that are supposedly outside the box of the philosophy of science. I would prefer update the philosophy to include inner synthesis and internal observations. We have other senses that are designed for the internal world of consciousness with spiritual things sensed by consciousness from within.