I think a lot of people mistake ghost hunting TV shows for actual science. The SciFi/SyFy channel is a shadow of its former self.
It seems also that you have a very caricatured understanding of scientists.
First of all, a claim of the existence of ghosts requires some evidence that cannot be explained by other, simpler means. The principle of parsimony (AKA Occam's Razor) is important because it works. So for our ghosts, we would need residents' observations of sounds, movement, or other unexpected events. They could keep a log of the time and place of every ghostly occurrence, and demonstrate that no other explanation (thermal expansion causing creaking floorboards, drafts moving the curtains, slightly asymmetrical mounting causing pictures to tilt, blood flow through the retina causing spurious visual patterns in the dark, etc.) explains the observations.
Then you bring in the scientists, and all of the observations cease as if by magic. There are still physical explanations. The scientists' movement may be masking subtler sounds. Their presence may have made the house warmer, so the joints are tighter and creak less. The lights may be on more of the time, so visual patterns caused by misfiring neurons aren't seen.
But even if you rule out all possible simpler explanations, you still have a way of fixing the ghost problem -- just sell the house to a family of scientists, or install cameras and microphones to scare the ghosts away.
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Responding to the comment by clock_tower, that is the sort of platonic notion of "existence" that science avoids because it doesn't yield results. I'd say science doesn't really deal with "existence" in that sense, but "occurrence". So if you ask, "Does decadence occur?" The answer would quite obviously be yes. Using a more pragmatic definition of existence, you could say that any phenomenon you can define "exists", but you are likely to run into the problem of knowing which definition of a word someone is using.
Thus, I think you also may have a caricatured understanding of scientists, caused in part by the "fun-house mirror" effect from mechanically transliterating scientific jargon into a philosophical context.
