You assume I mean spirits that physically exist separately from people. I do not. You have missed my point entirely.
Even the simple question of what the experience of color is like is totally beyond empiricism.
Not everything has a scientific answer, and that's ok.
I'm not really talking about belief so much as the fact that people need nourishment in unmeasurable ways: love, wonder, etc. I don't think it makes sense to exclude that from spirituality. I have found that 'spirituality = supernatural' is unnecessarily reductive.
But, at the end of the day it's just individual perspective as to what constitutes the spiritual.