But there are no methods or tests or anyway to confirm or disprove "spiritual nature." You can't even adequately define it. Supernatural claims are not consistant, and not predictable, and therefore any such claims are completely useless.
Like trying to explain quantum entanglement, or dark matter and dark energy.
DANG! You beat me to this!! I was going to say the same thing. (Also, inside black holes and singularities.) Science is currently opening up a whole new realm (sorry Hollie) of physics known as quantum mechanics and string theory. Pretty much all of it is untestable or confirmable because we lack the parameters needed in our regular physical dimensions.
"Supernatural claims" is a vague and mysterious term for a very wide range of things. Does science indicate 100% of the time they are false claims? Or does science say the door of possibility to anything remains open? Does science explore possibility, or does it draw conclusions?
Spiritual nature is not the same thing as "supernatural" because it is part of nature. The evidence is humanity. We are the evidence spiritual nature does exist and is very much real. Our religions are evidence that humans have a robust spiritual nature and an inspired imagination. Human behavior is very much a science and it's clear humans have always been spiritual creatures. Furthermore, it is a direct contradiction of Darwinian natural selection to not recognize this attribute as fundamental to the species, which means it can't be an invention. If so, it defies every behavioral attribute of all living species ever known in nature.