Consciousness might not be reducible to the material, or the material could all have a conscious component. There might be other things, like societies or biology, which are strongly emergent. Or maybe there is no material world. Maybe it's all mental. Perhaps there is a third substance, a neutral monism giving rise to mind and matter.

Maybe the noumena is beyond human categorization and perception. Perhaps our experience of the world is such because we are the animals we are, and not because we have access to reality in itself. Man is the measure and all that.

And on and on. There are various anti-realists debates. There is Humean skepticism of causality. None of these issues need invoke the supernatural, although they don't necessarily rule it out. David Chalmers can propose consciousness as an additional feature of nature which is nonphysical (tied to informationally rich processes like certain mental or computational states), without proposing any supernatural element.