I'm interested in knowing how you would explain it -- I can think of a way they might be explained as compatible also, but it seems like a bit of a stretch.
Okay, here's my attempt. Definitions are just for clarity in case we disagree on them to begin with. I've also never heard these terms explicitly before reading them on wikipedia; so if I'm making a mistaken assumption about animism or naturalism, please feel free to correct it.
http://en.wikipedia.org/wiki/Naturalism_(philosophy) said:
Naturalism commonly refers to the philosophical viewpoint that the natural universe and its natural laws and forces (as opposed to supernatural ones) operate in the universe, and that nothing exists beyond the natural universe or, if it does, it does not affect the natural universe that we know.[1] Followers of naturalism (naturalists) assert that natural laws are the rules that govern the structure and behavior of the natural universe, that the universe is a product of these laws and that the goal of science is to discover and publish them systematically.
This seems to be a viewpoint that the world is just a deterministic process that is uninfluenced by an outside force. The only assumed truth then is in knowing about that process.
This view of determinism asserts that there is no inherent purpose to this deterministic process, not even in the whole process itself; then any meaning assigned about that process that we create with our own minds is taken as false.
This is a contradiction however; deciding with one's own mind that the world has no inherent purpose is the same as assigning it a kind of purpose - that of no purpose. Also,
what people assign as meaningful (ghosts, souls, apparitions, etc.) becomes part of knowing about that process.
http://en.wikipedia.org/wiki/Animism said:
Animism encompasses the beliefs that there is no separation between the spiritual and physical[disambiguation needed ] (or material) worlds, and souls or spirits exist, not only in humans, but also in all other animals, plants, rocks, natural phenomena such as thunder, geographic features such as mountains or rivers, or other entities of the natural environment.[4] Animism may further attribute souls to abstract concepts such as words, true names, or metaphors in mythology. Animism is particularly widely found in the religions of indigenous peoples,[5] including Shinto, and some forms of Hinduism, Buddhism, Pantheism, and Neopaganism.
Animism on the other hand chooses to see purpose in things. Strictly speaking, it recognizes the philosophical problem of reductionism, where it is moot to argue whether we are more our parts or the sum of our parts, or whether or not one part is even more important than another, since they all function to form a whole, the universe.
To the animist, assigning meaning to these parts while understanding that they form a whole, is more important than taking the contradictory naturalist approach of deciding that all meaning is that there is no meaning. This deals directly with the philosophical problem of explaining our unconscious, which we all have, and which keeps our personal perspective from ever truly being deterministic or completely rational; the unconscious by nature acts on its own accord, and animists see significance in that, possibly a soul. And then these mystical properties that show up in our unconscious are not only very real, but spiritual in themselves.
Imagine a living being without an unconscious. Would it even be alive if it didn't have it's unconscious influences? Would it even have a will?
But it's also a contradiction to think that all things must be explained in terms of assigning it some particular abstract meaning that becomes a part of our unconscious or is assigned to explain it. It's not arguably more important that all things must be explained to have significance.
In terms of reductionism:
I appreciate the naturalist thought-of-mind is a focus on identifying what can be deterministic.
And I appreciate the animistic thought-of-mind deals with understanding what can't be deterministic.
Where they both contradict themselves is in not realizing that a world can include both non-deterministic and deterministic processes in different, yet equally important ways.
So in my mind, reductionist reasoning shows me they are essentially two opposite poles of reasoning of the same problem - that of approaching how we understand the world.