EB: Vic, you're trying to smuggle in something "more than natural" by predefining what "nature" can and cannot do. In your opinion electro-chemical reactions in a complex assemblage of neurons connected with acute sensory apparatus and plenty of memory (and self-reflective recursive overlays) cannot explain consciousness. But in the opinion of naturalists, it can.
You use the "nothing buttery" argument when you discuss "atoms and equations" as if they represented "nothing" but themselves, and you use the thought that "that is all there is" according to naturalists. So you cannot even imagine how a naturalist might get a "mind" out of such things. Of COURSE looking at a single atom isolated and alone, and looking at an equation is incomplete. But that has nothing to do with whether or not consciousness is natural.
Vic, ask yourself how do you get ANYTHING out of atoms and equations? Molecules? Organs? Colors? Sounds? Reproducing organisms with teeny brains and then larger and more complex and faster brains? None of that is inherent in atoms and equations if you want to press your initial premise. But naturalism does not begin and END with that premise of yours, naturalism may also include concepts like emergence in their philosophy.
WHAT YOU SHOULD ATTEMPT TO DO IS LOCATE AN UNCROSSABLE BOUNDARY BETWEEN TWO SPECIES EVOLUTIONARY RELATED ALONG A SPECTRUM OF DESCENDANTS, ON ONE SIDE OF WHICH THE BRAIN IS NATURAL, AND ON THE OTHER SIDE OF WHICH IT IS "BEYOND NATURE." Have fun attempting to discover such an inviolable boundary. I'd thought at one time that perhaps the ability of a species to recognize itself in a mirror might do. But that raises other questions, since that type of consciousness exists in some monkeys, but not all monkeys, and also in species that have evolved larger more complex brain-minds along separate evolutionary lines of descent, like dolphins and elephants.
VR: You have to have some idea of what nature can and cannot do, otherwise the term is vacuous. My dissertation advisor once said that the definition of the physical is whatever physics quantifies over, and there are theories that quantify over God, and therefore, as he understands it, that would make God physical. If that is permissible, then I am hard pressed to understand why so many mainstream science types have a cow when you want to bring ID into science.
The "supernatural" is not one that I would introduce, except to define seomthing that goes beyond the limits of what naturalists will accept as natural. My argument is that "the mental" can't find a purchase in the world unless it is metaphysically fundamental. Hence "natural" for me, means something fundamentally non-mental in nature. I take it this is what Dennett is getting at when he rejects skyhooks. Blue Devil Knight accepts this kind of definition whenever I present it, and it is standard in the literature.
On a standard interpretation of "physicalism" or of "naturalism," basic physics is defined by denying mental qualities to it. I don't see any other way of solving Hempel's dilemma. Hempel's dilemma is the argument that naturalism can't mean anything, because either it tells us that everything can be explained in terms of present physics, which is absurd, or it says that everything can be explained in terms of some future physics, which could include anything and everything, and is therefore vacuous.
So long physics is mental-free and closed, there are limits on the type of emergence that is permissible. Do you mean by emergence just something that isn't quantified over in basic physics? If so, then "solidity" or "liquidity" or "gaseousness" would not be physical properties, since these properties could not be predicated of individual atoms.
I would argue that the only kind of "emergent" properties that are accepable under physicalistic or naturalistic constraints are properties that logically must exist given what is true on the level of basic physics. If we know where all the bricks are in a wall, we know how tall the wall is, even though no brick in the wall has, say, the property of being six feet tall. The physical information closes the question. Whatever facts can be entailed by "physical" information are emergent in a benign sense. If the physical information leaves the emergent state undetermined, either the mental state isn't real, or there is some reality other than the non-mental substrate that explains its existence. It is "supernatural" not in the sense of being spooky, or weird, or even religious, but just that it won't fit in to the contraints of a naturalistic system as we have defined it.
When it comes to intentional states, I maintain that there are good arguments saying that there are no strict psychophysical laws, and that being the case, whatever mental states exist are underdetermined by the physical. The physical information is compatible with seeing a rabbit or seeing undetached rabbit parts. Or, there could be no inner states of meaning this or meaning that, at all. There is no perspective from which the entity perceives his perception as a perception of a rabbit or a perception of undetached rabbit parts.
Further, in order to capture our common-sense conception of rational inference, you need for mental states to have causal relevance. However, if the "physical" or "natural" or however you want to define the non-mental substrate is causally closed, that means that unless the existence of the mental state is logically guaranteed my the physical, it can have no possible causal relevance. It can never be true that you reject belief in God because you believe that there is gratuitous evil in the world. Darwin didn't come to believe that the changes in the characteristic of finches in the Galapagos islands occurred due to natural selection. That didn't happen, because states like "perceiving changes X, Y, and Z in the Galapogos finches" cannot cause or even be causally relevant to the formation of the belief "this happened by natural selection."
Molecules seem to be entailed by the physical. Given the state of the basic particles, you can't deny the existence of molecules. Organs would set of particles. Colors and sounds are a little more complex, because there are scientific descriptions of the light or sound waves, but then there is also what it is like to see red or hear sea waves crashing. The former is OK within naturalism, the latter requires an answer to the hard problem of consciousness. Would red exist if there were no one in existence to see red?
Again, human uniqueness is not an issue, since at least by the time we get to the higher animals I think their consciousness cannot be explained physicalistically either, so monkey and dolphin studies are a red herring. If you show that monkeys and dolphins have the sort of rich, inner mental lives that include the capacity for genuine rational inference, then naturalism, as I have defined it, has a problem with monkeys and dolphins as well as for humans. That makes it worse for the naturalist, not better. (I have no problem with doggie heaven, that means I'm going to get to see my late beagle Boots someday.)
There is a type of emergence that could be applied to this kind of a case, and that is where, given mental states, the laws that govern physical states change in such a way that the mental can be causally relevant. In other words, there are emergent laws. Again naturalists are going to object vehemently if you introduce this kind of causation, and you would also have to explain just how it is fresh laws are introduced into the system, especially if you want to exclude intelligent design as a possible explanation.