A Triple Aspect Theory
Does pain have a nature that goes beyond the feeling of pain? Pain has a phenomenology, which we experience internally, but does it have any other properties? Apparently it does, since it has a functional role—a way it functions in the mind and in relation to the body. This functional role forms part of what pain is. It is the same with other mental states such as desire: desire has an introspective appearance but it also functions in the organism’s psychophysical life. This is fairly uncontroversial. Much the same could be said about water and other natural kinds: they have a phenomenological appearance but they also have a causal role in the world—a set of causal powers. But is that all—does pain have no further intrinsic nature? Well, what does it have its functional role in virtue of? We might say in virtue of its phenomenology: it functions as it does because of the way it feels. But this is not plausible for the following two reasons: (a) the functional role of pain includes its bodily causes and effects, which are not themselves phenomenological, but physical; and (b) states of the brain are the de facto causal basis of these bodily phenomena. It is hard to see how phenomenology alone could give rise to physical functional role, and anyway the brain already has that job covered. So the natural assumption is that brain states are the basis of the functional role of pain, not the phenomenology of pain. But given that functional role is partly constitutive of pain, it follows that the necessary conditions of functional role are too: that is, states of the brain are also part of the nature of pain. So pain has three aspects (as do other mental states): its phenomenology, its functional role, and its neural correlate. In fact its neural correlate is not a correlate at all, any more than phenomenology and functional role are correlates of pain; it is part of what pain is. Pain isn’t just correlated with the feeling of pain, and it isn’t just correlated with its neural basis either—any more than water is just correlated with H2O. Water comprises three sorts of property: appearance properties, underlying molecular properties, and causal properties. But so does pain: its appearance to introspection, its functional role, and its neural basis. It is thus more than its first-person appearance as a feeling; it has another type of reality altogether. Pain is partly made of brain stuff.
This is not some sort of generalized materialism (whatever that means); it is a point specifically about the nature of pain and other mental states. Because mental states have functional roles as part of their intrinsic nature they also have neural states as part of their nature, since the latter are the basis of the former. The best hypothesis is that the brain, as we now conceive it, forms part of the essence of the mind. Neurons are really part of the inner nature of mental states. This doesn’t mean for all conceivable types of mental states—Martians may not have neurons in their “brains” but some other type of unit. The point is just that terrestrial animals have minds whose nature includes the nature of their neural brains. The brain is not extrinsic to the mind, located somewhere outside of the mind. Brain states form the hidden machinery of the mind in much the way that molecular states form the hidden machinery of water, and for essentially the same reason, namely to ground the causal properties of the things in question. Mental natural kinds are partly constituted by neural natural kinds (here on earth)—but only partly because they also have a phenomenology. This is not some sort of reductionism about phenomenology, just the pedestrian (but important) point that the reality of the mind is not confined to its appearance to introspection—the brain is also an aspect of the mind (as molecules are an aspect of water). Maybe the phenomenological aspect is irreducible to anything else; maybe it is a complete mystery how anything can have both phenomenological and physical aspects; maybe the whole thing is pure magic: but still, mental states have a physical aspect existing in the brain. To repeat, not a correlate (as in traditional dualism) but an intrinsic dimension of their being: states of mind actually are partly composed of states of the brain physically described. There need be no necessary connection between phenomenology and a specific brain physiology; it is just that functioning mental states must needs be partly constituted by brain states of some sort. In the case of terrestrial animals brains have a certain sort of physiology, so the minds of these animals are partly constituted by that physiology. They don’t float above the brain, as “nomological danglers”, but are intimately enmeshed in the brain. Brain states don’t merely correlate with mental states; they constitute them. Just as H2O molecules are intrinsically involved when you wash your hands, so neurons are intrinsically involved when you think your thoughts or feel your pains (with the emphasis on “intrinsically”). They aren’t somehow removed, existing in another parallel place; they are right there in the thoughts or pains. They are as much in your mind as its phenomenology is. Perhaps we have a bias in favor of phenomenology because that is the way our minds strike us internally, but from a more objective perspective our minds are equally brain involving. The mind is just as steeped in the brain as it is steeped in its own subjectivity, i.e. its own introspective appearance. To put it bluntly, mental states have a neural architecture existing alongside their phenomenological character. 
I introduced the brain directly into pain via the functional role of pain, but once we have taken that step we can probably limit ourselves to just the brain combined with phenomenology; for the brain’s states can substitute for functional roles, given that they determine functional roles. It is not customary to say that water is H2O plus the causal role of H2O, since the former determines the latter; likewise we can say, not that pain is (partly) C-fiber firing plus the causal role of C-fiber firing, but just the C-fiber firing itself, since that determines causal role. Strictly speaking, we have a trio of aspects in both cases, but to all intents and purposes the physical basis makes mention of the causal-functional role redundant. So we could simplify and say that pain is constituted by the feeling of pain combined with the neural basis of pain, with causal role entailed by neural basis. The essential point is that the brain is just as integral to pain as its phenomenology is. This gives us a good deal of what the classic identity theory proposed (token or type), but not all. Mind and brain are inextricably intertwined, which is not to say identical.