People often accuse me of being opposed to a science of consciousness. Nothing could be further from the truth. I see no reason of principle why there could not be a science of consciousness, though admittedly we do not yet have much in the way of such a science. I say that partly because I have a relaxed attitude about what constitutes a science, holding that even philosophy counts as a science—and I certainly have no objection to the idea of a philosophy of consciousness. But more substantively, I see no reason to doubt that consciousness can be subjected to scientific treatment of a very standard sort, as follows.
First, the science of zoology provides a model of what a systematic taxonomy of consciousness would look like, and indeed we have a fairly good taxonomy of the conscious mind. I can envisage how this might be made more rigorous, as well as how folk taxonomy might be questioned: there can be rational arguments about matters of mental classification (including whether there is any well-defined notion of “the mental”). This kind of thing has been going on for a long time—for example, are moral motives cognitive or non-cognitive? But second and more controversially, I see no reason to deny that consciousness can be treated mathematically—surely the mark of the “scientific”. In fact, I would encourage interested parties, especially mathematicians, to pursue this line of inquiry (they already have to some degree). The difficulties of the mind-body problem should not deter us from trying to develop a mathematical theory of consciousness. I have no definite proposals to make in this direction, but I think it is possible to make some sketchy, and possibly suggestive, remarks. It is not that consciousness is some misty and mystical realm that resists all scientific treatment; it might well be subject to rigorous mathematical investigation. Admittedly, we might need a new type of mathematics to achieve this, but that is hardly a novelty in the history of thought.
We can go back to old-fashioned psychophysics to get an idea of what such a mathematical treatment would look like. Psychophysics aimed to produce laws relating the intensity of a physical stimulus to the intensity of a psychological response—thus the Weber-Fechner law that psychological response is a logarithmic function of physical stimulus. What is significant in the present context is that this kind of law builds in a measure of psychological intensity, to be compared to the intensity of the physical stimulus: we have such notions as degree of subjective brightness or loudness or sweetness. Units of these magnitudes are selected, generally based on the idea of a “just noticeable difference” (“JND”). Thus we can compare two experiences according to their subjective intensity. The intuitive idea behind this is simply that conscious states come in degrees, as physical magnitudes do: sensations of brightness can be of different degrees of intensity, as can feelings of pain, or even states of belief. We can therefore measure consciousness.
But that is just the beginning. People talk about the “qualitative content” of consciousness, but there is also the “quantitative content”: how much content there is. We can think about this in terms of the quantity of information processed or the number of features perceived. Here is where we encounter notions like “channel capacity”—how much information can be processed by a system. Conscious processes have a channel capacity—perception, memory, and attention. Then there are questions of rate: at what speed conscious processes proceed. How long does it take to create an image from a percept? What is the velocity of thought? How quickly can one emotion be replaced by another emotion? How long does it take to wake up? These are all potentially quantifiable matters: psychologists could measure them, at least in principle. Maybe some kind of abstract geometry can be applied to such things as the space of colors or other phenomenal fields. It might not be standard Euclidian geometry, but then neither is it in physics. Or maybe some brand new mathematical apparatus could be invented that makes consciousness appear as a beautiful mathematical structure. There is no reason to believe that consciousness is inherently nonmathematical.
Accordingly, we might be able to develop a mathematical theory of intensity, quantity, rate, and form applicable to the conscious mind; and indeed such ideas are not unheard of today. My point is that all of this is fully compatible with deep-dyed skepticism about solving the mind-body problem. Even if we could find interesting correlations between the mathematics of consciousness and the mathematics of the brain, that would not solve the mind-body problem (it might even accentuate the problem). But by the same token, an inability to solve that age-old problem does not preclude making significant progress in developing a science of consciousness. By way of analogy: Newton confessed that he could not solve the problem of how gravitation arises from matter (specifically from mass), but that did not prevent him from formulating a rigorous mathematical theory of gravity. We might be able to develop a comparable mathematical theory of consciousness without being able to explain how consciousness arises from the brain. Instead of trying to solve that problem, perhaps by investing heavily in neuroscience, we might do better to invest in a direct mathematical treatment of consciousness (which would probably be cheaper). I look forward to the new field of “mathematical consciousness”. Let’s by all means mathematize consciousness as much as we can. The more scientific we can be about consciousness the better. 
 The label “mysterianism” is misleading: it suggests the idea that one who falls under the label is somehow opposed to applying science to the conscious mind. I am not a “mysterian” in that sense—any more than Newton was a “mysterian” about gravity. It is possible to have a rigorous science of the mysterious; indeed, that is the usual state of affairs.