If we understand the problem of qualia not to be of how to reduce qualia to abstract, quantitative representations but rather how to represent qualia in terms of abstract, quantitative representations, then that seems rather easy in a way. We can make a start on representing colour experiences as indicated here, for example. This then leads to a question: why is abstract, quantitative representation useful? The basic idea with science is that this sort of abstract representation reveals something important about the universe. So what does it reveal?
What is quantity? Quantity at its root is distinction. For example, we can quantify the length of the side of a rectangle by making distinctions – places – along it. We have a way to record these distinctions – 1, 2, 3, and so on, are placeholders for these distinctions. We could just as easily use different symbols – a, b, c, and so on. Mathematics is largely ways to understand the relationships between placeholders as such. That is, what can we say about placeholders, to the degree that they’ve been abstracted?
The problem with science is that reality isn’t abstract. Reality is concrete. My subjective experience instantiates certain things that can be ‘captured’ to an extent with abstract, quantitative representation. For example, my visual experience of a rectangle can be ‘divided’ up. These distinctions can then be mapped to abstract placeholders. (The trick is that many people mistake scientific representations for concrete things. “The deer is really a bunch of molecules,” for example, where the molecules are taken to be concrete. They aren’t – they are abstract representations of what was formerly represented by the ‘deer’ concept.)
Instead of thinking of science in this abstract, placeholder sense as revealing something, it is more like it is remembering something – in a symbolic language that can be ‘re-converted’ later on – much like letters can be converted to meaning later on, if one has some basic grasp of the meaning of letters arranged in such-and-such an order to begin with.
Certainly, science does reveal things. We use tools to perceive things hitherto unperceived. Yet, the language in which science records these things requires an interpreter on the other end, who can decode the ‘meaning’ of them (‘meaning’ here is understood in a disparate sense).
The same goes with scientific representations of subjective experience. The attempt to eliminate subjective experience as a phenomena itself, and in its place put only symbolic representations of it, is misguided. Rather, the symbolic representation can help us to understand the things (in various ways) – they don’t replace them, except when we are moving, rather, from one representational scheme to another. I.e., we can abandon one representational scheme for another in reductive science, where the new or ‘lower-level’ scheme is in some way more useful. However, even here they are both referring to something ‘real’, and so in a certain ontological sense of reference neither are primary.
In the case of fitting subjective experience into the physical universe, we are not moving from one mere representational scheme to another – rather, we have things (i.e., subjective experiences, say) and are looking for some possible physical representation of this that ‘fits’ with our other physical representations in some relevant sense.