(ETA: I've created three threads - color, computation, meaning - for the discussion of three questions posed in this article. If you are answering one of those specific questions, please answer there.)
I don't know how to make this about rationality. It's an attack on something which is a standard view, not only here, but throughout scientific culture. Someone else can do the metalevel analysis and extract the rationality lessons.
The local worldview reduces everything to some combination of physics, mathematics, and computer science, with the exact combination depending on the person. I think it is manifestly the case that this does not work for consciousness. I took this line before, but people struggled to understand my own speculations and this complicated the discussion. So the focus is going to be much more on what other people think - like you, dear reader. If you think consciousness can be reduced to some combination of the above, here's your chance to make your case.
The main exhibits will be color and computation. Then we'll talk about reference; then time; and finally the "unity of consciousness".
Color was an issue last time. I ended up going back and forth fruitlessly with several people. From my perspective it's very simple: where is the color in your theory? Whether your physics consists of fields and particles in space, or flows of amplitude in configuration space, or even if you think reality consists of "mathematical structures" or Platonic computer programs, or whatever - I don't see anything red or green there, and yet I do see it right now, here in reality. So if you intend to tell me that reality consists solely of physics, mathematics, or computation, you need to tell me where the colors are.
Occasionally someone says that red and green are just words, and they don't even mean the same thing for different cultures or different people. True. But that's just a matter of classification. It's a fact that the individual shades of color exist, however it is that we group them - and your ontology must contain them, if it pretends to completeness.
Then, there are various other things which have some relation to color - the physics of surface reflection, or the cognitive neuroscience of color attribution. I think we all agree that the first doesn't matter too much; you don't even need blue light to see blue, you just need the right nerves to fire. So the second one seems a lot more relevant, in the attempt to explain color using the physics we have. Somehow the answer lies in the brain.
There is one last dodge comparable to focusing on color words, namely, focusing on color-related cognition. Explaining why you say the words, explaining why you categorize the perceived object as being of a certain color. We're getting closer here. The explanation of color, if there is such, clearly has a close connection to those explanations.
But in the end, either you say that blueness is there, or it is not there. And if it is there, at least "in experience" or "in consciousness", then something somewhere is blue. And all there is in the brain, according to standard physics, is a bunch of particles in various changing configurations. So: where's the blue? What is the blue thing?
I can't answer that question. At least, I can't answer that question for you if you hold with orthodoxy here. However, I have noticed maybe three orthodox approaches to this question.
First is faith. I don't understand how it could be so, but I'm sure one day it will make sense.
Second, puzzlement plus faith. I don't understand how it could be so, and I agree that it really really looks like an insurmountable problem, but we overcame great problems in the past without having to overthrow the whole of science. So maybe if we stand on our heads, hold our breath, and think different, one day it will all make sense.
Third, dualism that doesn't notice it's dualism. This comes from people who think they have an answer. The blueness is the pattern of neural firing, or the von Neumann entropy of the neural state compared to that of the light source, or some other particular physical entity or property. If one then asks, okay, if you say so, but where's the blue... the reactions vary. But a common theme seems to be that blueness is a "feel" somehow "associated" with the entity, or even associated with being the entity. To see blue is how it feels to have your neurons firing that way.
This is the dualism which doesn't know it's dualism. We have a perfectly sensible and precise physical description of neurons firing: ions moving through macromolecular gateways in a membrane, and so forth. There's no end of things we can say about it. We can count the number of ions in a particular spatial volume, we can describe how the electromagnetic fields develop, we can say that this was caused by that... But you'll notice - nothing about feels. When you say that this feels like something, you're introducing a whole new property to the physical description. Basically, you're constructing a dual-aspect materialism, just like David Chalmers proposed. Technically, you're a property dualist rather than a substance dualist.
Now dualism is supposed to be beyond horrible, so what's the alternative? You can do a Dennett and deny that anything is really blue. A few people go there, but not many. If the blueness does exist, and you don't want to be a dualist, and you want to believe in existing physics, then you have to conclude that blueness is what the physics was about all along. We represented it to ourselves as being about little point-particles moving around in space, but all we ever actually had was mathematics and correct predictions, so it must be that some part of the mathematics was actually talking about blueness - real blueness - all along. Problem solved!
Except, it's rather hard to make this work in detail. Blueness, after all, does not exist in a vacuum. It's part of a larger experience. So if you take this path, you may as well say that experiences are real, and part of physics must have been describing them all along. And when you try to make some part of physics look like a whole experience - well, I won't say the m word here. Still, this is the path I took, so it's the one I endorse; it just leads you a lot further afield than you might imagine.
Next up, computation. Again, the basic criticism is simple, it's the attempt to rationalize things which makes the discussion complicated. People like to attribute computational states, not just to computers, but to the brain. And they want to say that thoughts, perceptions, etc., consist of being in a certain computational state. But a physical state does not correspond inherently to any one computational state.
There's also a problem with semantics - saying that the state is about something - which I will come to in due course. But first up, let's just look at the problems involved in attributing a non-referential "computational state" to a physical entity.
Physically speaking, an object, like a computer or a brain, can be in any of a large number of exact microphysical states. When we say it is in a computational state, we are grouping those microphysically distinct states together and saying, every state in this group corresponds to the same abstract high-level state, every microphysical state in this other group corresponds to some other abstract high-level state, and so on. But there are many many ways of grouping the states together. Which clustering is the true one, the one that corresponds to cognitive states? Remember, the orthodoxy is functionalism: low-level details don't matter. To be in a particular cognitive state is to be in a particular computational state. But if the "computational state" of a physical object is an observer-dependent attribution rather than an intrinsic property, then how can my thoughts be brain states?
We didn't have this discussion before, so I won't try to anticipate the possible defenses of functionalism. No-one will be surprised, I suppose, to hear that I don't believe this either. Instead, I deduce from this problem that functionalism is wrong. But here's your chance, functionalists: tell the world the one true state-clustering which tells us the computation being implemented by a physical object!
I promised a problem with semantics too. Again I think it's pretty simple. Even if we settle on the One True Clustering of microstates - each such macrostate is still just a region of a physical configuration space. Thoughts have semantic content, they are "about" things. Where's the aboutness?
I also promised to mention time and unity-of-consciousness in conclusion. Time I think offers another outstanding example of the will to deny an aspect of conscious experience (or rather, to call it an illusion) for the sake of insisting that reality conforms entirely to a particular scientific ontology. Basically, we have a physics that spatializes time; we can visualize a space-time as a static, completed thing. So time in the sense of flow - change, process - isn't there in the model; but it appears to be there in reality; therefore it is an illusion.
Without trying to preempt the debate about time, perhaps you can see by now why I would be rather skeptical of attempts to deny the obvious for the sake of a particular scientific ontology. Perhaps it's not actually necessary. Maybe, if someone thinks about it hard enough, they can come up with an ontology in which time is real and "flows" after all, and which still gives rise to the right physical predictions. (In general relativity, a world-line has a local time associated with it. So if the world-line is that of an actually and persistently existing object, perhaps time can be real and flowing inside the object... in some sense. That's my suggestion.)
And finally, unity of consciousness. In the debate over physicalism and consciousness, the discussion usually doesn't even get this far. It gets stuck on whether the individual "qualia" are real. But they do actually form a whole. All this stuff - color, meaning, time - is drawn from that whole. It is a real and very difficult task to properly characterize that whole: not just what its ingredients are, but how they are joined together, what it is that makes it a whole. After all, that whole is your life. Nonetheless, if anyone has come this far with me, perhaps you'll agree that it's the ontology of the subjective whole which is the ultimate challenge here. If we are going to say that a particular ontology is the way that reality is, then it must not only contain color, meaning, and time, it has to contain that subjective whole. In phenomenology, the standard term for that whole is the "lifeworld". Even cranky mistaken reductionists have a lifeworld - they just haven't noticed the inconsistencies between what they believe and what they experience. The ultimate challenge in the science of consciousness is to get the ontology of the lifeworld right, and then to find a broader scientific ontology which contains the lifeworld ontology. But first, as difficult as it may seem, we have to get past the partial ontologies which, for all their predictive power and their seductive exactness, just can't be the whole story.