Mr. Nicholas Humphry https://en.wikipedia.org/wiki/Nicholas_Humphrey was asked whether consciousness is an illusion and he replied: "Yes", that he believed it was. Nicholas is a self proclaimed Materialist, and a cognitive scientist. As such, it begs the question: is his belief in the concept of 'illusion' self-refuting, ironic, and paradoxical? The philosophical reason why this belief may be paradoxical is because the definition of 'illusion' in itself, is a 'metaphysical phenomenon' (or is it)?
Frankish talks about weak and strong illusionism re consciousness. Strong illusionism claims phenomenal conscious experience does not exist. That looks paradoxical because the having of a belief that phenomenal experience doesn't exist is itself a phenomenal experience.
Weak illusionism claims that phenomenal experience exists, but isn't what we think it is based on our own introspection. But it seems to me it's impossible to be mistaken about the content of our own experience, because the experience and its content are the same thing. To have a particular conscious experience (eg seeing a red apple) is to have knowledge of the content of that experience. Hence experience is directly known, and there is no gap between the experiencing and having knowledge of the experience where error can occur.
So Illusionism is as daft as it sounds.
That doesn't mean our experiences give us perfect direct knowledge about the world 'out there'. We can have optical illusions for example, because conscious experience is a flawed and limited representaion we create of the actual world. Because we are flawed and limited critters, who evolved for utility, not perfectly perceiving and understanding the everything about the actual world. (Our conscious representations have to be good enough to generally enable us to survive and reproduce). So you might as well say seeing a table as solid is an optical illusion, as it's mostly empty space, but seeing it as solid works for us.
One ancillary question to the foregoing is, how does he use logical concepts to arrive at the conclusion of consciousness being illusionary, I wonder? Well, this is one possibility:
2. Philosophically, does the explanation of consciousness itself break the rules of formal logic (a priori) and other logical axioms such as Bivalence and LEM? I would submit yes it does. It does by virtue of the infamous 'driving while daydreaming' scenario where both the conscious and subconscious mind is perceived to be operating independently of each other. This suggests that consciousness cannot be explained/described logically in the formal sense.
Brains are the body's physical command and control centre - stimuli come in, the brain's subsystems interact, and motor functions are activated. Some parts of that manifest correlated conscious experience, some don't, and of those that do some get the spotlight of attention or focus, some don't. This makes evolutionary sense, because if every neural interaction was conscious and had equal focus, it would be a confusing cacophanous overload and practically useless. So again in evolutionary terms, the way this works makes sense, there's no logic problem there.
Alternatively, should one be also prepared to embrace other absurdities about the perceptions of reality (Subjective Idealism https://en.wikipedia.org/wiki/Subjective_idealism ) and conclude that consciousness itself (which is apparently 'logically impossible' by formal definition standards, yet exists) is all that we know exists?
It's all we know exists for certain, but if we assume the content of our conscious experience is a representation of an actual world out there, it works so well as to make no difference to us.
Other philosophical concerns resulting from the limitations of 'pure reason' might include the questions about the paradoxical apperceptions of reality. Is "I think therefore I am" proof of a reality that exists only in one's mind? How can logic and rationality save us from this nightmare?
https://en.wikipedia.org/wiki/Cogito,_ergo_sum
It can't.
But then if we are flawed limited critters who evolved to perceive and reason on the basis of utility rather than perfect knowledge, we shouldn't expect it to.
There are genuine paradoxical headscratchers when it comes to the mind-body relationship, which our notions of logic (rooted in and abstracted from our physicalist understanding of how the world works) struggle to make sense of. But I don't think you've nailed the nature problem down here.