Question: Is it my brain that feels and thinks when I feel and think?
Argument A. Meat can't think. My brain is meat. Therefore, what thinks in me when I think is not my brain.
A in Reverse: What thinks in me when I think is my brain. My brain is meat. Therefore, meat can think.
The proponent of A needn't deny that we are meatheads. Of course we are. We are literally meat (and bone) all the way through. His point is that the res cogitans, that in us which thinks, cannot be a hunk of meat.
Both arguments are valid, but only one is sound. The decision comes down to the initial premises of the two arguments. Is there a rational way of deciding between these premises?
A materialist might argue as follows. Although we cannot at present understand how a hunk of living meat could feel and think, what is actual is possible regardless of our ability or inability to explain how it is possible. The powers of certain configurations of matter could remain hidden for a long time from our best science, or even remain hidden forever. What else would be doing the thinking and feeling in us if not our brains? What else could the mind be but the living and functioning brain well-supplied with oxygen-rich blood? The fact that we cannot understand how the brain could be a semantic engine, an engine productive of and sensitive to meanings, is not a conclusive reason for thinking that it is not a semantic engine.
It is worth noting that the reverent gushing of the neuro-scientistic types over the incredible complexity of the brain does absolutely nothing to reduce the unintelligibility of the notion that it is brains or parts of brains that are the subjects of intentional and qualitative mental states. For it is unintelligible how ramping up complexity could trigger a metabasis eis allo genos. Are you telling me that meat that means is just meat that is more complex than ordinary meat? You might as well say that the leap from unmeaning meat to meaning meat is a miracle. Some speak of 'emergence.' But that word merely papers over the difficulty, labeling the problem without solving it. You may as well say, as in the cartoon, "And then a miracle occurs." But then it's Game Over for the materialist.
Our materialist would do better to insist that unintelligibility to us does not entail impossibility. Our inability to explain how X is possible does not entail that X is not possible.
My response would be that while unintelligibility does not entail impossibility, it is excellent evidence of it. If you tell me that a certain configuration of neurons is intrinsically object-directed, directed to an object that may or may not exist without prejudice to the object-directedness, then you are saying something unintelligible. It is as if you said that .5 volts intrinsically represents 1 and .7 volts intrinsically represents 0. That's nonsense. Or it as if you said that a pile of rocks intrinsically indicates the direction of the trial. (See The Philosophizing Hiker: The Derivative Intentionality of Trail Markers.)
No rock pile has intrinsic meaning or intrinsic representational power. And the same goes for any material item or configuration of material items no matter how complex. No such system has intrinsic meaning; any meaning it has is derived. The meaning is derived either from an intelligent being who ascribes meaning to the material system, or from an intelligent being whose purposes are embodied in the material system, or both.
Thus I am rejecting the view that meaning could inhere in material systems apart from relations to minds that are intrinsically intentional, minds who are original Sinn-ers, if you will, original mean-ers. We are all of us Sinn-ers, every man Jack of us, original Sinn-ers, but our Sinn-ing is not mortal or venial but vital. Intrinsic, underived intentionality is our very lifeblood as spiritual beings.
So if the materialist says that the brain means, intends, represents, thinks, etc., then I say that makes no sense given what we understand the brain to be. The brain is a material system and the physical, chemical, electrical, and biological properties it and its parts have cannot be meaningfully predicated of mental states. One cannot speak intelligibly of a voltage drop across a mental state any more than can one speak intelligibly of the intentionality of synapses or of their point of view or of what it is like to be one.
Of course, the materialist can pin his hope on a future science that understands the brain in different terms, terms that could be sensibly attached to mental phenomena. But this is nothing more than an empty gesturing towards a 'possibility' that cannot be described except in the vaguest terms. It is nothing but faith, hope, and hand-waving.
There is also the dogmatism of the materialist who insists that the subject of thinking must be the functioning brain. How does he know that? He doesn't. He believes it strongly is all.
So I give the palm to Argument A: Meat can't think. My brain is meat. Therefore, what thinks in me when I think is not my brain.
I do not absolutely foreclose on the abstract possibility that there be thinking meat. For I grant that unintelligibility to us is not invincible proof of impossibility. But when I compare that vaguely described abstract possibility with the present certainty that matter as we know it cannot think due to the very unintelligibility of the idea, then the present certainty wins over the abstract possibility and over the faith and hope of the materialist.
If you need to pin your hopes on something, pin them on the possibility that you are more than meat.

In Does Matter Think? I wrote:
I now add that I am using 'thinking' in the broad Cartesian sense that covers all intentional or object-directed experiences; but I also hold that non-intentional experiences are unintelligible to us on the basis of current physics. My thesis is that, given what we know about the physical world from current physics, it it unintelligible that the phenomena of mind, whether intentional or non-intentional, be wholly material in nature.
I grant that what is unintelligible to us might nevertheless be the case. But if such-and-such is unintelligible to us, then that is a fairly good reason to believe that it is not possibly the case. A theological example may help clarify the dialectical situation. Christians believe that God became man. Some will say that this is impossible in the strongest possible sense: logically impossible, i.e., in contravention of the Law of Non-Contradiction. For what the doctrine implies is that one person has both human and divine attributes, that one person is both passible and impassible, omniscient and non-omnisicent, etc. One response, a mysterian response, is to say that the doctrine of the Incarnation is true, and that therefore it is logically possible. The fact, if it is fact, that the Incarnation is unintelligible to us — where 'unintelligible' means: not understandable as possibly true in a broadly logical sense – does not show that the doctrine is impossible, but that it is a mystery: a true proposition that we, due to our limitations, cannot understand.
A materialist can make the same sort of move in one of two ways. He could say that our understanding of matter at present does not allow us to understand how conscious experience could be wholly material in nature, or he can say that our understanding of matter will never allow us to understand how conscious experience could be wholly material in nature. Either way, conscious experience, whether intentional or non-intentional, is wholly material in nature, and falls entirely within the subject-matter of physics, whether a future physics achievable by us, or a physics which, though not achievable by us, is perhaps achievable by organisms of a different constitution who study us.
If I understand Galen Strawson's view, it is the first. Conscious experience is fully real but wholly material in nature despite the fact that on current physics we cannot account for its reality: we cannot understand how it is possible. Here is a characteristic passage from Strawson:
Strawson and I agree on two important points. One is that what he calls experiential phenomena are as real as anything and cannot be eliminated or reduced to anything non-experiential. The other is that there is no accounting for experiential items in terms of current physics.
In the Comments Vlastimil V. asked:
It is matter as understood by current physics. And yes, one can know a priori that matter so conceived cannot think or feel. Note that I am not saying that matter anyhow conceived can be known a priori to be such that it cannot think or feel. I admit the very vague, very abstract, epistemic (and perhaps only epistemic) possibility that God or some super-intelligent extraterrestrial or even human being far in the future could get to the point of understanding how an experiential item like a twinge of pain could be purely material or purely physical. But this is really nothing more than an empty gesturing towards a 'possibility' that cannot be described except in the vaguest terms. It is nothing but faith, hope, and hand-waving.
An experiential item such as a twinge of pain or a rush of elation is essentially subjective; it is something whose appearing just is its reality. For qualia, esse = percipi. If I am told that someday items like this will be exhaustively understood from a third-person point of view as objects of physics, I have no idea what this means. The notion strikes me as absurd. We are being told in effect that what is essentially subjective will one day be exhaustively understood as both essentially subjective and wholly objective. If you tell me that understanding in physics need not be objectifying understanding, I don't know what that means either.
As Strawson clearly appreciates, one cannot reduce a twinge of pain to a pattern of neuron firings, for such a reduction eliminates the what-it-is-like-ness of the experience. And so he inflates the concept of the physical to cover both the physical and the irreducibly mental. But by doing this he drains the physical of definite meaning. His materialism is a vacuous materialism.
Strawson frankly confesses, "I am by faith a materialist." (p. 69) Given this faith, experiential items, precisely as experiential, must be wholly material in nature. This faith engenders the hope that future science will unlock the secret. Strawson must pin his hope on future science because of his clear recognition that experiential items are incomprehensible in terms of current physics.
But what do faith and hope have to do with sober inquiry? It doesn't strike me as particularly intellectually honest to insist that materialism just has to be true and to uphold it by widening the concept of the physical to embrace what is irreducibly mental. It would be more honest just to admit that the mind-body problem is insoluble.