Consciousness is not what it thinks it is
Thought exists only as an abstraction
The self does not exist
I'm probably going to regret doing this because it always turns out rather long winded. I'm not a professional in philosophy, psychology or the neurological sciences, and if you have done any reading of recent work in the above fields (especially Daniel Dennett) then none of this will be new to you and you'd best go away as I'm likely to either bore the pants off you or irritate you with my gross oversimplifications (I'm not writing a 500 page book!)
For the rest of you here goes:
Thought is an abstraction in the sense that it is not a physical object. It is not even an attribute of a static physical object, it is in fact a process. Actually its only representation in the physical world is as spatio-temporal firing pattern of a collection of interconnected neurons. Obviously this doesn't do justice to its subjective qualities. But that is because the subjective meaning of that firing pattern exists at a higher level of abstraction than physical reality - what computer scientists call a "higher level of implementation".
Simple analogy: say you have a software program implementing a simulation of a bouncing ball , running on computer hardware. The bouncing ball has its physical reality manifestation in the spatio-temporal pattern of voltage changes within the computer's microcircuitry. But if you were to scrutinize those voltage change patterns directly it would be difficult to see the bouncing ball, because the ball-like qualities and the bounciness only appear at a higher level of abstraction, in a simple virtual world of its own which is implemented in software running on top of a hardware computer.
Now suppose the software program you are running is a program implementing a simulation of another computer. You might be running the program on a Cray supercomputer but in this case the program itself is an simulation of the hardware of a Pentium IV system. Now you load a linux kernel compiled for the Pentium IV into the simulation and then you load your bouncing ball simulation into that. The Bouncing ball is at a higher level of implementation than the Pentium (which is only a simulation) which is in turn at a higher level of implementation than the Cray, which is implemented in physical hardware.
In the same way your thought, your consciousness, exists at a higher level of implementation than the physical brain that resides in your skull.
OK, that was long-winded, but this does actually mean something. We would avoid expressing programs in voltage patterns or machine code because it would be too hard to understand its meaning, so instead we use high level programming languages to frame the very abstractions we seek to express in a more direct manner. But even expressed thusly, our programs (in general) do not directly express the real world, but a set of abstractions which bear a simple correspondence to features of the problem domain. And these abstractions may be viewed as structures inhabiting some sort of abstract space (I use "space" here in the mathematical sense) and which are real enough when viewed entirely within the context of that space.
Likewise the semantic contents of our thoughts (their subjective meanings) are only abstract high-level representations of certain aspects of reality. But again these abstract representations can be seen as structures and processes of a separate abstract space having its own subjective reality.
Consciousness is not what it thinks itself to be, because most people behave as if they believe their consciousness to have its own existence, independent of the world of physical matter. As if it is a thing, rather than a process. This is quite an obvious mistake when you consider just how contingent consciousness really is on (1) whether you are awake or asleep (2) your freedom from injury to various parts of the brain and (3) whether you are alive or dead. All of these things can determine whether consciousness is present, and the last two will determine whether it can ever return when it is not.
Consciousness may be an abstract thing, but as far as we can tell it does depend completely upon the continuing existence and health of the wetware it is implemented upon! (However, not everybody agrees that this is certain, go visit Hans Moravec's web pages or read Greg Egan's fascinating novel Permutation City for explorations of what this might mean).
Either way, I am led ineluctably to the conclusion that the self does not exist. IMHO those consciousness researchers looking for an explanation of purely subjective qualities of consciousness are wasting their time trying to understand their physical underpinnings (what they call the "neurological correlates" of consciousness). They seem to expect to find some magical brain structure that is responsible for the mysterious subjective quality that we call consciousness, sense of self, being self-aware etc. I do not think they will find it because they are actually looking for something that isn't even really there. We are alive, and we can observe and we can compute, and we have feelings and emotions and moods which are governed mostly by biology and to some extent by conditioning. But that's all, and in each of these categories exist numerous examples for which neurological correlates have already been conclusively identified.
The missing element that is the focus of consciousness researchers on the fringe of sensible science is the question of qualia, or subjective experience of what a thing is like. This search might be exemplified by a simple question like "Why does the colour purple seem to have a subjectively purplish quality?". But given that we can't actually share states of consciousness directly, I can never even know what "purple" feels like in your mind. For all I know it looks to you how green looks to me. Or maybe it feels to you like a sensory mode I've never experienced.
My point is, these things have no independent existence outside of our own individual heads. From an external point of view an individual qualium is only significant as some sort of internal label or meter, and its subjective qualities are beside the point.
There is a clue to the answer, I think, in a particular lesson that many people who think for a living are likely to learn eventually. It might be expressed as something like this:
If a question is perceived as very hard to the extent that people can't even seem to agree on what the question even means, then the question itself may be nonsense and the terms of reference in which the question is framed may not be logically self-consistent.
I believe that is the case with the search for self. We have convinced ourselves (and only relatively recently, some argue) that this magical being exists inside us. But like a horse designed by a committee, it has had so many different things shoehorned into the definition that there is no single comprehensive definition. Moreover, of most of the things on the list there isn't even any evidence for their existence other than (a) our own subjective experience, which must vary from person to person, and (b) the cultural expression of the same vague idea, with which we are indoctrinated all our lives. And behavioural psychologists are quite content to dispense with the notion altogether because it makes no difference to the results.
Mathematicians practice absolute freedom. -- Henry Adams