When people use the word "consciousness", they can be referring to many things. At a simple level, they could be referring to being simply awake, or having some awareness of the world. At a more complex level, they could be discussing awareness of one's own self. But there is another thing people talk about when they speak of consciousness-the ineffable sense of what it is like to be oneself. It seems reasonable to most people that the human brain should be capable of dealing with waking, as well as the harder task of thinking about one's own cognition.
However, it is less popular to think that the brain can produce this intangible feeling that we can only really observe in ourselves. Many people believe that this feeling will continue after death has taken our fleshy brain from us. Some people believe that the scientific study of consciousness will progress better if we treat consciousness as a fundamental property, something which cannot be broken down into something simpler, such as the biological and chemical processes underlying brain function (much like electric charge became seen to be a fundamental property in the 19th century,).
The neural correlate of consciousness!
A cool paper by Naotsugu Tsuchiya and colleagues discusses the search for correlates of consciousness with and without self-report. Self-report can be combined with clever methods used to make the same sensory input, depending on context, available or unavailable to awareness. Continuous flash suppression involves presenting one eye with a flashing stimulus and the other eye with a more constant stimulus. The flashing stimulus can lead to the other stimulus (which, remember, doesn't change) slipping out of consciousness, even though the sensation should still be there.
So let's say you're a research participant being subjected to continuous flash suppression. The experimenters need you to tell them what you're consciously perceiving, in order for them to observe what is happening in your brain as the subjective experience changes. However, in order to self-report on what one perceives, one needs to draw on cognitive processes other than "raw" consciousness. If you have to say what you see, you're using language processing. If you have to press a button when you see the white elephant, you need to use motor processing. Control conditions have to be carefully designed!
So there are a number of caveats about self-report. Methods that do not use self-report are not perfect either though-it's harder to tell whether the thinker is really (self-)aware of the information they're processing. However, what's really neat about a lack of self-report is that it can be applied in contexts where self-report may be difficult or impossible, for example in babies or in animals.
Of course, you might object that much of this is just about the not-so-hard problems of how we are aware or self-aware, not about what consciousness is like. I think this takes us from the methodology we use to study consciousness, to our account of what "ineffable" consciousness is about. Our subjective sense of what experience is like involves combining a wide variety of sensory inputs (not to mention memories, body schemas etc. etc.) into a unitary experience. The binding problem poses the question of how we perceive our experience as a unified stream of consciousness.When we talk of a "neural correlate of consciousness" it's probably too simple to think that one part of the brain can "bring it all together". In order to integrate various sensory inputs together we have to combine sensory processing occurring in distinct regions of the brain. Gerald Edelman has suggested that the thalamus plays a key role, as it carries information from the senses to various parts of the cortex. It is the re-entrant nature of these connections that may help to explain the process (as opposed to the place) where experience comes together to make up a unitary sense of consciousness.
You may hold fast to the idea that your experience cannot be just the product of your brain (and its interaction with the rest of your body). But if so, let me pose this question: just how complex is your conscious experience really? Are you sure it is more complex than the interactions of the trillions of neurons in your brain? If you or someone else really understood how it all worked, are you so confident that they might not be able to explain your lived experience, with no need to discuss anything outside the biological and chemical processes within you?
Tsuchiya, N., et al. (2015). No-report paradigms: extracting the true neural correlates of consciousness. Trends in Cognitive Sciences, 19(12), 757-770.
Where does the mind begin and end?
A review of "Intuition pumps" by Daniel Dennett