With all this, we have come to a more detailed definition of an NCC. The general case is something like the following:
An NCC is a minimal neural system N such that there is a mapping from states of N to states of consciousness, where a given state of N is sufficient, under conditions C, for the corresponding state of consciousness.
The central case of the neural correlate of the content of consciousness can be put in more specific terms:
An NCC (for content) is a minimal neural representational system N such that representation of a content in N is sufficient, under conditions C, for representation of that content in consciousness.
One might also give a general definition of the NCC for an arbitrary phenomenal property or for a phenomenal family, but I will leave those aside here.
The "conditions C'' clause here represents the relevant range of cases, as discussed above. If the reasoning above is on the right track, then conditions C might be seen as conditions involving normal brain functioning, allowing unusual inputs and limited brain stimulation, but not lesions or other changes in architecture. Of course the precise nature of conditions C is still debatable. Perhaps one could make a case for including a limited range of lesion cases in the definition. In the other direction, perhaps one might make a case that the requirement of correlation across brain stimulation or unusual inputs is too strong, due to the abnormality of those scenarios. But I think the conditions C proposed here are at least a reasonable first pass, pending further investigation.
Of course, to some extent, defining what "really'' counts as an NCC is a terminological matter. One could quite reasonably say that there are multiple different notions of NCC, depending on just how one understands the relevant conditions C, or the matter of necessity and sufficiency, and so on; and not much really rests on which of these is the "right" definition. Still, we have seen that different definitions give very different results, and that many potential definitions have the consequence that systems which intuitively seem to qualify as an NCC do not qualify after all, and that NCC hypotheses put forward by researchers in the field could be ruled out on trivial a priori grounds. Those consequences seem undesirable. It makes sense to have a definition of NCC that fits the way the notion is generally used in the field, and that can make sense of empirical research in the area. At the same time we want a definition of NCC to be coherent and well-motivated in its own right, such that an NCC is something worth looking for, and such that the definition can itself be used to assess various hypotheses about the identity of an NCC. It seems to me that the definition I have given here is at least a first pass in this direction.
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Have you ever been envious of people who seem to have no end of clever ideas, who are able to think quickly in any situation, or who seem to have flawless memories? Could it be that they're just born smarter or quicker than the rest of us? Or are there some secrets that they might know that we don't?