Reasons For NCCs
One obvious reason for holding that NCCs exist is empirical. Some physical events are found to correlate with consciousness in a way that other physical events are not. In almost all cases, these physical events are neural events. If I have a pain in my arm due to an injury there, then there are typically three events: the feeling of pain, some particular neural activity, and the actual physical damage in my arm. To stop the feeling of pain, I might heal the damage to my arm. How'ever, even if I do not heal it, I can stop the pain by stopping the neural activity being stimulated by the damaged arm. Indeed, even if I heal my arm, but that particular neural activity continues, I wall feel (phantom) pain. This may be taken to show that, if there is a certain kind of neural activity, then there is the feeling of pain, no matter whether my arm is healed or injured; but if there is no such neural activity, then there is no feeling of pain. This neural activity is an NCC.
NCCs also play an important philosophical role for physicalists. They hold to a physicalist view of the world. One principle of such a physicalist worldview' is that the world, along with being physical, is causally closed. The world is causally closed if and only if every physical event is caused by another physical event. No physical event is caused by something non-physical, such as an ectoplasmic spirit. If an egg rolls off a table, it is because something physical made it roll. If physicalism is true, and there is causal closure, it is never the case that an egg rolls because it was pushed by a ghost.
However, some theorists argue that consciousness is not fully explicable in terms of physical and biological laws, including neural activity. In particular, there is the Hard Problem of consciousness, the problem with reconciling the subjective, phenomenal feeling of consciousness wdth physical events correlated with it. This problem motivates some theorists to hold that physicalism must either be false or expanded to include conscious states (e.g., Freeman 2006).