What are neural correlates neural correlates of?

How should neuroscience research about social-psychological phenomena identify its objects of inquiry, so as to develop adequate experimental paradigms and tasks to elicit them, and then look for their neural correlates? How should it go about conceptualizing objects such as morality, empathy, art, love, creativity, or religious belief? If a neuroscientist is after the neural correlates of X, how can she tell X from non-X? This is an important...