Is the “Self” real? What’s the nature of the sense of being that remains when parts of the psyche fall away?
The answer depends on how you define “Self.” I use that word to refer to the central “I” that’s presumed in Western psychology and philosophy (and everyday usage) to be the owner of experiences and agent of actions, and which is defined and constituted by three attributes: unification (there’s just one “I”), permanence (the “I” stays the same, things happen to it but it doesn’t change), and independence (the “I” is just there, an innate part of the psyche, not created by anything, and fundamentally not dependent on anything [other than a brain] for its existence).
The facts that these three attributes that presumably constitute an “I” – unification, permanence, and independence – cannot be found in one’s own experience, nor in the neural processes that underlie I-related activations or representations in the brain. The actual experience of “I” is made up of parts (not unified), continually changing (not enduring), and affected by many factors (not independent; much the same has been seen in neuroimaging studies. (Check out these two papers: Is Self Special? and What Is Self-Specific?)
To use the language of Buddhism, the apparent “I” is empty: without substantial, essential nature; both phenomenologically and ontologically, the presumed “me, myself, and I” is empty. If you like, check out my book, Buddha’s Brain, whose last chapter is about this subject.
In general I think that we can have and value all sorts of experiences of witnessing, integration, beingness, spacious awareness, etc., while also recognizing that these experiences (and their dynamic neural substrates) are compounded, transient, and dependently arising . . . and thus empty of essence. Like others I’m sure, I’m leery of reifying or substantiating dynamic and insubstantial processes – even vital ones, such as the executive functions, subjectivity (ipseity), or the encompassing awareness that remains when the “parts” step back – into an entity, a being, a self . . . because this is when trouble and suffering begins, when we identify with and try to protect and glorify such an entity.