Of course, the material self flies in the face of the long-standing notion of a self as an immaterial thing that temporarily resides in the body and will endure after the body has turned to dust. It is easy to understand why someone would cling to this everlasting, immaterial self, but hard to understand how any scientist or scientifically-informed philosopher of the 21st century can seriously entertain it.
As far as I know, Peter Hacker is not an immortalist, but he demurs from the idea that only material things exist. Is Beethoven's Ninth Symphony not a thing? he muses. Well, yes, I'd respond, but Beethoven's Ninth is embodied in much the same way as a self is embodied. If there were no paper scores, or neuronally-encoded memories of the music, or modulated electromagnetic radio waves (broadcasts of ochestral performances) speeding away from Earth -- that is to say, no physical embodiments of Beethoven's Ninth, then the Ninth would not exist.
Have I understood Hacker rightly? Darned if I know. Consider a typical paragraph of his review:
The second half of Selves is dedicated to fundamental metaphysics that purports to show that there are such things as physical selves thus conceived. They in fact consist of a synergy of neural activity which is either part of, or somehow identical with, the synergy that constitutes an experience as a whole. So the thin concept of a subject of experience is of a process-stuff in the brain. But this suffices for being a sesmet [subject of experience-as-a-single-mental-thing]. Hence there is an indefinite plurality of temporally passing selves. The thicker notion of a self as a persistent mental thing is merely a construction out of such a "gappy" plurality. And both thin and thick notions are, of course, distinct from the human being, the person, as a whole. So, contrary to all the evidence from the use of natural language, the pronoun "I" is polysemic -- at least in the hands of a fundamental metaphysicist.If you know/understand what this means you are smarter than me.
Let Strawson, Hacker and their philosophical colleagues natter on about what constitutes a self. Several millennia of philosophical speculation have added little to our knowledge/understanding of self. For myself, like everyone else, I have an acute awareness of my own selfhood. How it arises from the electrochemistry of the brain I do not know. I'll bide my time as the neuroscientists and AI (artificial intelligence) researchers plug away in their laboratories, holding fast to Ockham's materialist razor, confident that a generation from now we will know more empirically -- and therefore understand more -- than we do today.