What is this thing called "self"? -- this inner image of "Ben Goertzel" that I carry around with me (that, in a sense, constitutes "me"), that I use to guide my actions and inferences and structure my memories?
It is nothing more or less than a habitual pattern of organization in the collection of patterns that is my mind ...
... which is correlated with certain habitual patterns of organization in the collection of patterns that is the mind of the portion of society I habitually associate with.
My "self" keeps telling itself that it is the mind associated with my body ... and in trying to make this story true, it usually succeeds to some degree of approximation (though rarely as high a degree as it thinks it does!) ... but ultimately it is not the mind associated with my body, it is just a portion of that mind which has some overall similarities to the whole.
Thomas Metzinger, in his wonderful "neurophilosophy" book Being No One, uses the intriguing term "phenomenal self" ...
Seeing the self as the self-constructed dynamical phenomenon it is, is one of the main insights that commonly results from meditation practice or psychedelic drug use.
The attachment of primal awareness to self is part of what characterizes our deliberative, reflective consciousness.
Self wishes and acts to preserve itself -- this is part of its nature ... and is also part of the intense aversion many humans feel toward death, and the intense drive some humans feel for immortality.
If the whole mind wants to be immortal, it will be partly satisfied by spawning children, writing books, and so forth -- things that extend the patterns constituting it further through time. (Woody Allen's charming quip "I don't want to be immortal through my works -- I want to be immortal through not dying" notwithstanding!)
If the self wants to be immortal, it doesn't really care much about offspring or literary works -- it just wants to keep churning along as a self-creating, self-persisting dynamical subsystem of the mind.
It is unclear the extent to which transhuman minds will have "selves" in the sense that we humans do. Part of "human selfness" seems to be an absurd overestimation, on the part of the self, of the degree to which the self approximates the whole mind. If this overestimation were eliminated, it's not clear how much of "human selfness" would be left. Some of us will likely find out ... ( -- although, the issue of whether it will be "us" that finds out, or some descendant of us, is precisely the question at hand!)