What is a Self?

What is a self or what is most essentially me? What persists in a person during the course of their life which enables them to refer to a person 20 years in the past as themselves? I believe that most people have an intuition that there is a center of consciousness or some such thing which persists through time. That center of consciousness is that thing which is most basically the person. Even if a person's moral fabric dramatically changes over a period of time we still want to say that it is the same person, the same center of consciousness. So, the particular person survives dramatic changes to their character over time because of the persistence of the center of consciousness (I speak of normal cases).

To help illustrate the intuition that I am referring to I contrast dramatic character change with death. When a person undergoes dramatic moral or character change we say that the person prior to the change is still the same person (numerically identical rather than qualitatively identical) as the person after the change. The person prior to the change does not cease to exist (so we think) to make room for the different person that results after the change. If we believed that the person who undergoes dramatic character change ceased to exist or was not the same person after the change we would react to character change much in the same way we react to death. We would feel an intense sense of loss, that a person we knew is gone and will be seen in this life no longer.

I believe we have a second, contradictory intuition. We believe that if all of a person's personality characteristics and moral fabric were removed from them they would no longer be the same person (despite the persistence of a center of consciousness). A totally blank consciousness, an empty subjectivity staring out into the world is not the same as me or you. We believe then that a person is both nothing over and above the center of consciousness that they are (otherwise the person could not persist through time/endure changes in personality characteristics) and that a person is more than their center of consciousness. Where then is the self in all of this? What actually is me and how do I persist through time?

What happens as I change over time? What connects me with who I was yesterday or 10 years ago? Once again, our intuition says something like a center of consciousness in which our personality characteristics adhere is what persists, but we have already seen how reducing the self to a center of consciousness goes against our other intuitions concerning what makes a person themselves. It would seem that we have no language for talking about what it means most basically to be oneself. Whatever process gave rise to language did not produce terms to adequately talk about self-hood. Whatever I am, whoever I am is ineffable.