One reason why the notion of the self comes in is that humans and animals could not cope with the world at all unless they saw things in terms of I. The notion 'I' belongs to te same group of notions as 'now', 'here', 'yonder', 'this', 'that', 'today', 'past', 'present', 'future', 'ago', 'hence'....What I would emphasize is that these words and the corresponding ideas have an irreplaceable importance, because they have a unique ability to guide action and emotion. If Adam Smith knows, 'An arrow gets to be fired through the window of Adam Smith's study on May 1 2004', he will have no idea whether precautions are called for, except insofar as he can also judge, 'I am Adam Smith', and 'Today is May 1 2004'. Otherwise Adam Smith might be anybody, and 2004 thousands of years into the past or future. These words therefore have a special action- and emotion-guiding force...
By a 'person' I mean someone who has psychological states and does things, by a 'thinker' someone who has thoughts. This having and doing can be summed up by saying that a person owns psychological states and actions. He or she also owns a body and bodily characteristics. A person is not just a stream of experiences and actions, but the owner of experiences and actions...
The meaning that I have ascribed to the word 'I', though vital, is a thin meaning, paraphrasable, for example, as 'the subject of this awareness', or 'this person'. But since 'I' does not refer to an entity separate from the embodied being that is rapidly acquiring a unique history, the reference of 'I' is a thick one. Moreover, the speaker's meaning on any given occasion may be much thicker than the strict meaning of the word itself. He or she may intend to draw attention to more or less of his or her personal history and circumstances and of his or her character as an embodied human being. As we pass beyond infancy, we tend to develop an autobiographical picture or pictures of ourselves. A thicker picture is employed in making decisions and in reacting emotionally. For decisions and emotional reactions may depend on one's being aware of oneself as a person with a certain standing, past history, culture, and aspirations. We thus build up a particular persona or identity, and this identity is often considered part of the self.
...what I have been emphasizing in this chapter is two things, the individual embodied owner and the owner's need to see himself or herself as me and me again. Given the familiarity of the first and the need for the second, the onus (of disproof that there is such a thing as self) should be on the person who attempta to deny that they correspond to reality.
from the chapter "The varieties of self and philosophical development of the idea"
Seneca Letters 24, 19-21
I remember you once treated the commonplace that we do not run into death suddenly, but proceed by degrees: we die every day....Just as it is not the last little drop that drains the water-clock, but what has flowed out before, so that last hour at which we cease to be does not on its own produce death; on its own it completes death. That is when we come up against it, but we have come for a long time.
...Hierocles...imagines the mind (dianoia) as being the center point of a set of concentric circles. He thus equates the mind with the self (each of us, hekastos hêmôn), which is entirely surrounded by circles. What draws the circles, to express the degrees of attachment it feels, is also a self (a given self, autos tis) and this is described not so much as identical with the mind as possessing it (heautou). Perhaps it is the composite of mind and body. The first circle outside the mind includes one's body, to which a sense of attachment is directed, and circles further out represent other people....
...The circles further out represent one's family, friends, fellow citizens, and foreigners. The context is ethical: one should learn to pull the circles inwards, so that one feels as much attachment to family as to one's own body, as much to friends as to family, and so on.
JL: There is a link here to what Appiah in Cosmopolitanism says about our obligations to strangers: our moral intuition suggests that it is right to care more for family than for friends, more for friends than for strangers. This idea is represented here by Hierocles as concentric circles, with family in an inner circle, friends on an outer circle etc. While Appiah may agree with the ethical move of learning to pull the circles inwards, I don't think he will agree that the goal is to feel as much attachment to friends as to family, and so on.
Hierocles, Elements of Ethics in Stobaeus, ed. Wachsmuth/ Hense, vol. 4, Florilegium, ed. Hense p. 671, lines 7-16:
Each one of us (hekastos hêmôn) is, as it were, entirely surrounded by many circles, some smaller, others larger, the latter enclosing the former on the basis of their different and unqeual relations (skheseis) to each other. The first and closest circle is the one which a given self (auto tis) has drawn as though around a center, namely his own mind (dianoia). In this circle is included (periekhetai) the body and anything taken (perieilêmmena) for the sake of the body. For it is practically the smallest circle and almost touches the center itself.
JL: The metaphor gives rise to a fine insight, or is it the other way round? The body circle "almost touches the center itself."