I'm going to pull my parenthetical about spells of unconsciousness out in a separate comment, because the point seems to have been lost in the course of the discussion:
DanArmak, you seem to propose that the key process which defines the identity of a person at one time with a person at the other time is the thread of consciousness trailing through spacetime from one to the other. How does your model deal with human beings - individual human organisms! - which undergo literal loss of consciousness? I do not refer to sleep, but to the actual shutdown of conscious perception, such as occurred to Jo Walton (papersky) when she hit her head and (I have heard) to many people under general anesthesia. In these cases, the persons describing their memories explicitly state that there is a finite period of time during which no conscious recollection occurs. Does that imply that the speculative fiction writer named Jo Walton living in Montreal on February 20th, 2006 is a different individual than the speculative fiction writer named Jo Walton living in Montreal on February 22nd, 2006? If not, why not?
To address the loss of consciousness scenario: I can't speak from experience, and as I said, my theory is not formal and strict and provable enough to be sure of things outside my experience.
The basic problem here is discontinuity. If the loss of consciousness is brief enough (a fraction of a second) and does not affect my future mental processes, it seems likely "I" will continue to exist. Any other boundary (of length and severity of unconsciousness) would be arbitrary, and so unlikely.
But my experience is discrete. I always have exactly one ...
From the dawn of civilization humans believed in eternal life. The flesh may rot, but the soul will be reborn. To save the soul from the potential adverse living conditions (e.g. hell), the body, being the transient and thus the less important part, was expected to make sacrifices. To accumulate the best possible karma, pleasures of the flesh had to be given up or at least heavily curtailed.
Naturally the wisdom of this trade-off was questioned by many skeptical minds. The idea of reincarnation may have a strong appeal to imagination, but in absence of any credible evidence the Occam’s razor mercilessly cuts it into pieces. Instead of sacrificing for the sake of the future incarnations, a rationalist should live for the present. But does he really?
Consider the “incarnations” of the same person at different ages. Upon reaching the age of self-awareness, the earlier “incarnations” start making sacrifices for the benefit of the later ones. Dreams of becoming an astronaut at 25 may prompt a child of nine to exercise or study instead of playing. Upon reaching the age of 25, the same child may take a job at the bank and start saving for the potential retirement. Of course, legally all these “incarnations” are just the same person. But beyond jurisprudence, what is it that makes you who you are at the age of nine, twenty five or seventy?
Over the years your body, tastes, goals and the whole worldview are likely to undergo dramatic change. The single thing which remains essentially constant through your entire life is your DNA sequence. Through natural selection, evolution has ensured that we preferentially empathize with those whose DNA sequence is most similar to our own, i.e. our children, siblings and, most importantly, ourselves. But, instinct excepted, is there a reason why a rational self-conscious being must obey a program implanted in us by the unconscious force of evolution? If you identify more with your mind (personality/views/goals/…) than with the DNA sequence, why should you care more for someone who, living many years from now will resemble you less than some actual people living today?
P.S. I am aware that the meaning of “self” was debated by philosophers for many years, but I am really curious about the personal answers of “ordinary” rationalists to this question.