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.
Operant conditioning. If I pull a lever and someone in Antarctica gets struck by lightning, nothing happens to my brain. If I pull a lever and I get struck by lightning, I instantly receive a strong desire not to let that happen again. The fact that nobody but me is conditioned by my experiences is what makes me me. If I suddenly began having the experiences of another person as well as my own, that person and I would both become me; if I accidentally wandered into a giant helium balloon and died, nobody would be me. If I for some reason developed anterograde amnesia, me would have a very short lifespan; there would be no reason to care about my long-future self any more than any other person.
Operant conditioning is an excellent answer as to why you do care more about your future self than a random future person. But the original post asks why should you care more.
Of course, it's open to you to argue that there's less room in between "should care" and "do care" than most people think. Perhaps when it comes to both whom and when we care about, there isn't much room at all.
Even going by what people do care about, however, I doubt that anterograde amnesia generally leads to disregard of one's next-day fate. Should it?