To play devil's advocate, why have a meta-care about the race if you will not be around to witness it? It's like planning your own funeral--you'll never know how it turned out. The whole game of evolution is a greedy contest of self-interest--why approach it selflessly with concerns about "the race?"
Normally, from instance to instance, each of us ceases to exist. A new person, under an illusion of being a "continuous" person and not merely one one in a sequence of related instantaneous persons, takes the place of the old person. And so it goes, from instance to instance. An instant from any given instance, the you of that instance will not exist. So why bother planning for those instances of you (who might remember being you, but are not you) that will exist (in their respective instances)?
That you that were you when "you" began reading this, is not the you that is you now. That former you left you his memories, but he cannot experience what you are experiencing now. So, why did he bother leaving any memories for you at all? Such bothering should have been pointless from his point of view, now that he is extinct. Yes? (...Unless he were under the illusion that he would somehow still exist, rather than the more-likely scenario of merely some creature like him, i.e. you, existing in his stead and who might be under the illusion that he is the same person as the person who kindly left the memories, the physical possessions, the bank account, the bodily health, etc.)
someone with a materialistic view of the world might also see the disintegration of a given corpus as the killing of a human being. The reassembled human might be considered a different sentience with the same memories as the original, as could be easily proved by constructing not just one, but several copies of the original and interrogating each as to the perceived uniqueness of each. Each copy constructed using merely descriptive data, but not matter, transmitted from the origin and new matter already at the destination point would consider itself to be the true continuation of the original and yet this could not logically be true; moreover, because each copy constructed via this data-only method would be made of new matter that already existed at the destination, there would be no way, even in principle, of distinguishing the original from the copies.
The problem of personal identity relates to change as applied to people. [...] The question is exactly why we call the old woman in 1998 the same person as that little girl in 1920.
It depends on what you define as "you". Honestly, I don't think the question is that interesting. It's like asking whether Linux 2.2.17 can be considered the same project as Linux 2.6.28. All we can say objectively is that they share a history and a name. Whether they are the same project is a subjective opinion.
The point is that -- given that you will in objective fact not exist tomorrow -- if you can find a reason to care about the impostor who tomorrow will take your place in society and pretend to be you, you should be able to apply the same reasoning to caring about your community as it might exist after you pretend to "die". That you are related to both is objectively confirmable.
In short: if you care about one, logically you should care about the other.
The "you" now shares a common history with the "you" a second ago. Other individuals do not. Your conclusion only follows if there is no objective difference between your past self and other individuals, and there clearly is.
I'm talking about the personal history an individual perceives through his memories. The history that connects the "me" of the now to the "me" of the past.
So, you would feel sensible in caring about (having altruistic feelings for) someone who could remember being you. Yes?
Would you feel sensible in caring about the future-you if (the present) you knew that he was going to have amnesia?
Me: "I'm going to drain my bank account and run wild, having a good time, because I know that tomorrow (and forever after) I won't remember having done such a dastardly thing to myself."
It's not about what _I_ feel sensible about caring about. We're talking about a hypothetical individual who cares only about versions of himself that share a common ancestor or descendant state.
If such an individual were given advanced knowledge of an irreversable amnesia, then logically he would commit acts that benefit him and cost the individual inhabiting his body in a day's time. So yes, it makes perfect sense.
But given the same circumstances, I'd behave differently, as I'm not a sociopath.