Parfit thinks we need an absolute proof for goodness because humans have only desires. But lots of science shows that human beings also have many inborn moral instincts, such as for fairness, group loyalty, and the concern for the well-being of others. See, for instance, Larry Arnhart's book, Darwinian Natural Right.
The real problem is how you make society such that inborn desires and moral senses lead to the the best oucomes.
To a philosopher like Parfait, our inborn desires and instincts are beside the point, though. If we do something "altruistic" because it gives us a nice warm fuzzy feeling, it isn't really an altruistic act. One could ask, would you still do it if you didn't get the fuzzy feeling, and if the answer is no, you were clearly just acting out of hidden self interest. Only if someone else's suffering is in and of itself reason to alleviate it was such a bona-fide altruistic act.
You also, of course, have the problem that you might find ways of giving yourself that warm fuzzy feeling without doing something good, and there's sort of the innate problem with desire-based morality. Parfit's absolute morality has the practical advantage that it's tied to the "real" concept of good by definition (we think), rather than by the happy accident of some genetic wiring.
I strongly disagree. As human beings, we have a moral obligation to make life good as it can be, and the only way we can do that is to understand people"s basic motives and try to use them to motivate good behavior. Do you really disagree?
Parfit's solution of a single absolute moral principle is simply not workable as a way of getting people to behave well. Again, do you really disagree? The reason he tries for it is he has a greatly distorted view of human nature. As the article say, he thinks that the human moral evalution that cruelty is wrong is "just a psychological fact—flimsy, contingent, apt to be forgotten." No, the prohibition against cruelty is a permanent part of human nature, the problem is that we have many other drives, and circumstances may favor them.
Instead of coming up with useless principles, what we need to do is understand in detail why people behave in good or bad ways. That is what, for instance, Aristotle did in his Ethics, and Smith in his Theory of Moral Sentiments. Let me add that Parfit is such a profoundly odd person that I am pretty sure his understanding of human nature is quite poor, and so he is simply the wrong sort of person for this job.
The real problem is how you make society such that inborn desires and moral senses lead to the the best oucomes.