A certain hedonist cares greatly about the quality of his future experiences. With one exception, he cares equally about all the parts of his future. The exception is that he has Future-Tuesday-Indifference. Throughout every Tuesday he cares in the normal way about what is happening to him. But he never cares about possible pains or pleasures on a future Tuesday... This indifference is a bare fact. When he is planning his future, it is simply true that he always prefers the prospect of great suffering on a Tuesday to the mildest pain on any other day.
We can judge such a preference to be irrational because it makes arbitrary discriminations. It is ad hoc, and fails to treat like cases alike. A more coherent desire-set would appreciate pleasure on future Tuesdays as for any other day.
Parfit also discusses "Within-a-Mile-Altruism". Rather than caring about the welfare of others in his general community, the Within-a-Mile Altruist cares only about those who are located within one mile of him. One step further, and he feels indifferent to their suffering.
I've discussed similar arguments from Michael Smith here. This leads to the core argument of my essay, 'Why be moral?':
We have already established that self-interested reasons would force the amoralist to develop an intrinsic appreciation of at least some other people as ends in themselves. But it would seem arbitrary to recognize only some people as having intrinsic worth or even agent-relative worth to him. We can ask the relativistic amoralist why others do not also have worth to him. It seems plausible to hold that his overall desire set could be made more unified and coherent by adding in a more general desire for human well-being. This would contribute to explaining and justifying the more specific values the amoralist holds in valuing himself and his friends. We thus have rational grounds to criticize his desire set, in that it fails to exhibit such a degree of internal coherence. Given the rational pressure towards coherence, we may thus conclude that even the amoralist has reason to care about morality.