What is the relationship between the two expressions?
When a welfarist talks about welfare he talks about things that are good "for" a person or a certain kind of creature, as opposed to good sempliciter or from the point of view of the universe:
"In the case of human beings the idea that we should promote their good surely owes at least part of its appeal to the fact that we can do so for their sake or on their behalf. In doing good for someone we are therefore not merely making the world a better place but also doing something for that particular person." Sumner "Welfare, Happiness and Ethics p. 211".Sumner is using "good for" and "for the sake of", to express different but related ideas:
- "individuation": when promoting people's good involves the virtue of benevolence, we are doing something for a specific individual, not for the sake of a more perfect universe.
- "benefit": the particular individual in question must be intended to benefit from my action; he must be intended to be made better off by it; (and maybe) this is to say that we must intend to augment his well-being
- "sake": the action must be done for the sake of the individual or something regarding him; not with a view to some further end.
Some people argue as if they presuppose that doing something for the sake of someone else implies doing something that is in that person's interests. I don't believe that this can be seen as an uncontroversial grammatical fact. The expression "for the sake of X" can cover different meaning; what it entails is a focus on a fact about X as the source of the reasons for this action, nothing further than that. Since very often, possibly always, when we value a person's life intrinsically we take that person's interests into account, we end up using the expression "doing somthing for the sake of X", where X is a person, to mean doing something that furthers his interests, doing something with a view to that person's good or to her advantage. Of course, folk theory regarding the grammar of "for the sake of" reflects common usage. So we shouldn't think of our intuitions about the "grammar" of "for the sake of" as carrying a special value.
Some people argue as if doing something for somebody's else sake (or for him) implies doing it with a view to improve their well-being. (This claim is different from the former since it is controversial that a person's best interest coincides with what furthers his well-being most.) But this must not be so. Doing something for the sake of someone else means doing something in function of someone else, that is, recognizing that person or a state of that person as the final value providing reasons for the action in question. (This also appears from the use of expressions such as "for the sake of the argument".) If one sticks to so-called "grammatical intuitions" doing something for the sake of another person is fully compatible with doing it with the aim of improving his level of perfection. (Notice that I do not believe that there are such things as "conceptual" or "grammatical intuitions", detached by what I prefer to call "normative claims.")
Of course, if you improve a person's level of perfection "for her" you must not see your action (simply) as a way to contribute to the perfection of the universe. This claim, that improving a person's level of perfection (as opposed to his well-being) does entail treating that person as a means (to improve the perfeection of the universe) is, even on the face of it, a substantive ethical claim about treating people as ends. This is the claim that welfarists shoud refuse, not a conceptual claim about the meaning of "doing something for the sake of someone else" or about the meaning of "good for."