If something is morally good, then everybody has a moral reason to prefer it, isn't it? But if Lucretia has a moral duty to do something, then, philosophers say, Lucretia -- and not necessarily anybody else -- has a moral reason to do it. Does that make sense: if it is a moral duty, it should give moral reasons to everybody, shouldn't it?

Suppose we accept your proposal that if something is morally good, then everybody has a moral reason to prefer it. It doesn't follow though, at least without additional argument, that if everyone has moral reason to prefer something, everyone has a moral duty to do that thing. For there may be moral reasons incumbent only on some rather than on others. If Lucretia has a child, I may concede both that her child's being well fed is morally good and that everyone has a moral reason to prefer her child being well-fed, but it may not be true that everyone (me included!) has a moral duty to feed her child. For instance, it may be true that I don't have such a duty precisely because Lucretia does have such a duty — she being her child's mother, she has a special duty to ensure that she is well fed that I (and others) have. Such special duties seem relatively common: A firefighter has a duty to rescue someone that I do not. I have a duty to educate my students that the firefighter does not. And so on. There is, in other words, a logical gap between something's being morally good or preferable from an impersonal point of view and it's being everyone's duty to bring that good about. That said, the intuition that seems to reside behind your thinking is a common one; indeed, it's been characteristic of impersonal theories of morality, such as utilitarianism, to maintain that each of us has a fundamental impersonal duty to bring about what is good, regardless of who we are or of which relations we bear to other specific people.

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