Mill thinks that:
An action is unjust if society has a utility-based reason to punish that actions of that type.
An action is wrong if there is utility-based reason not to peform that action.
Mill writes as if the unjust were a subset of the wrong. But it need not be. Suppose that powerful aliens have a weird religious view on which dyeing one’s hair green ought to be punished with a week in jail, and they announce that any country that refuses to enforce such a punishment as part of the criminal code will be completely annihilated. In that case, according to (1), dyeing one’s hair green is unjust. But it is not guaranteed to be wrong according to (2). The pleasure of having green hair could be greater than the unpleasantness of a week in jail, depending on details about the prison system and one’s aesthetic preferences.
The problem with (1), I think, is that utility-based reasons to punish actions of some type need have little to do with moral reasons, utilitarian or not, against actions of that type.
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