Michael Huemer on Fake Noûs

I don't understand what the objection to subjectivism is. It can't justify punishment? Why wouldn't the subjectivist say that the "justification" of punishment is subjective like everything else, and therefore it is "justified" precisely in the sense that he himself approves of it? Of course it isn't *objectively* justified, any more than anything else is, but why would that bother the subjectivist? Are you assuming that it's morally wrong to punish someone for X if X isn't objectively wrong, or if X isn't irrational? Wouldn't the subjectivist just say, "No, it's morally right to punish people who do things that I disapprove of, because I approve of punishing those people"?