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I read that essay many years ago from the link on you web site, and it is indeed magnificent and highly thought provoking, and has had a significant impact on my ethical philosophy. However, I now think that his refutation of point number three is not satisfactory. When doing such thought experiments, no matter how you try to change the nature of the subject, there is still a "meta-subject", you, the experimenter, who will always be there in any such experiment, and is stealthily making moral judgements about the situation. No matter what level of abstraction you go to, there will always be someone one level higher making the moral judgements.
I'm with Adam on the third point. Imagine in place of Nazism, some alternate concept like "free speech." The refutation now reads:
Still a true claim, by the way, unanimous liking is not sufficient to logically justify any claim. But the force of the attempted refutation relies on the reader's emotional response to Nazism, not on the logic of the assertion.
Adam: You say there is always the possibility that you'll sneak in your personal moral judgements. Maybe, but this seems to imply too much. Specifically, it implies one can't trust oneself to think clearly about something. You might wind up sneaking ideas past the your own complacent mind. But most of the time thinking really works out pretty well for most people, so I doubt that this is quite the problem you claim it is.
Mike G: The force of the argument is not based on emotional reaction. MH is attacking the belief that "For all X, if X has the attribute of being liked, then X has the attribute of being right." A single counterexample is sufficient to falsify a "For all X" type of statement and that's what MH is doing.
James: I'm not saying that people can't think clearly, I'm saying that they're deceiving themselves if they think that they can run an experiment and observe its results (thought experiment or otherwise) without affecting the experiment in any way. Most of the time, this does not invalidate the experiment, or the thought, but sometimes it must be taken in to account. Most people have moral intuitions that are very similar in most ways (I accept the rest of Huemer's theory of moral intuitionism), and thus there is strong agreement on moral issues, so it may seem that the standard you're using is objective rather than simply common to almost everyone.
Adam:
Actually, you said the experimenter is "...stealthily making moral judgements..." If so, the implication is that people really can't trust themselves to think clearly. (My mind sneaks ideas past itself! Would you trust such a defective apparatus?) I don't see how you can avoid this implication.
Well, the unclarity in people's thinking is normally not important, so it doesn't cause problems most of the time.
Adam: I'll have to take take your word on when unclarity is important and when it isn't. When I try to make that distinction, my mind sneaks things in.
Adam has raised the basic problem with MH's conception of "intuition". He states in his essay that certain moral values "are simply immediate intuitions. There is no difficulty in this proposal, since there are numerous examples outside ethics of synthetic, a priori judgements apprehended by intuition." The implication here is that we do not need language or concepts to mediate our apprhension of moral values ("objects", as he says- although I don't see how an action has the same ontological status as a chair), or there is some "third entity" that is given prior to any thought. Yet in order to assert this one has to stand in a view from no-where, since we manifestly always already mediate our apprhension through language and concepts (what would it mean to have a non-linguistic apprhension of something? I couldn't say anything, so the apprhension would be pointless). Even though he's using Kantian language here he seems to be in a pre-Kantian mode if he thinks that somehow the subject isn't involved with changing the object of thought...
This of course doesn't imply that there is no such thing as "objectivism". There are many philospohers who note both how reality is given ("objective), but also that our conceptions ("subjective") inform reality is a certain way as well (Hegel, Husserl, Wittgenstein, etc.). In that way, "relativists" are not entirely incorrect, but on the other hand, they surely are absurd, considering nothing is "relative" or fluid and in flux except in reference to something stable and objective.