In that case, we can skip directly to “W implies E” and go on with the second numbered argument.
There are two different matters in question here:
- “Objectively wrong” is a meaningful concept.
- There are actions that are objectively wrong.
The first does not imply the second. I can understand the concept of a dragon without having to acknowledge that they exist. Likewise, just because “objectively wrong” has a meaning, that doesn’t mean that we have to admit that the concept actually applies to any real actions. If we believed that the goodness/badness of chocolate were subjective, we would say that the statement “Chocolate is objectively bad” is not meaningless, but simply false.
(And I should emphasize that the statement “Chocolate is not objectively bad” is not the same as “Chocolate is objectively not bad.” The latter presumes that the goodness/badness of chocolate is an objective issue, while the former does not.)
That said, I will attempt to provide a definition of “objectively wrong.” To say that an action is “objectively wrong” is to say that a person should refrain from that action, no matter what the person’s own ultimate ends are. If it’s impossible for the person to change their own preferences such that the statement “You should not do X” no longer applies to them, then we say that it is “objectively wrong” for the person to do X.
It’s fine to be skeptical of how any statement “X is objectively wrong” can be justified, because that is not my aim. My aim is to show that certain actions are such that the statement “X is objectively wrong” is certainly false regardless of whether or not we grant that X’s ethics is an objective issue.
With regard to the alien example:
This doesn’t follow, because the alien’s adversary does not necessarily reject the statement “X is not pan-galactically wrong.” It’s perfectly consistent to say “The ethicality of X is not a pan-galactic issue, and X is not pan-galactically wrong,” just as most people believe that chocolate is not an objective ethical issue and that chocolate is not “objectively bad.” All that this type of reasoning demonstrates is that if “pan-galactically wrong” means something, then one cannot reject “X is not pan-galactically wrong” without affirming that “X is a pan-galactic issue.” While “pan-galactically wrong” and “wqxfzogyt” might not mean anything at all, “objectively wrong” does mean something, at least enough so that statements containing it cannot simply be dismissed without asserting them to be false.
As far as I know, there are no self-referential statements in what I have given, and the system is far too weak to allow for any Gödel-type indirect self-reference, so I don’t think paradoxes like this are a major concern.