Anyway, here's his argument:
Suppose someone denies that there are objective moral obligations, e.g. moral obligations that persons everywhere are bound by. Imagine also that our skeptical friend is hesitant to accept the idea that something concrete could be logically necessary, but is willing to concede that propositions may be logically necessary. An example of a logically necessary proposition (one true in all possible worlds) would be this: "there are no square circles." Finally, suppose that objectivity entails logical necessity.
1. There are no objective moral obligations in the actual world. (Premise)
2. There are objective moral obligations in W. (Premise)
3. If there are objective moral obligations in W, then there are objective moral obligations in all possible worlds. (S5)
4. Therefore, there are objective moral obligations in all possible worlds. (From 2 and 3)
If you don't know, "S5" refers to an axiom in modal logic that, "If possibly p, and p necessarily, then necessarily p."
According to the Wikipedia, "The axiom is given as either
Possibly P implies Necessarily Possibly p
Possibly Necessarily P implies Necessarily p
Both of these axioms are properly called axiom 5."
The thrust of Doug's argument is that, if a necessarily true moral axiom is possible in some world, then that axiom is necessary in every world. Further, since it is obviously possible for there to be at least one such axiom in some world, it is necessarily the case in our world that there is such an axiom.
I replied to Doug by saying that I'm always a bit shaky on how S5 cashes out. For example, is it legitimate to import transworld necessity into W-indexed objectivity? Consider:
1. There are no objective moral obligations in the actual world (AW). (Premise)
2. In W it is objectively morally wrong to kill Smurfs.
3. It is objectively wrong in all worlds to kill Smurfs. (S5)
4. Therefore it is wrong to kill Smurfs in AW.
The problem is that there are no Smurfs in AW, so the necessary moral validity of 3. is objectively vacuous in AW.
Doug's initial response was:
I think the moral realist (myself included) would say that even if there are no Smurfs in AW, it would still be true that if there were Smurfs in AW it would be wrong to kill (murder) them. It's kind of like saying that even if there are no bachelors in W, then it would still be the case that if bachelors ever did come to exist in W, that they would have to be unmarried.
So, instead of saying that (3) is vacuous in AW, I would prefer to say that it is inapplicable, yet still meaningful in AW.
I replied that was my intuition as well, so going on from here, it seems a key gap to fill in this argument is against the objection that in AW there are no actual correspondents to fill the categories of any moral law. For example, "torturing babies is always wrong" The nihilist could equivocate forever about what "torture" means (noises too loud, nutritiously deficient food, less than angelic handling on a daily basis, etc.). Further, she might object to free will altogether and therefore evacuate the torturer's actions of malignancy. Or if we assert, "it is wrong to commit evil that good may result," she'll just deny good and evil result from anything in the first place. Of course, with an interlocutor like that, her horrid vacuity its own punishment and the quality of her voice in a moral debate would speak for itself--against her standing in nearly all other eyes.
This leaves me with two thoughts:
1. At least this argument forestalls the categorical assertion that moral absolutes are in principle impossible.
2. It might not get us practically farther than standard moral realist arguments, but it least it needn't keep reinventing the wheel about whether moral realism is possible.
It's an interesting argument, so I'm just thrashing it out to see what wheat falls from what chaff. Keep up the good work.