Relativism and absolutism in deontic logic
Consider a world where eating doughnuts is illegal and where everyone thinks it is OK to torture animals for fun. Suppose Norman at w is eating doughnuts while torturing his pet kittens. Is he violating the laws? Is he doing something immoral?
In one sense, yes, in another, no. His doughnut eating violates the laws of w, but not the laws of our world. Conversely, his kitten torturing violates a moral code accepted at our world, but not a code accepted at w.
In general, when we ask whether people at other worlds do what they ought to do, we can evaluate their actions relative to their norms, or we can evaluate them relative to our norms. Both perspectives make sense. But they lead to different deontic logics.
Let's assume a Kripke semantics for deontic logic. (The issues carry over to neighbourhood semantics.) Here, `it ought to be the case that p' is regarded as true at a world w iff p is true at all deontic alternatives to w. A world v is a deontic alternative to w iff everything that ought to be the case at w is the case at v.
This formal definition leaves open how we should understand 'ought to be the case at w'. Is this a matter of the norms accepted at w, or is it a matter of the actual norms that we hold fixed when we consider w?
On the first approach, a world v is a deontic alternative to w iff v is permissible by the standards that are accepted or endorsed at w. Let's call this the relativist approach.
On the second, absolutist approach, we don't care what norms are accepted at the relevant evaluation point w (unless our own norms say that this makes a difference). Here v is a deontic alternative to w iff v is permissible by our norms.
(You might suggest that there's yet another approach, on which we evaluate the actions at w relative to the true norms, which don't depend on what anyone at any world endorses or accepts. If the true norms are constant between worlds, this approach yields the same logic as the absolutist approach. If the true norms vary from world to world, we can again distinguish a relativist and an absolutist version, whose logic will look like the logic of the two approaches I just introduced.)
What difference does this make to deontic logic?
Consider the "Utopia" principle, that it ought to be the case that whatever ought to be the case is the case: O(Op → p). In Kripke semantics, this corresponds to the hypothesis that any deontic alternative to any world is a deontic alternative to itself. On the relativist approach, this is highly implausible. The fact that a world w conforms to our norms surely doesn't entail that it conforms to the norms at w. On the absolutist approach, however, the principle looks highly plausible. If w conforms to our norms, and we use those same norms to evaluate what ought to be the case at w, then plausibly everything that ought to be the case at w is the case at w.
One might argue that on the absolutist approach, the very same worlds are deontic alternatives to any world. The logic of obligation and permission would then be KD45.
On the relativist approach, even the minimal logic K is arguably too strong. For example, consider a world at which there is nothing but empty spacetime, and so no norms are accepted or enforced at all. At such a world, arguably nothing is obligatory and nothing is permitted, on the relativist interpretation. But O(T) is a theorem of K. We even have to give up the duality of obligation and permission, since at the empty world we have neither O(p) nor P(~p).
Since the question of absolutism vs relativism makes such a big difference to deontic logic, you'd expect it to be discussed upfront in introductory texts on deontic logic. I have looked at a good handful of such texts, but I've never seen the question even mentioned. Instead, people seem to take one or the other approach for granted, and you have to read closely between the lines to figure out what approach that is.
For example, Brian Chellas's Modal Logic textbook, which extensively discusses deontic logic, clearly adopts the relativist interpretation. (Which partly explains why Chellas is so critical of Standard Deontic Logic.) The Anderson/Kanger reduction, discussed for example in the SEP entry, clearly assumes absolutism. Lewis also seems to assume absolutism in his writings on deontic logic. But as I said, there is little explicit discussion, and people often seem to talk past each other.