So one player choosing a Lawful approach and another choosing a Chaotic approach to do Good is “moral relativism” if both are right.
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Alignment posits two axes, Good/Evil and Lawful/Chaotic. Arthur and Robin Hood are Good. Will they agree on how to deliver Good? Likely not – one is lawful and one is chaotic.
But one player wishing the prisoner to face the punishment for her crimes and the other sparing her of that punishment, with both being right, is not moral relativism.
On the second quote - who said they're both right? I never did. My point is that I don't have to decide as part of my adjudication of the game. Nor as part of my enjoyment of the game. (Just as, say, I can watch Pulp Fiction without having to form a definitive view on the morality of the hit-men characters.)
On the first thing, I don't actually understand it. (And never have - it's a part of the AD&D alignment system that has never made sense to me.) The way you put it, doing good via a lawful approach and doing good via a chaotic approach is like doing good by being a blacksmith (it's handy for people to have horseshoes and ploughshares) or doing good by being a weaver (it's handy for people to have cloth). But nothing in the blacksmith/weaver set up suggests that smiths should hate weavers, or vice versa. They're just different approaches to living a virtuous life.
But in D&D 9-point alignment the LG character is meant to have moral objections to the CG character - not to simply regard him/her as someone who chose different means. To try to give it some sort of (caricatured) context, when Superman regards Batman as somewhat suspect for not being fully above-board in his approach to crime fighting, Superman is suspecting that Batman is not entirely, or really, good. Conversely the idea that Superman would regard Batman as entirely good,
and would regard Batman as using objectionable methods, makes no sense. And if Superman regards Batman as entirely good because he regards Batman's methods as
not objectionable, although not the ones Superman himself chooses to deploy, then there is no conflict between law and chaos - contrary to what D&D's alignment system asserts.
How can you have the eternal struggle of good vs. evil if we cannot have either “good” or “evil” in any way defined?
Here is a candidate definition of "good": a general terms of commendation. Here is another: "good" = "admirable or worthy of emulation". Those are both mine. Dictionary.com gives me 41 definitions of "good" as an adjective. Some of the relevant ones include "morally excellent", "virtuous", "righteous", "satisfactory in quality", "excellent". As you can see, those are also all general terms of commendation, used to describe things that are admirable or worthy of emulation. "Admirable" and "worthy" are themselves general terms of commendation.
There is no more specific, generally accepted definition of "good" - it's one of the most flexible words in the English language, in terms of the objects, states, persons, behaviours etc it can be applied to.
The eternal struggle of good and evil is a trope because we are familiar with it as part of both religious and literary traditions going back for thousands of years. We recognise it in virtue of trappings (eg light vs dark) and context (eg betrayal of innocence or seduction by power), not to mention the deployment of other stereotypes (eg nobility and honour vs deceit and expedience).
Gygax incorporates the trope into Greyhawk by giving us Iuz and the Horned Society at war with Furyondy, Veluna and the Shield Lands. We can recognise the trope without needing any sort of definitive account of what constitutes good or evil: there are Knights of the Hart and Knights of Holy Shielding, guarding lands ruled by an archcleric and a paladin, from a group of hierarchs (already a sinister appellation!) who lead orcs and goblins, and from the child of a witch and a demon prince.
In fact, in some ways - as with Tolkien's LotR - the fiction works better if we
don't inquire too closely into what makes Sauron or Iuz evil, because when we do make that inquiry we tend not to find much of an answer, at least if modernist sensibilities are deployed. Likewise, it's helpful if we don't inquire too closely into what makes Aragorn, or Furyondy, or The Shire for that matter, good. After all, is it
really good that Bilbo and Frodo live in wealth from birth, while Sam only gets to move out of his gaffer's digs as a reward for saving the universe? And how many contemporary readers of Tolkien or players of D&D really regard any form of monarchy (and associated notions of "noblesse oblige") as a good form of government that best maximises altruism and minimise harm to the common folk?
This is not just a feature of contemporary fantasy, either. It's also a feature of superhero comic books. (Obviously there are exceptions - Wagner's Ring would be an exception in the domain of fantasy, and Watchmen in the domain of super heroes, where the audience is expected to engage in that closer inquiry, and to be impressed by what the author offers up as an answer.)
Good is defined in the rules. In game, that is the definition of “good” as it is used in the alignment context. It overrides all other definitions for that purpose.
As I've already pointed out, that definition relies upon using other evaluative language - such as "altruism" (= furthering the interests of others - but what counts as an interest?), or "harm" (=, let's say, wrongly setting back the interests of others - but what counts as an interest, or as wrongful setting back?).
You have indicated that only the player’s determination of whether their code is being followed matters.
Yes. That's not saying that they define their code. It is saying that their interpretation is paramount. But interpretation is not definition - and that's not just a point of semantics, either in general or in the context of RPG play. The general point probably doesn't matter here, but the RPG point is this: definition corresponds roughly to backstory; interpretation corresponds roughly to play, including action resolution. I have never said that players have sole authority, or even necessarily primary authority, over backstory. I've said they have primary authority to play their PCs, including interpreting what does or doesn't fit with their PCs' moral convictions.
So, the Demon Prince wants what RQ has – again, why can that not be interpreted as “The Demon Prince longs to join the Raven Queen’s legions of Undead warriors with his own, the better to conquer all the lands.”
If you want to change the campaign backstory, that's either something that happens prior to play; or, alternatively, is something that might unfold as a big reveal arising out of actual play and action resolution. I don't see it's relevance to who, if anyone, is obliged to evaluate the conduct that a player declares for his/her PC.
I do not believe my interpretation of the words – to cast the RQ is a cold, ruthless, feared Monarch of the Dead – is a less reasonable interpretation of the words above. So why is a character who holds those beliefs categorically “wrong” rather than someone whose beliefs can be tested in play?
There seems to be some confusion here over what "belief" means when a game like Burning Wheel talks about "beliefs being tested in play". Beliefs in that usage is synonymous with "commitments", or "moral convictions". It's not about testing whether your belief that the Raven Queen likes pizza but not donuts is true or false.
So if you want to change the backstory of the Raven Queen so that she is a cold, ruthless, feared Monarch of the Dead then - at least at my table - that is typically not something to be done in the course of play. That is something to be established by general consensus prior to play. Much like, if one of the players wants to play a seafaring character, then before play starts we would have to all agree on whether the starting town or village is coastal or inland.
(I know there are some RPGs, and some approaches even to 4e, that allow the players to make far-ranging determinations about backstory as part of the process of action resolution. My game is not one of those, though.)
If they have to invoke RQ to guard their loved ones from the threat of undeath, how does that mean she is diametrically opposed to it?
Because the word used is "curse", not "threat", and the entry is written from the point of view of explaining why the god is worthy of devotion.
The character who believes that killing people is a service to the Raven Queen, bringing them to her realm of death. You are judging that character. You are saying your judgment is to be preferred over mine.
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And why does your judgment whether my attempts are sincere relevant?
I'm not judging that character. There is no character. There is no play or prospect of play. And that is also the relevance of sincerity. You haven't sat down, read through the 4e PHB, and said "I know what, I want to play a murder who slays people in devotion to the Raven Queen." As best I can tell, you didn't even know the backstory for the Raven Queen until I posted it. You haven't talked about a class that might make this character work (I would suggest Avenger, or perhaps Executioner Assassin with an Avenger or Cleric multi-class). You're not pitching a character at all.
So I'm not making any judgement of any actual or prospective character.