So I find the Law-Chaos axis in alignment fascinating, Chaos in particular. I've spent a lot of time thinking about it. Unfortunately, I've got a very busy weekend ahead of me and honestly might not should even be throwing my hat into the ring because this discussion could distract me from things I have to get done, but I'm compelled to say at least something.
Yes, which is why in the original Moorcockian philosophy, extreme chaos OR extreme law was bad for, well, people.
So the Agents of Neutrality (?) tended to the Cosmic Balance.
Moorcock is my go to for how Law and Chaos should be defined, at least at its purest extremes. Most Lawful or Chaotic characters exist on a spectrum and don't reach the far extremes of Law and Chaos, though some get closer than others.
To put it in simpler terms, say that someone thinks that a standardized, global language shared by all people should be developed to make it so people all around the world can easily communicate. This is a Lawful goal because it seeks standardization, reduces alternate possibilities, and applies to everyone. It's easy to imagine that there would be a great deal of pushback to this idea from people who argue that diversity of language is itself valuable, that a "universal" language would likely more closely resemble languages familiar to the creator of said language, that emphasizing a universal language would cause works in other languages to fall into disuse and obscurity, etc. This is a point of view that values Chaos over Law, but it is also a very understandable and sympathetic point of view that illustrates "Chaos" does not necessarily mean "bad".
In fact, I tend to think of Law and Chaos in general as representing "Standardization" and "Possibility". Law isn't inherently good, it just seeks to eliminate possibilities that increase uncertainty. Moorcock illustrated this by depicting a truly Lawful plane as a grey void. Lawful Good wants to eliminate possibilities that could lead to Evil, Lawful Evil wants to eliminate possibilities that could lead to Good, and Lawful Neutral just wants there to be a standard.
The Paradox of Law is that even if there were a number of people who agreed with the idea that there should be a standard, universal language, different people would come up with different ideas about what is best.
Imagine the furthest ends of Chaos as an unruly tangle of vegetation. Agents of Law seek to reshape that tangle into a meticulously planned garden. However, various Lawful organizations will disagree on what to shape from Chaos, thereby paradoxically creating Chaos between competing Lawful factions. This means that a Lawful Good character in a society where certain actions they found objectionable were legal would face a difficult decision over how to act. Should they do the Good thing and immediately act against Evil, or the Lawful thing and, at most, take actions to try and change the law, afraid that opposing Evil on a whim could lead to unintended complications that makes the situation worse rather than better?
Now to try to apply the ideas of Law and Chaos as "standardization" and "possibility" to real world individuals. I find myself reading discourse on social media and trying to imagine what alignment various statements could be indicative of, saving those I think are particularly interesting to a text document.
Here's an example from a discussion regarding a science fiction series (paraphrased to remove unnecessary specifics) :
Side A: The grievances of that leader were legitimate and remained legitimate even after political opportunists coopted his campaign for independence to solidify their own positions of power.
Side B: Which is why the fact these opportunists were not dealt with is such a tragedy. Not to mention that the various leaders engage in a number of heinous war crimes.
Side A: Here's where you and I differ: I don't begrudge the oppressed resorting to more and more drastic measures as other avenues of achieving freedom from out under a bootheel are exhausted.
Side B: They killed a great number of civilians, though.
Side A: The trick of imperialism is to slowly crush a populace in ways that are mostly invisible, to make the horrifying responses from an oppressed group seem entirely unjustified.
And here's another from a discussion in which posters debated whether enacting a certain type of legislation would be a good thing or if it carried to much risk from possible unintended consequences and individuals who abuse such laws for their own gain:
"If we fight for something and get it, what if unintended consequences make things even worse? Better to keep everything as it is and not risk it."
We lose 100% of the fights we're too scared to take on, we miss all of the shots we don't take. If you want to sit around and keep asking "what if" because everything might blow up in our faces and decide it's not worth fighting back, then that's your choice. But even if it blows up in our face, we took a stand and did something to try and fix things instead of moping around, thinking everything is terrible and doomed.
We need to fight back even if it could possibly make things bad or worse in the future.
Using these as a base, you could say characters who are Chaotic Good are interested in taking actions that they hope will turn out for the best and deemphasize the risks posed by their actions because they believe the status quo is already intolerable. From their point of view, Lawful Good characters worry too much about unintended consequences and end up accomplishing little, in effect enabling Evil by letting existing suffering persist indefinitely because they're too afraid of what might happen. A Lawful Good character might argue that a corrupt nobility might need to be reformed through the system or deposed carefully to avoid instability in the region. A particularly zealous Chaotic Good individual wants the nobility deposed immediately, rules and regulations be damned, and all their ill-gotten gains redistributed, a "rip the band-aid off" approach. If this leads to negative consequences the Chaotic Good character will just come back and take down whatever new threats arise, repeating as necessary.
Personally, I find Good and Evil more confusing than Law and Chaos. Take PETA, for example. I recently learned while doing research for a class paper that PETA is opposed by "no-kill" animal shelters because the organization performs a shockingly high rate of euthanasia. PETA's own website defends this practice thusly:
Shelters cannot humanely house and support all these animals until their natural deaths—they would be forced to live in cramped cages or kennels for years, lonely and stressed, and other animals would have to be turned away because there would not be room for them. Turning unwanted animals loose to roam the streets is not a humane option. If they don’t starve, freeze, get hit by a car, or die of disease, they may be tormented and possibly killed by cruel juveniles or picked up by dealers who obtain animals to sell to laboratories. Because of the high number of unwanted companion animals and the lack of good homes, sometimes the most humane thing that a shelter worker can do is give an animal a peaceful release from a world in which dogs and cats are often considered “surplus” and unwanted.
The emphasis here is that euthanasia is a "peaceful release" and is preferable both because being housed in an animal shelter is a miserable existence and because just turning an animal loose could possibly result in suffering in a myriad number of forms.
This latter point is of particular interest to me because I am also aware of antinatalism, an even more extreme stance that defines coming into existence as undesirable and the act of bringing new life into the world (be it human or otherwise) as morally wrong. Creatures can only suffer if they exist, so bringing new life into existence is effectively inflicting upon them all the suffering they will ever experience. I even found one quote encouraging the sterilization of animals:
By sterilising animals, we can free them from being slaves to their instincts and from bringing more and more captive animals into the cycle of being born, contracting parasites, ageing, falling ill and dying; eating and being eaten.
Law and Chaos look simple to me, in contrast with views such as "conscious existence is inherently Evil and preventing consciousnesses from coming into being is inherently Good" and "euthanasia is Good because creatures might possibly suffer if their consciousnesses aren't terminated."
I would identify both of these views as Lawful, at least, as they are risk averse and seemingly emphasize that potential can bring suffering while deemphasizing the possibility for happiness. It stands in sharp contrast to my prior observations about Chaotic individuals, who emphasize positive potential and deemphasize possibilities that their actions could bring about horrible, unintended consequences.
Looking at it this way, perhaps Lawful characters most often have personality traits such as pessimism, realism, and a desire for certainty, while Chaotic characters are more likely to be optimistic idealists who are undeterred by uncertainty.