No One of Consequences uses definitions quite similar to my own.
Alot of peoples problems with alignment is that they fail to accept how truly complicated the system really is. They can hardly be faulted for that, since D&D has never put much of an emphasis on the system or explaining it despite its ubiquitousness in the mechanics. But, on the whole, despite all its limitations, there is no reason to use the system to create cookie cutter paper thin characters unless that is what you want.
There are somethings that alignment is not.
Edna, my biggest problem with your post was that you seemed to be overlapping the chaos/law axis with Charisma. It was almost as if you were saying, high charisma = lawfulness, and low charisma = chaotic.
Charisma is not alignment, but it does effect how alignment is expressed, and in turn, charisma effects how people percieve alignment. A chaotic evil person with low charisma will probably express himself as a brutish bully. A chaotic evil person with high charisma will probably express himself as a charming rake. Because both individuals are choatic evil, they will have a natural respect for each other. The rake sees the bully has honest to his nature (the only kind of honesty worth respecting) and brave for expressing himself naturally. The bully looks up to the rake as a sophisticated personality, and admires his ability to get other people to do what he wants them to do. A lawful good sees both as enherently detestable people, and the rakes high charisma only serves to make him seem more detestable, frightening, and unnatural.
Conversely, a lawful good person of low charisma might express himself as crude, strict moralist, prone to harsh criticism, self-righteous comments, giving unwanted advice, and shouting at people whose behavior he finds reprehensible. To the chaotics, he probably appears evil, no matter what his intentions, and no matter how charitable he might be in a crisis. To a lawful, he probably just appears misguided. A lawful good of high charisma is the sort of person who always manages to seem like a loving and devoted friend, no matter what your relation to them. An interesting story could revolve around the relationship of a high charisma CE with a high charisma LG and how thier 'friendship' might ultimately degenerate.
Intelligence is not alignment, but it does effect how alignment is expressed. The more intelligent a character, the more sophisticated thier alignment principals. A low intelligance neutral is probably an apathetic survival minded person who has never even really considered questions of morality. He has no moral stand on anything. But a high intelligance neutral is unlikely to have not considered questions of morality closely. A high intelligence neutral probably believes in a philosophy of balance and harmony, something like the Greek 'golden mean' or some of the Hindu paths. Life he believes should be experienced in its complexity, and not merely a peice of it. Too much focus on good and evil, is to him like a man who eats only candy, or who is addicted to alchohol. Too much of a good thing, he says.
Both neutrals respect each other more than an examinatino of their mutual charisma alone would suggest. The high intelligence neutral finds the neutral simpleton's way of living to be admirable in its simplicity. He probably has great respect for primitive cultures which he believes to be in a 'natural balance'. The low intelligence nuetral admires that the high intelligence neutral is pragmatic and not to his opinion overly intellectual or pretentious. He probably esteems his intelligence above those of other people with to his mind strange beliefs about life.
The same is true for every alignment, and intelligent people of any alignment can have philosophies that are expressed differently from other intelligent people of the same alignment. A chaotic neutral of low intelligence simply does his own thing no matter what anyone else thinks. A chaotic neutral of high intelligence might be a Bohemian, a Hedonist, or a Existentialist. He might even believe in some comparatively high minded philosophy wherein everyone (not only himself) had a right to do thier own thing, and oppose those that 'oppressed' anyone (and not just himself). Or, he might be a delusional skitzophearnic, whose beliefs cause him to live within his own bizarre, albiet quite harmless world.
Both the beat cop and the hitman can be lawful neutral, each with a duty to a particular agency and a particular code of honor. If they do, although they are enemies, they probably have a certain degree of respect for each other, and a mutual loathing for the chaotic neutral thief who has no honor that either can respect.
Wisdom is not alignmentment but it does effect how alignment is expressed. The higher the characters wisdom, the more closely he actually adheres to the set of beliefs he holds. This set of beliefs does not have to be the one he professes (he can deceitfully disguise his beliefs for some reason). A character with low wisdom believes something, but seldom is able to hold to his beliefs. Either he lacks the will to continue with his beliefs when tempted to stray, or he lacks the discernment to judge 'good' and 'evil' according to his own standards and often does something that is actually the opposite of what he should have done - all the while believing that what he is doing is the 'right thing to do'. A truly low wisdom character may not even know what his real alignment is. He could be a chaotic evil inquisitor who sincerely beleives that he is following the path of righteousness and professes every good thing. He could be street thief with a heart of gold. Morality is a confusing cloud to the low wisdom person, and if good hearted, he probably finds himself in need of contrite atonement quite frequently. A low wisdom person might not even be able to judge thier own heart.
A person of differing alignment (or low wisdom) percieving another low wisdom character generally misjudges thier alignment. They might percieve the chaotic evil inquisitor as the true representation of lawful good, or the golden hearted thief as the true representation of chaotic evil. They might percieve another person with quite different alignment as having the same beliefs as they do. Alot of Victorian/Edwardian stories can be read as concerning several characters misjudging each others alignments - usually against the advice of some other wiser but less charismatic character. Thus, a low wisdom lawful good might percieve a chaotic rouge as a charming and noble hero.
In general, two people of the same or similar alignment (assuming at least average wisdom) will recognize each other, despite the incongruties in behavior. The high wisdom character sees in himself the struggles to achieve a goal in the lower wisdom character, and is sympathetic (albiet frequently frustrated). The low wisdom character probably percieves the higher widsom characters as perfect and fails to note his many failings. He might either resent or admire this (or both). However, while this is the usual case, the aberational cases where they don't recognize each other keep things interesting like the Paladin failing to realize that the Inquisitor is a vile deluded self-centered arrogant man until too late. Or maybe even more interestingly, a honorable and just Inquisitor failing to realize that the Paladin providing the evidence is a Blackguard until it is too late.
And as I've hinted, even two characters of the same alignment, same wisdom, same charisma, and same intelligence could be quite different despite all they have in common. Personality and profession and social station play a big roles in shaping who people are and what they believe. Chastity is normally associated with lawfulness (or goodness if you are of a lawful group that upholds chastity), but it is not an inherent aspect of lawfulness. There is nothing that prevents a lawful from being permiscious if that lawful's social station and social code permit it (perhaps a nobleman in a chauvanistic society or a trained courtesan), and there is nothing that prevents a chaotic from being chaste (other than thier own personality). However, each person's behavior would be motivated by entirely different beliefs. A chaste lawful is chaste (whether they admit it or not) because thier social codes forbids sexual interactions. A chaste chaotic cares not a bit for social codes, but could be chaste out of respect for thier own body or out of a belief that no one is good enough for them or out of narcicism or out of belief that he or she can better use thier sexuality as a weapon if they only tease and never give in. A chaste lawful's behavior might change if thier social code (like a reformation of church doctrine) or situation (like marriage or rank) changes (though all lawfuls resist change in social code). A chaste chaotics code will remain the same regardless of social code or standing, but might change in respond to changes in personal situation (that is it become clearly more advantageous to give up chastity).
To further complicate things, even if you don't believe that morality is relative, how people will define moral terms IS relative. Thus, when a lawful evil person says the word 'good' and a chaotic good person says 'good' they mean entirely different things. It is possible that both believe that they are 'good people', and in fact that is the usual situation. It is rare that a evil person recognizes his beliefs as evil and celebrates them (though this is possible too), and I've even met people that celebrate thier own beliefs as 'evil' even though they aren't (in which case they claim to be evil but are celebrating good as often as not). Of course the situation can get complicated by the fact that people may rightly or wrongly lump some subset of thier beliefs together under the same ruberic of 'good' or 'evil' even though upon examination the category contains a pretty diverse set of beliefs. This is particularly easy to see with sexual behavior, where every sort of perversity, proclavity, and simple preference can all get lumped together as 'good' or 'evil' largely because of historical 'lawful' definitions. A quick examination finds some pretty tame and harmless behavior lumped together with some really vile stuff by both sides of the debate, as if there was no difference between say rape and a married couple just being playful. (I don't really want to be graphic, just provoke some thoughts in those that want to consider the question. However, I find it amusing what the designers of Online Purity Tests consider to cause the loss of equal amounts of 'purity' and often wonder with less amusement whether that is a real reflection of the beliefs of our society.)
I don't believe that the alignment system reflects the real world. I don't believe that there is a law/chaos moral axis. Things are either good or they are not, and those things which are not in opposition to good are good. That's my belief, but I do find it interesting how often I find that the dual axis system can be used to describe simply some very complex things. For instance, while I see no moral difference - at least no inherent moral difference - between the communist and the capitalist, between the stoic and the epicurian, or between the agnostic and the fundamentalist, it is possible to describe the philosophies at least in brief by adding additional axi. The law/chaos axis can be used to represent the group/individual, or as NOOC put it, the responsibilities/rights axis, and a variaty of other rather common related ways of perceiving the world ethicly.
I've never really understood why people find the rather vaguely defined Alignment system constraining. I suppose some people object to it on moral grounds because they don't believe absolutes exist, or because they find anything remotely like a 'system' too biased towards a lawful universe. I suppose there are a variaty of definitions out there that turn out to be rather unworkable. I suppose there are in the real world people having one alignment code that prefer to believe that they have another, and thus object when someone claims thier behavior belongs in a different category than the one that they would like to claim. I find most players, not suprisingly, play thier characters with little real concern for the moral implications of thier actions. For one thing, it is hard to be too concerned with the moral implications of an imaginary action by an imaginary character. For another, most real people have little real concern for the moral implications of thier actions. I generally advise most people who object to the alignment system to play neutrals, since I find that that is what they are going to end up playing anyway.