My own take on alignment:
Good characters help others, at personal cost or risk.
Evil characters hurt others, for their own personal gain or pleasure.
Neutral characters (on the Good/Evil axis) do neither.
I'd ammend that slightly.
Good characters help others, regardless of personal cost or gain.
Evil characters hurt others, regardless of personal cost or gain.
Neutral characters see no difference between helping or hurting others, and make their choices based on other considerations.
The problem I have with your formulationi is it seems to be equivalent to:
Good characters are selfless.
Evil characters are selfish.
Nuetral characters are neither selfless nor selfish.
I reject that formulation. I believe that there can be selfless evil (a kamikazi pilot, a suicide bomber, a SS fanatic, a Southern soldier fighting to defend slavery...) as well as self-centered good. That is not to say that everyone sacrificing themselves in an evil cause is evil, but that its at least concievable that some or many of them are.
Lawful characters seek to uphold the social order.
Chaotic characters seek to subvert or overthrow the social order.
Neutral characters (on the Lawful/Chaotic axis) do neither.
Likewise, while this is somewhat on target, I reject this formulation as actually too specific as well. I'd prefer.
Lawful characters believe that external standards are more important than the dictates of their conscious.
Chaotic characters believer that the dictates of their conscious are more important than external standards.
Neutral characters do not see a clear preference between external standards and what their conscious compells them to do, but make their moral choices based on other considerations.
The problem with your formulation is that 'society' is not actually an easily identifiable group. Suppose for example you have a nation state, and a group of rebels. It's easy to say, "Well the nation state is the society and therefore those that support it are lawful.", but this turns out to have all sorts of problems. The nation state might not be actually upholding the rule of law, in which cases the rebels are rebelling against it at least in part to restore order rather than overthrow it. But, on the other hand, you can't actually say that the rebels are 'society' either since they are but a subset of the community as a whole. But, on the other other hand, if a person were born into the community of rebels, then that persons society would certainly be the rebels and their standards of what constituted social behavior would certainly be set by the rebels.