The rules for alignments are clear on one topic. They are very obscure. Yep obscure.
@Celebrim is mostly right, alignments should be set by the players and the DM right at the beginning. What is good and evil lawful and chaotic will depend greatly from table to the next.
What most people forget is that Gygax was a wargamer and would look at alignment from both the novels he read, but also from what was seen as good in medieval times. Also, the fact that Gygax saw D&D as humano centric would also taint how alignments would be viewed. These would always be referred from the human perspective and nothing else. Thar is why we saw so many articles on the Point of view of: "Elves, Halflings, Dwarves, Orcs" and so on. Because the whole system was biased from the human perspective.
The elves certainly do not see themselves as chaotic nor would the halfling see themselves as lawful. But, it is how humans perceives them so that is the general alignment that was given to them. All races were given this treatment and so were the monsters.
As the game evolved, this notion got forgotten and completely ignored by the newer generations of DMs and players. The fact that alignments are so humano centric means that for good or bad, some of Gygax's affirmations might seems contradictory if not downright aberrant from the modern mindset.
One example that comes to mind is the paladin slaying a repentant orc. Remember the premises. Lawful Good, humano centric and values from medieval point of view. A crusader, that is where the paladin was inspired from, would certainly do this back during the crusade. Not doing it would be seen as evil and traitorous. A quick merciful death was always seen as charitable as the other alternative was prison and torture most of the time. Better a quick death than a slow one, knowing famine and torture. Also, a prisoner was a heavy burden as that prisoner would need food... In our modern society, not a big deal, in medieval times where not everyone ate their fill it could mean the death of children as parents would be forced to choose which of their children would get to eat. Food directed at prisonners would normally be given to the poor but not if prisonners were there.
Punishment in medieval times was harsh. An eye for an eye was the norm and the sentence for the guilty was usually death. The more heinous the crime, the longer the death. Just think of the Inquisition or the Muslim purges in India...
So this means that Gygax was not entirely incoherent in his examples (I might even argue the opposite). But when you look at it from a modern mindset, it is impossible to agree with him.
This means that depending if you want to put yourself in a modern mindset, a medieval one or a different culture, alignments might and will mean very different things.
