THE SIGNIFICANCE OF THE MOONThere are a lot of arguments over what the meaning of the moon is for Saix and why it is so significant. The following information is an assumption made by myself, and is not fact. However, I do believe it is a good argument as to why the moon is a significant symbol for Saix.
Saix himself is the Luna Diviner, which literally translates to Demon Dancing in the Moon. During his last battle he says outloud, "Do you feel it? The moons power!" All of his weapons are references to astronomy or astrology, especially the moon, have blue and yellow patterns. One theory for the symbol of the moon talks about how the moon represents light and dark at the same time. It appears in the dark, yet it has guidance to people looking up in the night sky. As the second-hand member to Xemnas, Saix leads the way to the ultimate Kingdom Hearts, especially seen in Kingdom Hearts II. Saix has the ability to control the moon, putting it into his heart. When he goes into a Berserk state, it almost reminds me of a werewolf coming out on a full-moon, literally possessing his body and his mind. His Claymore changes in Berserk mode in Kingdom Hearts 358/2 Days to be a "moon rabbit," which represents Saix's ideals and climb to hierarchy, or literally "Shooting for the moon." In some of the games, the moon has the ability to heal him.
Another interesting thing to point out is that the moon's on his Claymore and the moon that appears on Isa's hoodie, his somebody, are all just crescent moons, never full. In astronomy, the crescent is the shape of the lit inside circle. The word crescent is derived etymologically from the present participle of the Latin verb crescere "to grow", thus meaning "waxing" or "increasing", and so was originally applied to the form of the waxing moon (luna crescens).
"The direction in which the two "horns" of the crescent moon point indicate whether a crescent is waxing (young and increasing) or waning (old and decreasing). In the Northern hemisphere eastward pointing horns indicate a waxing crescent, whereas westward pointing horns indicate a waning crescent. However, in the Southern hemisphere just the reverse applies."
Isa's crescent moon is a waxing crescent, which indicates that he is young and increasing. This is very fascinating because it shows that even as a human boy, Saix was gaining his moon powers. It is said that if the moon is a waxing crescent, its a propitious time to begin a new venture and experiment with new ideas. Isa creates a goal in his life and goes for it, even if it goes against his best friend. When he transforms into Saix, a nobody, he continues to venture in his goal and his moon is still a crescent. He was unable to fully turn into a full moon, which might symbolize how Kingdom Hearts didn't complete while he was alive.