Symbolism, Imagery, Allegory
Often, black and white stand for evil and good, respectively. In The Sunset Limited, however, this gets inverted: Black is optimistic and believes in life, whereas White is pessimistic and believes in death. Also, Black believes there really is such a thing as good and evil, but since White has no beliefs (except for his belief in death), this kind of language is meaningless to him:
WHITE: You see everything in black and white.
BLACK: It is black and white. (105)
Thing is, while White takes a jab at Black in the excerpt above, in this play, things really are pretty black and white (metaphorically speaking, that is)—after all, it's not like White possesses some super nuanced understanding of the world. From where he's sitting, life is simply and completely pointless. As much so, in fact, as Black believes the opposite.
So the characters races highlight differences they have that aren't actually all that racially related—race is about polarity in perspectives instead of more racially-specific things. Black is a man of faith, whereas White is a man of reason; Black puts his mind at the service of a God who transcends the human mind, while White's mind is serving… White's mind (since he believes in "the primacy of the intellect"—i.e., that brains come first).
In what is perhaps the biggest inversion of the typical black/white symbolism, though, Black represents life while White represents death. Thinking of black and white as colors instead of characters or metaphors, something else emerges: Black is the presence of all colors, while white is the absence of color completely. Black, then, in representing life, represents fullness and presence; White, on the other hand, represents death and absolute nothingness. Go team.