Gwyn is gone. The rest of the Knights have remained in Anor Londo or lost their minds in the Kiln. But you have not. You remain strong, the last of your kind. You flee the Kiln to save yourself from your insane comrades. Darkness approaches, but you are determined to halt it. You saw Gwyn link the fire once, you know that someone has to do to again, and you know that because of your training you could pull it off. So you set off, trying to repeat Gwyn's success, this time for a permenant solution to this immediate threat.
