How we cite our quotes: (Chapter.Paragraph)
Quote #7
The question was not simply one of how well one practiced one's skills, but to what end one did so […]. As professionals, the surest means of doing so would be to serve the great gentlemen of our times in whose hands civilization had been entrusted. (4.5)
Stevens here suggests that great butlers serve "great gentlemen"—specifically, gentlemen who seek to better civilization.
Quote #8
A butler of any quality must be seen to inhabit his role, utterly and fully; he cannot be seen casting it aside one moment simply to don it again the next as though it were nothing more than a pantomime costume. (6.127)
Stevens takes his job so seriously that even in his "off" time, hanging out alone in his butler's pantry, he still maintains his butler-ness.
Quote #9
"First came here in 'forty-nine. Socialism would allow people to live with dignity." (7.24)
Just in case you didn't get the fact that "dignity" in the novel is not just about greatness in butlers but also in human beings in general, Dr. Carlisle's offhand comment here makes the link clear. Ordinary people, not just gentlemen, deserve dignity, although Dr. Carlisle is skeptical about whether socialism is the way to do it.