I doubt Elrond & co. were too impressed by Aragorn's claim of a long life, having several thousand years on him. I'd imagine these words were spoken with a long hard look at Boromir.
The phrasing does seem archaic, even poetical, but as with the thee and thou discussion, Aragorn does seem to switch between 'casual' and 'heroic' speech patterns depending on who he's chatting with. The Council is necessarily formal, heroic and certainly archaic, or at least most of its members were!
Er, yeah Morth, was thinking that Alatar had been hijacked by spammers until I read the post
.