The Joker is a liar. He's always scheming. He's borderline insane, and everything he does he's doing his best to hold a veneer of sanity to be able to accomplish his goals. In every scene Ledger is in, he is the Joker in presence, but you can also see him as the Joker in mind...and that is a performance worthy of an Oscar.
Well, the plot requires that Joker is a truthful man. Yes, I know the movie also shows he's a liar! Stuff like that is why I'm not so impressed. Further, although I haven't had a large amount of experience dealing with mentally ill people, I have had some. The Joker's "insanity" is completely out of Hollywood mythology, not anything real, or even simply human. (As the years go by, I'm starting to get really pissed by the usual backward depiction of mental illnesses!) I never bought into Joker. I just was amused by his antics. Fundamentally the character was no more serious or truthful than Caesar Romero's Joker.
But as I say, that's why I admired Ledger's competence in selling this nonsense, which was the prime reason the movie was tolerable! (With Aaron Echkart's performance being the second, by the way. Where's the love for him?) But in the end, I ask myself, would it really be a tribute to memorialize Ledger for the Joker?