Why Doesn't Batman Just Kill The Joker?

First Joker commits a crime, then Batman catches him and locks him up. Then, Joker invariably escapes and the cycle starts anew. So, wouldn’t it be far easier if Batman just killed his archnemesis? What’s stopping him?
That wasn’t an idle comic store chit-chat – rather it was an example given by philosophy professors to introduce coursework:

William Irwin, a philosophy professor at King’s College in Pennsylvania, edits the Blackwell Philosophy and Pop Culture Series, which includes titles such as Batman and Philosophy, and X-Men and Philosophy.
He says there’s nothing unusual about using popular references to illustrate complex theories.
"This is what philosophy has tried to do from the very beginning," he says. "Philosophy starts with Socrates in the streets of Athens taking his message to the people and speaking in their language – agricultural analogies and common mythology."

Katie Connolly of BBC News writes about the growing use of comic book characters to teach philosophy: Full Story