It's interesting how that objective has changed over time.
"We will make no distinction between the terrorists who committed these acts and those who harbor them." -- George W. Bush, 9/20/01
"Every nation has a choice to make. In this conflict, there is no neutral ground. If any government sponsors the outlaws and killers of innocence, they have become outlaws and murderers themselves. And they will take that lonely path at their own peril." -- From George W. Bush's speech announcing that attacks on Afghanistan had begun
"And you all also may remember that early on, I said if you hide a terrorist, if you feed a terrorist, if you provide comfort to a terrorist, you're just as guilty as the terrorist. The Taliban now knows what we mean. They're gone. And, guess what? People in Afghanistan don't miss them one bit." -- George W. Bush rallies the troops in Alaska on 2/16/02