President Bush decided to call this unexpected new struggle "the war against terror." It is most certainly a war, and, at least for the moment, the favorite technique of the enemy is terror -- meaning small-scale atrocities, from suicide bombs to beheadings. It is a long way from overthrowing the nations of the Western world, but it is devilishly difficult to stop.

To stop it, Bush has offered Muslims something he is confident they will perceive as better than their present life: political and economic freedom on the Western model, resulting in democracy and prosperity beyond their dreams. That is what he has offered the people of Iraq, by ousting Saddam Hussein and encouraging democratic change. It is a bold offer, and one Iraq (and after it, the world's Muslims) would do well to accept.

But the fanatics among them have no such intention. Democracy is unnecessary; sharia is the only law a Muslim needs. Who would reject it, in favor of the gross immorality so prevalent in the West? Rather, it is the West that must succumb to sharia.

That is the struggle that will dominate the 21st century, until one side or the other prevails. For the United States, it may mean only (only!) a steady drumbeat of terrorist incidents, some smaller and others quite possibly far larger than those of Sept. 11 -- not to mention the casualties that our soldiers must yet sustain in Iraq. But do not suppose we can avoid the battle by pulling out of Iraq and turning the White House over to Hillary Clinton. Our enemies in the Muslim world are going to be a lot harder to appease than that.