"Our war on terror begins with Al-Qaeda, but it does not end there. It will not end until every terrorist group of global reach has been found, stopped, and defeated," Bush said.
The attacks of 11 September prompted an outpouring of sympathy from around the world. Within a month the United States had assembled a wide coalition to root out Al-Qaeda and its supporters in Afghanistan.
For the United States and its allies, it marked the beginning of a global war necessary to defend against attacks on civilians and core values. Four years later, are they winning the war on terror?
Speaking late last year, Bush offered this status report: "More than three-quarters of Al-Qaeda's key members and associates have been detained or killed. We have led, many have joined, and America and the world are safer." Since then, there have been further arrests, like the May capture in Pakistan of Abu Faraj al-Libbi, said to be that country's most-wanted terrorist.
The United States cites other gains in the war on terror. Terror cells have been disrupted in Europe, the Middle East, and Asia. Millions of dollars of terrorist finances have been blocked. Libya has given up its programs to develop banned weapons. And new allies in the war -- Pakistan, Yemen -- are tackling militants on their own territory (though ties with another, Uzbekistan, cooled this year following the bloody suppression of antigovernment unrest.)
The U.S. government also cites the wars in Afghanistan and Iraq as successes in the fight against terrorism. And it says it's tackling terrorism's root causes, by working to advance democracy throughout the greater Middle East.
"If you believe, as I do and as President Bush does, that the root cause of 11 September was the violent expression of a global extremist ideology, an ideology rooted in the oppression and despair of the modern Middle East, then we must seek to remove the very source of this terror by transforming that troubled region," U.S. Secretary of State Condoleezza Rice has said.
Yet the number of attacks worldwide appears to be increasing: 651 significant attacks last year, according to the U.S. State Department -- three times as many as in 2003. And this year brought more outrages -- including, notably, London's first suicide bombings.
To many this indicates a weaker, but more dispersed enemy. "The real question is how do you measure success?" asks Vincent Cannistraro, a former CIA counterterrorism official in New York.
"Many of the people that have been killed have been replaced, so a reduction in the leadership is not a meaningful indicator because their people are replaceable parts," Cannistraro continues. "However, what we have accomplished by the antiterrorism program over the last few years is to remove experienced people and...they don’t have a secure base from which to launch their operations.... They can do smaller operations, like the London Underground bombings, the Madrid ralway bombing,... But while these are horrific incidents, they don't approach in any way the destruction that was accomplished on [11 September], so by that measure there has been some success."
Then there's Iraq. To the U.S. administration, the U.S.-led war is part of the broader war on terror -- Iraq is no longer a regional threat or a state sponsor of terrorism. The insurgency has led Bush to call Iraq the central front in the war on terror.
Critics say that might be true -- but only because the U.S.-led invasion opened that new front. Paul Cornish of King’s College, London, and co-author of a British report this summer that said the Iraq war had boosted Al-Qaeda's recruitment, told RFE/RL: "There is or seems to be a connection between what we are doing in Iraq and part of the grievances against Britain and the West.... Even though it's certainly the case that terrorist attacks by Al-Qaeda began before Afghanistan and Iraq,... we can't pretend that what we've done --- whether right or wrong -- is not part of the grievance against us."
These grievances include the presence of U.S. and other foreign troops in Iraq, Afghanistan and other Muslim countries, Russian actions in Chechnya, and U.S. support of Israel.
Some doubt whether figures such as Osama bin Laden really care about the causes they claim to champion. But even if it's just propaganda, they make a powerful rallying call -- to defend Muslim lands, as well as Islam’s core values against an onslaught of Western culture that dates back to the colonial era.
Faisal Devji, who is the author of "Landscapes of the Jihad" and teaches history at New School University in New York, told RFE/RL that he believes militant global jihadism is a short-lived movement, but added: "That's not the most important thing about it. The most important thing about it is what such a movement spurs in the Muslim world at large, how it changes attitudes, not simply towards the West or military incursions on Muslim territories. But how it reconstructs what it means to be Muslim, and Islam, whether this be militant or nonmilitant."
Experts say addressing the grievances and frustrations that drive people to extremism will be crucial to countering terrorist violence. They advocate programs that will better integrate Europe's Muslims, and investment in education in Islamic countries.
Jerrold Post, an expert on the psychology of terrorism at George Washington University, said he has pictures of a 13-month-old infant with a suicide bomber’s belt around his waist.
“So we’re talking about hatred being bred in the bone very early," he continued. "We’ve already lost this generation, and I believe we really need to be thinking not about the so-called ‘war against terrorism,’ but about a campaign to be gradually attacking some of these really quite extreme attitudes within what is basically a humane and compassionate religion. And those changes can only come from within Islam.”
Until that happens, he said there can be no victory in the war on terror.
The second part of our series looks at how the enemy in the war on terror is changing.
(RFE/RL correspondent Jeffrey Donovan contributed to this article.)
World: Four Years Later, No Clear Winners In War On Terror (Part 1)
World: Who Is The Enemy -- And How Is It Changing? (Part 2)
World: Can West Fight Terror And Still Maintain Civil Liberties? (Part 3)
World: Global War On Terror Faces Government With Unique Enemy (Part 4)
For all of RFE/RL's coverage on the global fight against terrorism, visit our War On Terror website.