In a striking admission, George W. Bush said the other day that that"We actually misnamed the war on terror. It ought to be [called] the struggle against ideological extremists who do not believe in free societies and who happen to use terror as a weapon to try to shake the conscience of the free world."

This important concession follows growing criticism of the misleading term"war on terror" (how can one fight a tactic?) and replaces it with the more accurate"war on ideological extremists." With this change, the battle of ideas can begin.

But who exactly are those ideological extremists? The next step is for Mr. Bush to give them a name.

In fact, on occasion since September 11 he has spoken candidly about their identity. As early as September 2001, he referred to the enemy being"a fringe form of Islamic extremism" which seeks"to kill Christians and Jews, to kill all Americans, and make no distinction among military and civilians, including women and children." This Islamic extremism also is heir to"all the murderous ideologies of the twentieth century," including"fascism, and Nazism, and totalitarianism."

In January 2002, Mr. Bush was more specific yet, adding that the terrorist underworld includes"groups like Hamas, Hezbollah, Islamic Jihad, [and] Jaish-i-Mohammed." In May 2002, he pointed out that a"new totalitarian threat" exists whose adherents"are defined by their hatreds: they hate … Jews and Christians and all Muslims who disagree with them" (implying that they are Muslims). Those adherents, he noted, feel entitled to kill"in the name of a false religious purity."

A year later, in May 2003, the president provided details about the Islamists' goals, observing that"nineteen evil men—the shock troops of a hateful ideology—gave America and the civilized world a glimpse of their ambitions. They imagined, in the words of [Ramzi Binalshibh, the Al-Qaeda leader accused of directing the 9/11 operation], that September the 11^th would be the ‘beginning of the end of America.'"

The terrorist acts of the past two decades, Mr. Bush noted in April 2004, are the work of fanatical, political ideologues who"seek tyranny in the Middle East and beyond. They seek to oppress and persecute women. They seek the death of Jews and Christians, and every Muslim who desires peace over theocratic terror."

Last month, Bush for the first time used the phrase"Islamic militants," perhaps his most explicit reference until now to the Islamist threat, saying that until he closed a so-called Islamic charity based in Illinois, the Benevolence International Foundation, it" channel[ed] money to Islamic militants."

Rolling these comments into a single summary statement establishes how Mr. Bush – and by extension the whole of the U.S. government – sees the enemy: A false doctrine of Islamic purity inspires a totalitarian ideology of power and domination. In its ruthlessness, murderousness, and global ambition, it resembles the Nazi and communist ideologies. The extremists who advocate this doctrine see America as the chief obstacle to achieving their goals. To defeat America, they initially seek Washington's retreat from the outside world. Ultimately, they hope to bring about a collapse of America as it now exists. Toward this end, they are prepared to murder any number of Americans.

This is a fine description of Islamism, its mentality, methods, and means. It also shows that Mr. Bush draws the subtle distinction between the personal faith of Islam and the political ideology of Islamism (or militant Islam).

In this, he parallels what a number of Muslim leaders – including even some Saudis – have said. Following acts of terrorism in Riyadh in May 2003, Interior Minister Prince Naif publicly attributed this violence to"ideology" and"fanatical ideas." And if Naif – himself an Islamist – attributes the problem ultimately not to acts of violence but the ideas behind them, surely Americans can say no less.

Mr. Bush has already alluded to America having to confront its third totalitarian ideology. Now he should name that ideology. I hope he will surround himself with a group of distinguished anti-Islamist Muslims, foreign and domestic alike, and formally announce America's acceptance of leadership in the war against Islamism.

Only with such specificity can the civilized world start on the path to victory over this latest manifestation of barbarism.

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This article is reprinted with permission by Daniel Pipes. This article first appeared in the New York Sun.