IMAGINE THAT on 9/11, six hours after the assault on the twin towers and the Pentagon, terrorists had carried out a second wave of attacks on the United States, taking an additional 3,000 lives. Imagine that six hours after that, there had been yet another wave. Now imagine that the attacks had continued, every six hours, for another four years, until nearly 20 million Americans were dead. This is roughly what the Soviet Union suffered during World War II, and contemplating these numbers may help put in perspective what the United States has so far experienced during the war against terrorism.

It also raises several questions. Has the American reaction to the attacks in fact been a massive overreaction? Is the widespread belief that 9/11 plunged us into one of the deadliest struggles of our time simply wrong? If we did overreact, why did we do so? Does history provide any insight?

Certainly, if we look at nothing but our enemies’ objectives, it is hard to see any indication of an overreaction. The people who attacked us in 2001 are indeed hate-filled fanatics who would like nothing better than to destroy this country. But desire is not the same thing as capacity, and although Islamist extremists can certainly do huge amounts of harm around the world, it is quite different to suggest that they can threaten the existence of the United States.

Yet a great many Americans, particularly on the right, have failed to make this distinction. For them, the “Islamo-fascist” enemy has inherited not just Adolf Hitler’s implacable hatreds but his capacity to destroy. The conservative author Norman Podhoretz has gone so far as to say that we are fighting World War IV (No. III being the Cold War).

But it is no disrespect to the victims of 9/11, or to the men and women of our armed forces, to say that, by the standards of past wars, the war against terrorism has so far inflicted a very small human cost on the United States. As an instance of mass murder, the attacks were unspeakable, but they still pale in comparison with any number of military assaults on civilian targets of the recent past, from Hiroshima on down.

Even if one counts our dead in Iraq and Afghanistan as casualties of the war against terrorism, which brings us to about 6,500, we should remember that roughly the same number of Americans die every two months in automobile accidents.

Of course, the 9/11 attacks also conjured up the possibility of far deadlier attacks to come. But then, we were hardly ignorant of these threats before, as a glance at just about any thriller from the 1990s will testify. And despite the even more nightmarish fantasies of the post-9/11 era (e.g. the TV show “24’s” nuclear attack on Los Angeles), Islamist terrorists have not come close to deploying weapons other than knives, guns and conventional explosives. A war it may be, but does it really deserve comparison to World War II and its 50 million dead? Not every adversary is an apocalyptic threat.

So why has there been such an overreaction? Unfortunately, the commentators who detect one have generally explained it in a tired, predictably ideological way: calling the United States a uniquely paranoid aggressor that always overreacts to provocation.

In a recent book, for instance, political scientist John Mueller evaluated the threat that terrorists pose to the United States and convincingly concluded that it has been, to quote his title, “Overblown.” But he undercut his own argument by adding that the United States has overreacted to every threat in its recent history, including even Pearl Harbor (rather than trying to defeat Japan, he argued, we should have tried containment!).

Seeing international conflict in apocalyptic terms — viewing every threat as existential — is hardly a uniquely American habit. To a certain degree, it is a universal human one. But it is also, more specifically, a Western one, which paradoxically has its origins in one of the most optimistic periods of human history: the 18th century Enlightenment.

Until this period, most people in the West took warfare for granted as an utterly unavoidable part of the social order. Western states fought constantly and devoted most of their disposable resources to this purpose; during the 1700s, no more than six or seven years passed without at least one major European power at war.

The Enlightenment, however, popularized the notion that war was a barbaric relic of mankind’s infancy, an anachronism that should soon vanish from the Earth. Human societies, wrote the influential thinkers of the time, followed a common path of historical evolution from savage beginnings toward ever-greater levels of peaceful civilization, politeness and commercial exchange.

The unexpected consequence of this change was that those who considered themselves “enlightened,” but who still thought they needed to go to war, found it hard to justify war as anything other than an apocalyptic struggle for survival against an irredeemably evil enemy. In such struggles, of course, there could be no reason to practice restraint or to treat the enemy as an honorable opponent.

Ever since, the enlightened dream of perpetual peace and the nightmare of modern total war have been bound closely to each other in the West. Precisely when the Enlightenment hopes glowed most brightly, wars often took on an especially hideous character.

The Enlightenment was followed by the French Revolution and the Napoleonic wars, which touched every European state, sparked vicious guerrilla conflicts across the Continent and killed millions (including, probably, a higher proportion of young Frenchmen than died from 1914 to 1918).

During the hopeful early years of the 20th century, journalist Norman Angell’s huge bestseller, “The Great Illusion,” argued that wars had become too expensive to fight. Then came the unspeakable horrors of World War I. And the end of the Cold War, which seemed to promise the worldwide triumph of peace and democracy in a more stable unipolar world, has been followed by the wars in the Balkans, the Persian Gulf War and the present global upheaval. In each of these conflicts, the United States has justified the use of force by labeling its foe a new Hitler, not only in evil intentions but in potential capacity.

Yet as the comparison with the Soviet experience should remind us, the war against terrorism has not yet been much of a war at all, let alone a war to end all wars. It is a messy, difficult, long-term struggle against exceptionally dangerous criminals who actually like nothing better than being put on the same level of historical importance as Hitler — can you imagine a better recruiting tool? To fight them effectively, we need coolness, resolve and stamina. But we also need to overcome long habit and remind ourselves that not every enemy is in fact a threat to our existence.

David A. Bell, a professor of history at Johns Hopkins University and a contributing editor for the New Republic, is the author of “The First Total War: Napoleon’s Europe and the Birth of Warfare as We Know It.”