This file image taken from an online video released by the Islamic State group's al-Furqan media arm on Tuesday, Jan. 20, 2015, purports to show the group threatening to kill two Japanese hostages that the militants identify as Kenji Goto Jogo, left, and Haruna Yukawa, right, unless a $200 million ransom is paid within 72 hours. (AP/AP)

Robert H. Scales, a retired Army major general, is a former commandant of the U.S. Army War College.

The centerpiece of a national security strategy is to isolate and exploit an enemy’s vulnerable “center of gravity.” Carl von Clausewitz, the 19th-century Prussian military philosopher and father of modern military theory, defined center of gravity as “the source of power that provides moral or physical strength, freedom of action, or will to act.”

Conventional wisdom inside the Pentagon and among defense intellectuals is that the vulnerable center of gravity of today’s enemy is its extreme Islamist ideology. Speaking on “Fox News Sunday” after the Charlie Hebdo attacks in Paris, Gen. Martin Dempsey, the chairman of the Joint Chiefs of Staff, suggested that the rise in the terrorists’ power has been mainly due to the inspiration that comes from an increasingly radical ideology. Thus, most of the Obama administration’s “nine lines of effort” to defeat radical Islam are, in fact, non-military actions meant to counter this ideology, such as disrupting the finances of terror groups and disseminating alternative messaging.

But the numerous attacks we have seen around the world suggest that this ideology is not a vulnerable center of gravity, if it ever was. Dedication to an ideological cause does not appear to be in short supply. Likewise, after the Abu Ghraib scandal and 12 years of perceived atrocities against Islam at the Guantanamo Bay prison, the United States long ago lost its ability to effectively fight an ideological war against Islamic terrorism.

Our political masters need to distinguish between ideology and the enemy’s true vulnerable center of gravity: hope. The differences are subtle. Hope is the belief that ideology will prevail. Hope drives motivation or, in the psychologist’s jargon, a “response initiation.” To the extent that hope is present, a terrorist will translate belief into action. As hope is removed, even the most ideologically attuned enemy will become passive. As Clausewitz advises: Strike the center of gravity and the enemy loses the will to act.

The history of war suggests hope is a fuel that induces young, post-adolescent men to turn ideology into action. And hope rises with the perception of military success.

Confederate soldiers were given hope of eventual victory after the Union debacle at the First Battle of Bull Run. A similar rise of mindless hope occurred among German youth after the fall of Paris in 1940 and, sadly, within the U.S. Army after the fall of Baghdad in 2003.

Hope extends wars and makes them bloodier through the euphoria that comes with a rush to share in the glory. Hope gives young men surety and confidence. It provides a moral sanctuary and is the glue that binds soldiers together in war. Soldiers — and, by extension, terrorists — simply won’t fight if there is no hope.

Arab cultures have a history with the mercurial collapse of hope. The huge swings in hope among Arab forces before and after defeats in the 1948 and 1967 Arab-Israeli wars and the U.S. victory in the Gulf War against Saddam Hussein’s army in 1991 are instructive. The apathy that followed Osama bin Laden’s killing also suggests that terrorists can lose hope after the death of a single icon.

Think of hope as a material formed in a crucible over time by a series of successful terrorist strikes against the West and Western-affiliated countries in the Middle East. Since violent actions filled this crucible, only a violent military counterresponse can crack the crucible and empty it of hope. The object of a campaign against hope is not necessarily to kill in large numbers but rather to find the greatest vulnerability and shatter it dramatically and decisively.

The terrorist’s greatest source of hope today comes from Islamic State battlefield successes in Syria and Iraq. A defeat there cracks the crucible. The question is how to do it with enough drama and speed that terrorists the world over lose hope and become passive. From any perspective, the Islamic State enclave in Syria is militarily unassailable. But Iraq is a different story.

A campaign against hope must start from Baghdad and move northward up the Tigris and Euphrates rivers. The Islamic State’s vulnerability rests with its disconnected garrisons spotted astride the rivers like a string of pearls. Thanks to U.S. bombing, Islamic State fighters cannot easily move among these enclaves. Thus, a sequence of patient ground assaults against garrisons in cities such as Taji, Hit, Tal Afar and eventually Mosul will create momentum sufficient to push the Islamic State’s forces to the Syrian border. These won’t be victories so much as public humiliations, the antidote to hope.

Can the Iraqis do it? If so, can they do it before the Islamic State solidifies its grip on the river cities? One thing is certain: The last best hope for a decisive outcome against the hopefulness of these killers rests with the Iraqi army and the Americans who are trying to turn them into a viable fighting force.