In hindsight, what tripped Bush up was more than just misjudging how long the insurgency would last, or how long US troops and their allies would need to stay. He was there to declare victory—the fall of Baghdad and, memorably, of a statue of Saddam Hussein, one month earlier. But in fact the war had hardly begun. Bush had sent in American troops, and celebrated victory, without fully articulating what “victory” actually meant.

Ten years later, in the second term of a new presidency, we still don’t know. With tens of thousands of American troops deployed overseas, and more certain to be committed in future conflicts, it’s critical for us to understand what we’re aiming for when we speak of victory.

“Having clear language on victory is necessary because it’s the only way we can establish any coherence on what a society—both its policy makers and its public—can expect to achieve when they decide to use military force,” said William Martel, associate professor of international security studies at Tufts University and author of “Victory in War: Foundations of Modern Military Policy.”

Martel is among a handful of scholars and military experts trying to solve one of the most nettlesome problems in modern foreign policy: coming up with a new definition of “victory” that matches the complexity of our conflicts.

When Martel and others look at the American public conversation about going to war, they see expectations still profoundly shaped by World War II, a conflict marked in our memories by the idea of unconditional triumph and a total remaking—as Bush put it in his speech aboard the USS Abraham Lincoln—of “enemies into allies.” Armies were crushed in that war, but so were ideologies.

It’s commonplace to note how much warfare has changed since then, but what we don’t often think about is how our public conception of victory has failed to change with it. The seemingly interminable military engagements in Iraq and Afghanistan have exposed the fuzziness of our stated objectives, such as defeating terror or spreading democracy. Without a clearer idea of what winning looks like, we risk falling into situations where wars could go on forever or—another possibility—where political leaders will never want to take us to war, because they won’t be able to anticipate an end.

To head off either of these futures, political scientists and military strategists are trying to formulate a new idea of victory, one that fits both the reality of today’s conflicts and our own limited capacity to engage in large, transformational wars. They suggest that it’s time to abandon World War II as a model, and some think that we should reach further into the past for a more realistic view of what we can achieve in war. Others argue we should do away with “victory” as a benchmark altogether. At least, they say, we need to come up with a model that is less ambitious about what we think we can win, and more clear-eyed about why we fight at all.

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Part of the confusion that day aboard the USS Abraham Lincoln was that instead of just touting the tanks rolling into Baghdad, Bush aimed rhetorically at a much broader and deeper idea: a sweeping victory in the “war on terror” that his administration had declared worldwide. “The war on terror is not over; yet it is not endless,” Bush said. “We do not know the day of final victory, but we have seen the turning of the tide.”

The breadth of his language was no accident. After 9/11, political leaders consciously defrosted an idea of victory that had served FDR and Churchill so well in World War II and positioned winning in the “war on terror” in terms that echoed our fight against Nazism—a total and utter annihilation of forces and ideas that threatened the “free world.”