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When French President Francois Hollande said Friday's attacks on Paris were an "act of war," he was following a script set by George W. Bush in the aftermath of the Sept. 11 attacks. Rhetorically, invoking the language of war to describe a terrorist attack sends a message of seriousness and outrage. But as the United States's post 9/11 wars show, it isn't always wise to elevate a terrorist group to the level of the sovereign entities that traditionally have the authority to make war.

This was a mistake with respect to al-Qaida, but it's a greater mistake when it comes to Islamic State, whose primary aspiration is to achieve statehood. By saying that Islamic State is in a war with France, Hollande is unwittingly giving the ragtag group the international stature it seeks.

The consequences of Hollande's declaration go beyond the public relations boon to the Sunni militant group, which has otherwise been struggling to stay in the headlines and gain the adherents it needs to control territory. A head of state who says that war has been made against his country must have a credible response in mind.

The appropriate response depends on whether the state of war is construed legally or metaphorically. The legal angle is somewhat important. Under Article 5 of NATO's Washington Treaty, an act of war from outside the North Atlantic Treaty Organization against one of the member states triggers obligations of support from the other treaty members.

The Sept. 11 attacks marked the first time Article 5 was invoked. That required all the NATO members to support the U.S. war against al-Qaida. (When it came to Iraq, several NATO members famously balked, reasoning that there was no proof the terrorist attack had anything to do with Saddam Hussein.)

If France invoked Article 5, NATO members would be obligated to support it in a war against Islamic State. Yet the disillusioning aspect of this legal position is that France has been bombing Islamic State strongholds in Syria since late September, and its attacks on the group in Iraq are old news.

In other words, France is already at war with Islamic State. The Paris attacks aren't the first salvo. They are, at most, the Islamic State response to French assaults that expanded after the terrorist attacks on Charlie Hebdo and a Jewish market in January.

As a result, considering the recent terrorist attacks to be an act of war won't change the basic legal state between France and Islamic State. The newspaper Le Parisien ran the headline, "Cette fois, c'est la guerre" — "This time, it's war." But whatever French public perception may have been, France was already engaged.

That leaves the metaphorical sense of war. Here it's useful to review Hollande's options.

Saying that the attacks were an act of war could motivate public opinion for a more rigorous response than France has so far pursued against Islamic State. Because France is already bombing, that would mean a significantly stepped-up participation in the air war — or the introduction of French ground troops.

To be sure, the war against Islamic State almost certainly can't be won without ground troops. The remarkable longevity the group has so far shown is primarily attributable to the fact that no regional power has been prepared to commit such troops. Kurdish militias backed by Western air power and Iranian-backed Shiite militias in Iraq are the only troops to have made any real inroads against Islamic State, unless you consider the Syrian regular forces supported by Soviet planes.

French ground troops, then, would be a great boon to the battle. But it seems overwhelmingly likely that Hollande has no intention of sending French troops, no matter how angry the public may be.

The strategic rationale for withholding ground troops hasn't changed. The U.S. won't provide any because of public skepticism after the Afghan and Iraqi disasters. And if the U.S. isn't willing to commit troops, neither is anybody else, from Saudi Arabia to Jordan to, yes, France. The Paris attacks won't move the needle sufficiently for Hollande to pursue a different course.

That leaves Hollande with no military option but contributing more to the air war. That's fine, but it points to a deep flaw in his declaration. If Islamic State has really committed an act of war against France, shouldn't France do more than send a few planes?

More concretely, Hollande must certainly realize that by acknowledging a war against France, he's acknowledging a war that France can't win, at least in the short to medium term. More air attacks won't defeat Islamic State definitively. Thus, the metaphor of the "act of war" puts France into a disadvantageous position: It's at war with an enemy, but it lacks the political will or military capacity to defeat that enemy. The best it can hope for is to degrade the enemy's capacities. Yet given that the enemy isn't even a proper state, the failure to beat it in fact looks very much like defeat.

Painful as it might have been, the right course for Hollande would have been to denounce the terrorists as murderers unworthy to be considered in a war against the great republic of France. He should've said that a handful of ideologues who killed innocent civilians couldn't threaten or move the republic — and that France wouldn't allow Islamic State to dictate its domestic or foreign policies.

If President Bush had treated al-Qaida this way, it would've enabled a calmer, more rational approach to the wars in Afghanistan and Iraq. The U.S. almost certainly would've still bombed the Taliban. But it might not have committed itself to destroying that regime. It might've been sufficient to force the Taliban to stop harboring al-Qaida terrorists.

Meanwhile, eschewing the notion that al-Qaida had made war on the U.S. would've made it much harder to say that Iraq should be invaded on national security grounds. The elision of the threat from al-Qaida with the threat from Iraq was eased by the idea that al-Qaida was an entity capable of making war on a great nation.

Morally speaking, a terrorist attack may be as evil as an act of war. But practically, the two are very different — and preserving the distinction is wise foreign policy.

Noah Feldman is a professor of constitutional and international law at Harvard University.