Over the weekend, White House Chief of Staff Denis McDonough was asked on NBC's Meet the Press what victory would look like in the new struggle against Islamist extremists in Iraq.

"Success looks like an ISIL that no longer threatens our friends in the region, that no longer threatens the United States," McDonough said.

Vague as that is, it may be the best answer available at the moment. And that is a problem.

The U.S. is undertaking another major, if primarily aerial, combat role in another Middle East conflict. This is happening because a new monster has emerged there, threatening to destabilize the never-too-stable region in worse ways than we have seen to date.

But most Americans are far from clear as to what this "ISIL" monster is, other than a few shadowy, portentous figures on disturbing videotapes.

This new monster is a murky creature, even in its naming. It calls itself the Islamic State, but is also referred to by the acronym ISIL (for Islamic State in Iraq and the Levant) or ISIS (Islamic State in Iraq and Syria).

The group is also hard to pin down in size, as some say it has tens of thousands of active fighters and others say fewer than 20,000. As for origins, the group sprang from the Syrian civil war and spilled over much of Iraq. Its fighters come mostly from these two countries, but there are also significant numbers from other Sunni Muslim states, and recruits from Muslim communities as far away as Michigan.

The aims of this new terror champion, as it relates to the U.S., are similarly unclear. We hear again that they will re-establish the Sunni caliphate that transcends the modern borders of several Middle Eastern countries. This was a theme of President George W. Bush's administration when it was urging the U.S. to fight al-Qaida more than a decade ago, and indeed the old al-Qaida in Iraq was one of the antecedents of the current ISIS thrust.

But for most Americans, the Bush wars of a decade ago were really about avenging the terrorist attacks al-Qaida had perpetrated on New York and Washington, D.C., on Sept. 11, 2001. It started with a fight against al-Qaida and its host regime the Taliban in Afghanistan. But much of the national anger over Sept. 11 was soon diverted by the White House to the bête noir of an earlier decade, the Iraqi dictator Saddam Hussein.

That was a natural target for the second President Bush and Vice President Dick Cheney and their inner circle of advisers because they had been through the first Persian Gulf war with Iraq under the first President Bush in 1990-1991.

The first Persian Gulf war began when Saddam invaded and annexed neighboring Kuwait. It occasioned a high-minded and substantive debate in Congress preceding votes in the House and the Senate to support the war.

In the end, that engagement was one-sided and quickly over. It humbled Saddam but left him in power in Baghdad and frustrated the warriors in Washington who saw the al-Qaida provocation in 2001 as the opportunity to settle accounts in Iraq once and for all — even without proving any connection between him and Sept. 11.

In pursuing these fights, the administration and Congress and the country had fairly clear notions of what it was looking to accomplish. They may have been delusions, but they were clear to us at the time. We expected to see al-Qaida leader Osama bin Laden taken "dead or alive," as even the president said at the time. And we expected to see Saddam overthrown and either jailed or executed.

We had our highly defined and visible villains, and we demonized them as latter-day Hitlers.

So it took years to find and kill bin Laden. And it took many months to arrest, try and execute Saddam. But these symbolic victories were achieved — after a fashion.

Our other clear goal was to see democratically elected governments in Afghanistan and Iraq. Standing up such regimes in Kabul and Baghdad has proven far more difficult. Depending on your definition of democracy, you might well say it has not happened yet in either nation. But surely there has been tremendous effort toward these goals.

What will be the goals of the fight against ISIS? At this point, we know only that we want to stop the beheading of Western journalists and aid workers. The videotaped evidence of these barbarities has been the goad to the latest American re-commitment to fighting in Iraq.

Just prior to that, the U.S. had recommenced airstrikes in northern Iraq to protect a population of Yazidis — a religious minority driven from their homes by ISIS. Here again, our involvement was driven largely by the TV images of the Yazidis provided by CNN and other Western cameras.

When ISIS moved on, the Yazidis vanished from the screen and the Western consciousness. Will that happen if the decapitation videos stop?

In the weeks ahead we can expect to see much video footage of F-18s leaving the decks of aircraft carriers, and surveillance video of targets being "degraded and destroyed." But how will we know if the same is happening to ISIS? Is this movement a collection of all-terrain vehicles carrying heavy machine guns, or is it something more?

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