Working with Turkish special forces to get the PKK out of Iraqi Kurdistan would not necessarily be a bad idea.
The one thing we should be trying as hard as we can to avoid is a Turkish invasion of Iraq. That would be a genuine, full-bore catastrophe. (I'm using "invasion" here to mean an invasion by substantial Turkish forces, as opposed to an incursion by special operations forces or something.) And Turkey could well invade. It has forces massed on the border. It has been making threats for months.
Between the fact that the PKK is a repellent terrorist organization and the fact that it introduces a whole new range of tensions into a relationship between two of our allies that would be strained in any case, I would support action by special forces against the PKK under the following conditions:
* We think it would work. This is a serious concern: wholesale Turkish invasions have not worked in the past. This is very, very difficult mountainous terrain.
* The Kurdish government in Iraq signs off, at least privately. They might well do this, though I think it would cost them to support us publicly.
* We believe that it would be better if we did this than if the Kurdish government did. This might be true for a number of reasons: internal Kurdish politics and the government's need to deny involvement, for instance, or the fact that the Kurdish forces are fighting elsewhere as part of the Iraqi army. (They are.) On the other hand, it might be better for the Kurds to do it, in which case, if they are willing, they should.
* We have the forces available, and this would be the best use for them. (Obviously, if we could get the forces needed only by causing even greater problems elsewhere, it would not be worth it.)
Hilzoy takes a very reasonable tone towards this issue, but there are a lot of problems with her approach, which I'll try to address.
First off, let's be clear that the PKK is in fact a terrorist organization, and it's not only the Turks who think so. Since it instigated a guerilla war against the Turkish government in the 80's, the PKK has been responsible for the deaths of thousands of Turkish civilians and military personnel. So repellant, yes. However, the PKK operates largely with the support of the mostly disenfranchised Kurds, an ethnic group spread out over a substantial part of the northern Middle East that lacks any state representation outside of the mostly autonomous Kurdish Iraq. The PKK is hardly the only voice of the Kurdish people, but is has much of the sympathy of Iraq's Kurds, who are familiar with Turkey's repression of their Kurds, and who are intimately familiar with repression themselves having suffered it at the hands of Saddam Hussein. In other words, the PKK is but one symptom of the geo-political circumstances that the Kurds find themselves in; a minority in every state, subject to discrimination and disenfranchisement at the hands of far larger ethnic minorities. The sympathy Iraq's Kurds have for Turkey's Kurds and the goals of the PKK are not surprising. For this reason alone, it's unlikely that the Iraqi Kurdish authorities would take part in or desire to be seen as acquiescing to any attacks on PKK havens in their territories. As overbearing as the PKK can be (what group of armed militants in Iraq aren't lately?) any irritation the average Iraqi Kurd has as a result is unlikely to transform into support for attacks on the PKK.
But there's another reason that Kurdish authorities are unlikely to support or acquiesce to such attacks. In april Massoud Barzani, President of the Kurds autonomous government and leader of one of two of the Iraqi Kurds prominent political organizations the KDP (as opposed to the PUK, which is headed by Kurdish Iraqi President Jalal Talabani) threatened to "interfere" with the Kurds in Turkey if the Turks interfered in Kurdish Iraq, specifically the referendum over Kirkuk. You don't have to be a genius to understand what he means by "interfere" or to understand that he would do so via the PKK. So the PKK may sometimes be a nuisance, but they may also be a tool.
Of course, Barzani's comments are partially what provoked the recent crisis between the Kurds in Iraq and Turkey, which has been irritated enough to shell and chase PKK militants into Kurdish Iraq and threaten a more significant military incursion. But the Turks face significant obstacles to any military operation. They've carried out operations of varying scale into northern Iraq before in the hunt for PKK militants, and those operations have at best been a mixed success. And while the Kurdish Peshmerga may be no match in a stand-up fight with the Turkish army, the Turks also have no real desire to chase the PKK and Peshmerga fighters throughout the mountains of northern Iraq.
Lastly, there's the fact that a Turkish incursion in Iraq is a very different operation now than it was during the days of Saddam Hussein. Saddam couldn't do much about the Turks during the 90's, but we have over 150,000 troops sitting in Iraq at this moment, and a crucial interest in bringing stability to the region. As you can imagine, a Turkish invasion of what is currently the "success story" in Iraq-Kurdish autonomy and stability-does not comport with that goal. It's difficult for me to imagine the Turks deliberately carrying out a significant military operation without our implicit or express approval, even if they overcame significant reasons of their own not to launch just such an operation. And it's as difficult for me to imagine even the Bush administration giving their approval to significant operations.
Right now there exists peace and stability in Kurdish Iraq, at least compared to other more contentious regions of the country. But there's plenty reason to think that such peace is not guaranteed to last. The Iraqi constitution mandates a referendum in December of this year that will decide the fate of oil-rich Kirkuk, and whether it will join the Kurdish autonomous region or remain a part of Iraq. It is largely expected that the Kurds will win this referendum, a result that nearly everyone opposes in Iraq but the Kurds, and that the Turks also oppose for fear that it will presage a later declaration of Kurdish statehood. If the results of the referendum are as expected, there's really no telling at this stage what the Turks will do, or what the Sunni Arabs or Shiite or the Iraqi national government will do. It's on top of this underlying tension that we have PKK incursions into Turkey, and Turkish incursions into Kurdish Iraq.
The balance of interests is very delicate, and not something that we really ought to consider treading in. Turkey is our ally in the region, and by virtue of their membership in NATO, and we must respect their concerns about the PKK and Kurdish autonomy. At the same time, the Turks must understand that our greatest interest right now-above all other national security interests save the threat of al Qaeda-is peace and stability in Iraq. Weighing in on so intractable and delicate a matter as the hostile relationship between the Kurds and Turkey by employing military force against the PKK is in no way advancing that interest. The only reason we might consider doing so is if a Turkish invasion were imminent absent any action our part, but the Turks are unlikely to go so far. While attacking the PKK via special forces, airstrikes or whatever, might be some kind of gesture of goodwill to the Turks, it would also be throwing away what goodwill we've accumulated among the Iraq Kurds-who let's not forget-we steadfastly defended against Saddam Hussein throughout the 90's. We should also not forget that the Kurds have compelling interests of their own; the Turks seek to protect their security interests, but the Kurds seek to protect their autonomy (and likely statehood someday.) And given the oppression they have faced in other Middle Eastern nations, it's an autonomy that they deserve.
Unfortunately, this is one of those situations where a balancing of competing interests makes clear that we have no choice but to engage primarly in diplomacy in resolving these points of contention. There's no reason to believe that clever diplomacy can resolve this conflict alone, but at this point a military option is simply unjustifiable.