So how do we fight ISIS? Giving Baghdadi more time as caliph might only make him more plausible in the role and allow him to draw more fighters to his state. If that is true, one concerned Western scholar told me, we would be wise to kill him fast. Right now only an infinitesimal number of Muslims have sworn fealty to him. The biggest danger is letting that number grow. Once he becomes a popular figure instead of a divisive one, his death will have spillover effects. “Killing the religious leader of even a small minority of Muslims is not good propaganda,” says Cole Bunzel.

But a massive invasion by the United States would have equally deplorable effects, because it would instantly convert Baghdadi’s squalid army into the world’s premier terrorist organization. A balanced and effective approach, then, would be to kill him as fast as possible and to use Kurdish and Shia proxies to arrest his state’s expansion. By confining U.S. action to surgical raids and proxy war, we might avoid accidentally anointing him or his successor Grand Poobah of the Mujahedin.

It’s also true that killing one caliph can extinguish a whole line. Consider the fate of Baghdad’s last Abbasid caliph, al-Mustasim Billah. When the Mongols sacked Baghdad in 1258, their leader Hulagu Khan (grandson of Genghis) ordered slaughter on a scale rarely witnessed in history. His men murdered as many as a million Muslims in a week, in an age when death was still dealt manually, with blades and cudgels. Even in victory, Hulagu treated the caliph with circumspection. Because it was bad luck to let royal blood touch the earth, Hulagu rolled Mustasim in a carpet before loosing a whole stable of horses to stampede over his body. Whether by drone, or by a well-placed bullet from one of Kurdistan’s famous female commandos, it seems likely that Baghdadi’s death will be less tidy.