A Kurdish fighter keeps guard against Islamic State militants near Mosul in northern Iraq, August 19, 2014.
Youssef Boudlal / Courtesy Reuters

In 2005, Ayman al-Zawahiri, deputy head of al Qaeda, had a killer idea: the al Qaeda franchise in Iraq (AQI) should declare an Islamic state. In a letter to Abu Musab al-Zarqawi, the brutal leader of AQI, Zawahiri explained how it would work. The Islamic state, he wrote, would fill security vacuums around Iraq left by departing American forces. Once the Islamic state successfully fended off the attacks from neighboring countries that would undoubtedly follow, it could proclaim the reestablishment of the caliphate, the one-man institution that had ruled a vast empire in early Islamic history. For the scheme to succeed,

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