The jihadist insurgent group ISIS, or as it now prefers to be called, the Islamic State, appears well on the road to achieving its stated goal: the restoration of the caliphate. The concept, which refers to an Islamic state presided over by a leader with both political and religious authority, dates from the various Muslim empires that followed the time of the Prophet Muhammad. From the seventh century onward, the caliph was, literally, his “successor.”

The problem with this new caliphate, which, an ISIS spokesman claimed on Sunday, had been established under Abu Bakr al-Baghdadi, an Islamist militant leader since the early days of the American occupation of Iraq, is that it is ahistorical, to say the least.

The Abbasid caliphate, for example, which ruled from 750 to 1258, was an impressively dynamic and diverse empire. Centered in Baghdad, just down the road from where ISIS is occupying large areas of Iraq, the Abbasid caliphate was centuries ahead of Mr. Baghdadi’s backward-looking cohorts. Abbasid society during its heyday thrived on multiculturalism, science, innovation, learning and culture — in sharp contrast to ISIS’ violent puritanism. The irreverent court poet of the legendary Caliph Harun al-Rashid (circa 763-809), Abu Nuwas, not only penned odes to wine, but also wrote erotic gay verse that would make a modern imam blush.

Centered on the Bayt al-Hikma, Baghdad’s “House of Wisdom,” the Abbasid caliphate produced notable advances in the sciences and mathematics. The modern scientific method itself was invented in Baghdad by Ibn al-Haytham, who has been called “the first true scientist.”

With such a proliferation of intellectuals, Islam itself did not escape skeptical scrutiny. The rationalist Syrian scholar Abu’l Ala Al-Ma’arri was an 11th-century precursor of Richard Dawkins in his scathing assessments of religion. “Do not suppose the statements of the prophets to be true,” he thundered. “The sacred books are only such a set of idle tales as any age could have and indeed did actually produce.”

It is this tolerance of free thought, not to mention the supposed decadence of the caliph’s court, that causes Islamist radicals to hark back to an earlier era, that of Muhammad and his first “successors.” But even these early Rashidun (“rightly guided”) caliphs bear little resemblance to jihadist mythology. Muhammad, the most “rightly guided” of all, composed a strikingly secular document in the Constitution of Medina. It stipulated that Muslims, Jews, Christians and even pagans had equal political and cultural rights — a far cry from ISIS’ punitive attitude toward even fellow Sunnis who do not practice its brand of Islam, let alone Shiites, Christians or other minorities...