IS also decided to run away with its tail between its legs after planning a ghazwa against Jordan, where Zarqa, the birthplace of Abu-Misaab al-Zarqawi, the patron saint of the caliphate, is located. However, that ghazwa, too, had to be shelved for another day when it became clear that, unlike the Iraqi and Syrian armies, the Jordanians were determined to give the caliph a run for his money.

IS is not a classical terrorist organisation. It is an enemy of humanity, what Roman law classified as hostis humani generis. Thus, despite what President Obama says about merely “containing and degrading” it, it must be defeated and destroyed.

So far, IS has been relatively successful because it has not hit anything hard on its way. The homeopathic air strikes reluctantly ordered by Obama have boosted IS’s narrative of Islamic victimhood without doing much real damage. The last report of the strikes I saw from Secretary of State John Kerry in November put the figure at more than 3,700 over 15 months, a third of them against IS targets in Raqqa. IS has simply factored in the attacks as part of daily hazards, especially because its agents can warn about the approach of bombers over their mobile phones. (Yes, the cellular network operates perfectly in Syria because the company providing it belongs to a cousin of President Assad.) IS has been in control of the rhythm and tempo of this war, even choosing the cadence of the occasional battles it fights.

If Hollande manages to create a new coalition, something still uncertain at the time of this writing, the aim should be to wrest the initiative away from IS. That means turning what is a low-intensity war into one of medium intensity with wider and more frequent air strikes and raids by Special Forces to destroy IS’s logistics and fragment its territorial control. This could be done only if local militias, many of them temporarily allied to IS because of fear or in exchange for arms and money, are confident that the major powers seek IS’s defeat and destruction, regardless of how long that might take. If IS begins to lose its aura of easy winning, it would face numerous hostile armed groups nominally allied with it, because, in the Middle East at least, everyone prefers to be on the side of the winner.

In his message to Congress, Obama asked for permission to take action in Syria but insisted that he was not looking for something “unendurable”, by which he presumably meant a short campaign. In November, Kerry corrected that by inventing a word of his own: “multi-year”. That is how long he thinks fighting IS will take.

There are plenty of people who want to fight IS in Syria and Iraq: the Kurds, the Turkmens, the Druze and the less obnoxious Islamist groups such as Ahrar al-Shaam (Free Men of the Levant), not to mention Sunni Arab tribes on both sides of the border.

In many areas IS is in overall, largely nominal control of territories held by countless emirs who could be persuaded to switch sides. With their help IS territory could be turned into a patchwork of conflicting authorities vulnerable on all sides. IS’s decision to masquerade as a state, a caliphate, may be its chief attraction for Western “volunteers for martyrdom” in search of an Islamic dream. But in military terms this could be IS’s Achilles heel because it offers a range of easy targets for air strikes.

It was precisely by raising the intensity of a low-intensity war that US General David Petraeus managed to destroy al-Qaeda in Iraq. An adapted version of that strategy — the “surge” — could help to get rid of IS. But that requires leadership — US leadership.