The grey zone is where I want to live. Islamic State hates it, that place between black and white, where nothing is ever either/or and everything is a bit of both. Those who have studied the organisation tell us “the grey zone” – Isis’s phrase – is high on the would-be warriors’ to-eradicate list, along with all those other aspects of our world that so terrify them: women, statues of the past, the pleasures of the present.

Specifically, the grey zone refers to the sphere of coexistence where Muslim and non-Muslim might live together. That’s anathema to the frightened young men of Isis, who yearn for a world divided on binary lines, with room for only two categories – them and the infidel. Such a world would be as clean and neat as computer code, with Isis the ones and the rest of us reduced to zeros.

No wonder a city such as Paris – indeed, the very idea of a city – appals them. Such places are all about mixing, like with unlike. The modern city, whether Paris or Beirut, scares them because it suggests that human beings might just be able to rub along, those who are Muslim and those who are not, living in the same places, visiting the same shops, watching the same football matches, listening to the same music.

“Refugees welcome” scares them. It undermines their insistence that the west has an ingrained hostility to Muslims and could never be their home. Isis despises empathy and longs instead for polarity and conflict. They want atrocities such as last week’s in Paris – or today’s siege in Mali – to sow fear and loathing, so that non-Muslim majorities turn on their Muslim neighbours until the latter conclude the only place they can ever truly belong is the caliphate. One or the other, either/or. In the Isis mind, ambiguity, like a hybrid identity, is weakness and decadence.

In this last, trembling week, the grey zone has sometimes seemed to be shrinking. Not in the way Isis planned, but rather, under internal pressure. Our own debate about what to do next, about how to deal with a force that we struggle to describe, let alone understand, has polarised too, as it often does at moments of great strain. We’re losing sight of the grey.

Take what has been a perennial element of these conversations since 12 September 2001. Are terror attacks such as these “blowback” for western foreign policy? Stop the War rushed to make that point, too quickly even for its own tastes: within hours of the attacks, it had posted a blog headlined “Paris reaps whirlwind” of western action, only to take it down soon afterwards. Meanwhile, others slam such talk as a sophisticated form of victim-blaming or even western self-hatred, in which everything is always our fault, a worldview that strips Isis of moral agency and responsibility.

It can be hard to hear yourself think above the clamour; the voice of the grey zone gets drowned out. But there’s a distinction to make. There are the motives, even theology, of the hardcore Isis ideologues; and there’s what drives previously uncommitted people to rally to their flag. For example, it might be true that Isis ideology is rooted in something deeper than a desire to avenge western foreign policy – yet also true that lethal western interference in mainly Muslim countries has recruited disaffected young Muslims to violent jihadism. Both statements could be true at the same time. Yet too often people argue as if it’s one or the other, 1 or 0.

For my own part, I can see the appeal of the “blowback” case. Since 9/11 the west has kept intervening, and the terror has not stopped. But it’s such an incomplete account. Shiraz Maher of the International Centre for the Study of Radicalisation at King’s College, London, has interviewed more than 100 Isis volunteers and reads the group’s propaganda diligently. He is clear that militants have been radicalised by western “sins of omission” just as much as the west’s “sins of commission”.

Many headed to Syria in 2013, for example, before Isis had established its caliphate or made the descent into outlandish barbarism, having come to the disgusted conclusion that the west was not going to bomb the Assad regime and that, if they wanted to defend Syrians from Assad’s barrel bombs, they would have to do it themselves. Similarly, the 1990s generation was radicalised by the west’s failure to intervene earlier to save Muslim lives in Bosnia.

In other words, attributing Isis terror – or even Isis recruitment – to western action is a temptingly neat explanation, but it fails to account for the fury at western inaction. In the violent jihadist worldview, western intervention has been a provocation – but so has western non-intervention.

What’s more, it’s not just military action that triggers a fierce Isis response. Recall the beheading of the US journalist James Foley. It came after US planes had been circling over the Sinjar mountains of Iraq. Except those aircraft dropped not bombs but food parcels, water supplies and blankets to the desperate Yazidi people then threatened with starvation, the murder of their men and the sexual enslavement of their women.

It seems Isis regards any nation that gets in the way of its caliphate restoration project as a legitimate target – and that’s almost everyone. On this logic, the only way to be safe from its grasp is to do nothing, to repress even our humanitarian impulse to help people dying of cold on a mountainside.

And yet even that acquiescence would not make us safe. Isis theology, warns Maher, compels true believers to force a confrontation with “Rome” – the dominant west – eventually. Even if we leave them alone, even if we stand aside and let them rule the entire Middle East, “Ultimately they will come for us.”

It’s possible to know all this and, simultaneously, to know that action against Isis with no accompanying action against Assad will be seen as tacit support for the butcher of Damascus and drive more recruits to Isis. And to know the same would be true if intensive bombing of the Isis bastion of Raqqa led to heavy civilian casualties. A UN-mandated force involving Turks, Saudis and the Gulf states might look better, but even the scantest US participation will see the operation branded and damned as the handiwork of the hated west.

Every question we now face – surveillance, shoot-to-kill, border policy – is like this. There’s a strong moral instinct to act, and there are the attendant dangers. To point out the latter does not weaken your commitment to the former. We can be both ruthless in our determination to defeat this mortal enemy and mindful of the risks. We have to be both. We have to inhabit that space that is neither black nor white, but grey. It is the only place any of us can breathe.