Responding to the revelation that Extinction Rebellion (XR) had been identified as extremists by counterterrorism police, Sara Khan, the government’s chief adviser on extremism, called for a clearer definition of extremism. Khan was quoted as saying that a clearer definition would “help build a whole-society response by providing a better understanding”.

It’s hard to disagree with this but actually developing a clear definition is not easy. The cynical view is that an extremist is simply someone whose political stance I strongly disagree with, and that there is no neutral way of determining who is an extremist. On this account, “extremist” is a term of abuse rather than a serious tool of political analysis. But the notion that there is no factual means of determining whether, say, Isis is extremist seems absurd. Isis really is an extremist group. This is not just a matter of personal opinion. But then we are back to the challenge of defining “real” extremism.

The simplest suggestion is that extremists use or support the use of violence in pursuit of their political objectives. Since it is a fact that Isis uses extreme violence in support of its objectives, it is a fact that it is extremist. By the same token, XR is not extremist given that its strategy is one of non-violent civil disobedience. The Guardian commentator George Monbiot has argued that “if seeking to defend life on Earth defines us as extremists, we have no choice but to own the label”. But can XR afford to “own the label” if it wants to dissociate itself from any suggestion that it endorses the use of violence?

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The use of violence alone is not enough to provide a clear definition of extremism. The African National Congress used violence in its struggle against apartheid in South Africa, but this did not necessarily make it an extremist movement. Nelson Mandela defended the ANC’s commitment to armed struggle on two compelling grounds: it was violence in a just cause, and there was no alternative. This suggests that whether using or endorsing violence makes one an extremist is highly context-dependent. Arguments about whether using violence makes an organisation “extremist” are therefore partly arguments about the justice of its cause, and the availability of effective alternatives.

Another way to think about extremism is in terms of left and right. Suppose that political outlooks are arranged on a left-right spectrum. Extremists can be defined as those whose political views are at the far ends of the spectrum. Yet there are extremists who are hard to classify in left-right terms. Isis is a case in point, despite suggestions that its ideology is fascist – and fascism is itself difficult to place on the left-right spectrum.

A more promising approach is to define extremism in psychological terms. To be an extremist is, first and foremost, to have an extremist mindset. It is often pointed out that people at opposite ends of the political spectrum have much in common. What they have in common is their mindset: their preoccupations, attitudes, thinking styles and emotions. To understand these elements is to understand why the extremist label is not one that anyone should be happy to own.

A key extremist preoccupation is victimisation – the perception of themselves as victims of persecution. While extremism can be a reaction to genuine persecution, many extremists are obsessed with fantasies of persecution. For example, so-called “incels”, men who describe themselves as “involuntarily celibate”, believe that they are oppressed by women who refuse to have sex with them. This is a classic extremist persecution fantasy.

Another extremist preoccupation is purity. The purity that extremists are obsessed with can be ideological, religious, or ethnic. Ideological extremists are not just strongly committed to a specific ideology or belief system. Their commitment is to what they see as the purest or most unadulterated version of their favoured ideology. Their biggest fear is dilution, and they see themselves as virtuous because of the purity of their beliefs.

Extremism’s preoccupation with purity explains one of its key attitudes: its attitude to compromise. Extremists hate compromise because it detracts from purity. Being an extremist is as much a matter of how one believes as what one believes. Extremists see compromise as a form of betrayal, and while extremists may hate their opponents, this is usually milder than their hatred of people on their own side who have, as they see it, “sold out”.

Another key extremist attitude is indifference to any adverse consequences of one’s actions or policies. To not be deterred by the practical or emotional damage incurred is the essence of fanaticism, so it follows that extremists are also fanatics. The reverse, however, is not true; one might be indifferent to practicalities, but not preoccupied with purity and victimhood as extremists invariably are.

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As for extremist thinking styles, these are powerfully articulated in Richard Hofstadter’s essay, “The Paranoid Style in American Politics”. Extremists are prone to both utopian and conspiracy thinking. They think in terms of a future utopia to which their policies will lead, and they see conspiracies everywhere. Many extremist conspiracy theories, such as the notorious Protocols of the Elders of Zion, are anti-Semitic.

In Hofstadter’s terms, extremists are also uncommonly angry, and this points to the emotional components of the extremist mindset. Extremist anger is rooted in feelings of resentment about their lot. Another fundamental extremist emotion is self-pity. Anger, resentment, and self-pity are a potentially lethal emotional cocktail, especially in combination with other elements of the extremist mindset.

Thinking of extremism in psychological terms has implications for the relationship between extremism and violence. Having an extremist mindset does not necessarily lead a person to carry out or support acts of violence, but is undoubtedly a risk factor for violence. It is hardly surprising if fantasies of persecution, indifference to the practical consequences of their actions, and anger lead some people to resort to extreme methods.

Is any of this relevant to politics in Britain today? There are violent extremists in the UK, but the extremism that blights mainstream politics is of the non-violent variety. During the toxic Brexit debates, for example, it became fashionable for ardent Leavers and Remainers to accuse one another of extremism. The implication was not that either side endorsed the use of violence but that extremism in some other sense was at play. The relevant sense can be explained by using the idea of an extremist mindset.

For example, a preoccupation with victimhood is evident in what author Fintan O’Toole has described as the strange sense of imaginary oppression that underlies Brexit – the vision of “an oppressed nation throwing off the yoke of the EU”. A preoccupation with purity is also detectable in the preoccupation with a “clean”, unadulterated Brexit. From this “Brextremist” standpoint, there is no room for compromise.

For Brextremists, any damage to the economy is a price worth paying for the utopia of a “free” and independent UK. The emotional drivers of Brextremism include not just anger and resentment but also self-pity. Brexit, O’Toole argues, makes sense for a nation that is ‘full of hysterical self-pity’.

On this account, ardent Remainers are not extremists, even if they are open to accusations of dogmatism, closed-mindedness, and an unwillingness to compromise. However stubborn they might be, ardent Remainers are not preoccupied with purity or victimisation by the EU, and they can hardly be accused of indifference to the consequences of leaving or remaining. They can be accused of indifference to the potentially dire consequences of ignoring the referendum result, but this is not enough to make the Remainer mindset an extremist mindset.

The emerging picture of the extremist mindset is not a pretty one, and it is hard to exaggerate the extent to which this mindset leads to conflict and polarisation. As extremist preoccupations, attitudes and ways of thinking become mainstream, politics becomes more toxic. What is to be done about this development? Is extremism curable?

The good news is that people do sometimes change. Our preoccupations aren’t set in stone and our attitudes aren’t fixed and unalterable. Even strongly felt emotions can fade and people can and do change their thinking. In this sense extremism is curable, though there is of course no guaranteed cure. Ultimately, the single most important lesson of the psychological approach is that tackling extremism is not just about changing minds, but about changing mindsets.

Quassim Cassam is Professor of Philosophy at the University of Warwick. He is the author of Conspiracy Theories and Vices of the Mind: from the Intellectual to the Political.

This article is part of the Agora series, a collaboration between the New Statesman and Aaron James Wendland, professor of philosophy at the Higher School of Economics. He tweets @ajwendland.