Universities should be safe spaces – safe spaces for free speech. When I started working on freedom of expression some years ago, I never imagined that threats to it in the university itself would become such a hot topic. But today, a great debate about this is echoing across the English-speaking world.

The dean of students at the University of Chicago recently wrote to inform all new students that: “We do not support so-called trigger warnings, we do not cancel invited speakers because their topics might prove controversial, and we do not condone the creation of intellectual safe spaces where individuals can retreat from ideas and perspectives at odds with their own.” And a mighty row erupted when the University of Cape Town rescinded (quite wrongly, in my view) a lecture invitation to Flemming Rose, the journalist who commissioned the Danish cartoons of Muhammad.

On Wednesday, the prime minister, Theresa May, condemned the idea of safe spaces in answer to a parliamentary question. Yet the main reason British universities have been wrestling with the issue of free speech is the duty imposed on them by the government’s counter-terrorism legislation Prevent – introduced by the Home Office while she was home secretary, which in its outrageous original version asked academics to be spies on, and censors of, even non-violent “extremism” (never properly defined). So she May be for free speech, or May be not.

One trouble with this debate is that the important and sometimes difficult balancing judgments that should be its focus are obscured by the silliness, hyperbole and hysteria that accompany it like the raucous camp followers of a medieval army. It also comes with a whole new jargon: trigger warnings, safe spaces, no-platforming, microaggressions.

And it is highly politicised. At this year’s Republican convention in Ohio, speaker after speaker garnered a surefire round of applause by attacking “political correctness”. No one had to explain what they meant: just spit out the two words and trigger the Pavlovian response.

But what might loosely be called the other side is often its own worst enemy. The New York Times recently reported a presentation to new students by the chief diversity officer at Clark University. Among her examples of microaggressions to be avoided, she included saying “you guys”, since the phrase could be interpreted as excluding women. One female Hispanic student, who had repeatedly committed this heinous error, commented gratefully: “This helped me see that I’m a microaggressor too.” What a dreary, anxious, puritanical kindergarten a campus would become if students were constantly worrying whether this or that word might cause offence to someone or other.

‘Alumni may chunter against the political correctness of the Rhodes Must Fall movement at Oxford.’ Photograph: Carl Court/Getty Images

But having spent many hours discussing these issues with students and colleagues, I think we need to make a few distinctions. For a start, peaceful if provocative student activism around the renaming of buildings, statues, titles, curriculums and so on is not usually a threat to free speech, and can be an enhancement of it.

Alumni may chunter against the political correctness of the Rhodes Must Fall movement at Oxford, and threaten to withdraw their donations, but if student activism has contributed to Georgetown University’s admirable attempt to make amends for having used and sold slaves in the early 19th century, that is surely a good thing. Interestingly, some younger scholars at Oxford are initiating a similar discussion around the Codrington library at All Souls College. (Christopher Codrington was a slave owner.)

A Chicago student defends trigger warnings against the dean’s criticism, saying they simply involve a professor warning his class that, for example, the reading for this week includes a graphic description of sexual assault. In principle, that’s hardly an infringement of free speech. After all, we’re used to television news anchors saying that the next item contains images that some viewers may find disturbing. Some of the suggested trigger warnings – on Ovid’s Metamorphoses, for example – are absurdly over the top, and we do need to watch out for a creeping chilling effect, but in moderation, where reasonably called for, why not?

The same student explains safe spaces as areas on campus where “students – especially but not limited to those who have endured trauma or feel marginalised – can feel comfortable talking about their experiences”, and gives the example of a Hillel House for Jewish students.

Now if that is all it means, this can also be an enhancement of free speech: people may speak more freely when they feel among their own and, since it involves no compulsion of others, they should be free subjectively to define “their own”. (Whether the safe space idea extends to privileged white men, of the kind known in England as Hooray Henrys, is an interesting question.)

But this is not how the slogan of safe spaces is often used in British and American universities. Rather, the suggestion is that the whole university or college should be a safe space. I have several times heard British students say that to invite a fascist or transphobic speaker to their college is like “having them in your living room”.

Here, anyone who believes that free speech is vital to a university must draw the line. For what these student activists are claiming when they insist that, for example, Germaine Greer may not speak on a particular campus (because of her view that a woman is not “a man without a cock”), is that one group of students has the right to prevent another group of students hearing a speaker whom the second group actually wants to hear. Such no-platforming is, in effect, student-on-student censorship. It is an abuse of language to suggest that anyone can seriously be “unsafe” because someone whose views they find offensive or upsetting is speaking in a room on the other side of campus.

In fact, one underexamined question is precisely this: what kind of space is a university? And the answer, which also explains some of the confusion, must be: several different kinds of space, which should have different standards.

Thus, no one should be obliged to have Donald Trump in their dorm, or as a special guest at the Hispanic social night. Nor would I want to see him as a lecturer in political science, let alone on race relations. But I would want to see him invited to speak at a student debating society, where I’m sure the other speakers and student audience would subject him to a well-deserved roasting.

I think it’s fair to say that the erosion of free speech is still only at the margins in major western universities, and mainly concerns a few particular subjects. But we must always watch out for the thin end of the wedge, whether it is being pushed by student activists or government. That’s why I drafted, together with Ken Macdonald, a former director of public prosecutions and now head of an Oxford college, a statement on free speech that is now on Oxford University’s website and has been formally adopted by a number of its colleges.

“Free speech is the lifeblood of a university,” it begins, going on to observe that “inevitably, this will mean that members of the university are confronted with views that some find unsettling, extreme or offensive. The university must therefore foster freedom of expression within a framework of robust civility.”

To many, this may seem like a statement of the self-evident. But there are times when a fundamental liberal position needs to be stated explicitly, and these are such times.