JIMMY Carr is on tour at the moment: what a surprise.

He has a new DVD out: I think I could have guessed. The comedian has meanwhile been in the papers for the second time in as many months because some people have found a joke offensive. I wonder if there’s a connection between these facts?

The “hardest working man in show business” has dates booked, according to his website, until September 2013. Being very well paid works wonders for the sense of humour. Being very popular helps in both respects. Carr’s site also carries a disclaimer, of sorts, for next year’s performances: “Everybody’s welcome. Just leave your conscience, sense of common decency & moral compass at home & come on out for a laugh.”

That seems fair enough, either as an enticement or as a warning. As I write, Carr even tweets a free sample: “This week is National Anti-bullying Week. If you’ve got a problem with that then let’s take it outside, you loser. Yeah, you heard.” It doesn’t seem profoundly funny. If you have a child left terrified by bullies it might not seem funny at all. You might have to broaden your mind beyond the usual boundaries. You might even have to stop praying that Carr one day finds himself as the parent of a bullied child, or under a bus.

He does bus jokes, too. This one got him his latest quota of tabloid headlines (bearing no connection, obviously, to the tour, the DVD, the TV appearances, and the need to maintain a reputation as an edgy comic): “Why are they called the Sunshine Variety coaches when all the kids on them look the f***ing same?”

Carr is the co-author of a book – The Naked Jape: Uncovering The Hidden World of Jokes – that attempts to explain how humour works. So what’s going on, as they say, in his Variety Club gag? Variety means difference, but children with Down’s syndrome all look the same. And that’s funny – I think I’ve got this right – because they’re different “from us”. And you laugh at anyone who’s different, right, especially when they’re children?

Carr apologised for that one. He doesn’t make a habit of standing up for free speech, comedy’s right to challenge taboos, or the universal need for a jester who will say what others think. Carr apologises often and easily, and moves on.

He’s had his quota of headlines for jokes about aircraft disasters, soldiers who have lost limbs in Afghanistan and, last month, car crash victims in the wake of the M5 pile-up. Strangely enough, this Cambridge political science graduate seems never to learn. Perhaps it’s a psychological condition.

Still, as best as I can tell, our Jimmy hasn’t yet told the hilarious one about the two sons of a millionaire who accused their dad of harassment only for the old man to be acquitted and paid a bundle by the Metropolitan Police – you couldn’t make it up – for false arrest and false prosecution.

It’s wrong to pick on an individual. For a couple of weeks recently, Ricky Gervais – who just happened to have a new TV show in the works – was bravely defending his witty use of the word mong, as in mongoloid, meaning (yet again) Down’s syndrome. Gervais insisted that any offensive connotation had passed into history. When people who know better said otherwise, he too apologised. He had been, he said, naive. That’s one word for it.

Frankie Boyle is a different, more interesting case. Down’s syndrome sufferers (is there a compulsion at work?), Katie Prince’s disabled son, the Queen, Israel: Boyle has found something scintillating to say about each of them. He resists the standard apology, however, leaving that to others. Boyle seems to believe, in fact, that a comedian who isn’t causing offence now and then isn’t doing his job.

You can make the case easily enough. It is easier still to make the case that freedom of speech is indivisible: it either exists or it does not. Easiest of all is to observe that it is almost impossible to open your mouth in the modern world without offending someone. Gender, ethnicity, culture, belief, age, politics, habits, social differences: God help the comedian – unless he’s making jokes about religion – who forgets that human variety is these days defined in terms of constituencies. And that barn doors are easier to miss.

But here we have three comedians who have each discovered hilarity in children with Down’s syndrome. What’s that if not bullying with a cheeky grin, pain inflicted for a laugh? It’s not yet clear how any one of the three would react if a close family member in distress – you never know – was the butt of a few “risky” laughs.

Last month Facebook was refusing to take down pages dedicated to “rape jokes” on the grounds that “groups that express an opinion on a state, institution, or set of beliefs – even if that opinion is outrageous or offensive to some – do not by themselves violate our policies”. Objectors were quick to point out that the statement was false: Facebook forbids content that is “hateful, threatening, or pornographic”, or liable to incite violence. The pages came down.

So should we therefore ban anything liable to offend? That wouldn’t leave much. It would certainly punch a hole in any notion that free speech, even offensive speech, is preferable to censorship. There are plenty of countries in which “insulting the state”, or the head of state, or a crony of the head of state, or the local political and religious leadership, will get you locked up.

But here’s the trouble: plenty of things are already banned. Carr, Gervais and Boyle know as much. We have laws covering defamation and obscenity. Are the comics who test those laws doing us a favour, or doing harm? They might argue that anyone who pays to see them perform is making a free and informed choice. Do the rest of us want it put about, then, that it’s OK to laugh at Down’s syndrome?

Despite all the grisly complaints against political correctness a lot of nasty little words have disappeared from public discourse simply because they became, as Carr might say, unacceptable. If racist jokes have gone to the same pit as Bernard Manning, why tolerate Down’s syndrome gags?

Because otherwise there would be no end to it. Because that sort of comedy would retreat, yet again, to the pub, the football terraces, and the recesses of the internet. Carr, Gervais and Boyle are very successful at what they do. The greatest part of their audiences are not offended. You could always argue that minorities must be protected. But which minorities, how many of them, how often? Comedy is nasty when humanity is nasty. Comedy echoes its audience. But that’s an old joke.