On Monday, the British Prime Minister, Theresa May, tried to explain a baffling contradiction in her government’s Brexit policy, but she only made it worse. The problem is the border between the Republic of Ireland and Northern Ireland. Under a series of commitments, including the Good Friday Agreement, of 1998, Britain has promised to keep that frontier open—something that is easy when both regions are part of the European Union. But the plans for Brexit call for a border with controls of some kind between the United Kingdom and the nations of the European Union; indeed, that is more or less the point. Since Northern Ireland is part of the U.K., and Ireland will remain in the E.U., what does that mean? How do you promise both a border and a non-border, in the same place?

The answer from May’s government, essentially, has been to keep repeating that there will be both, interrupting this patter not with rationality but with gaffes. Monday’s blunder came when May was briefing the House of Commons on the latest plans, laid out over the weekend, in which she had said that there would be no “hard border” on the island of Ireland, adding, “We have ruled out any physical infrastructure at the border, or any related checks and controls.” At the same time, she said that “we are clear that, as we leave the E.U., free movement of people will come to an end.” Are we clear? A Labour M.P., Emma Reynolds, wasn’t sure.

“Could the Prime Minister name an international border between two countries who are not in a customs union, who have different external tariffs, where there are no checks on lorries carrying goods at the border?” Reynolds asked, to murmurs of “Hear, hear.”

“There are many examples of different arrangements for customs around the rest of the, uh, around the rest of the world,” May said. “And, indeed, we are looking at those, including, for example, the border between the United States and Canada.” Behind her, Boris Johnson, the Foreign Secretary, nodded his head vigorously, as if making his trademark untamed hair even more dishevelled would somehow settle the question.

It didn’t. A few minutes later, another Labour M.P., Jenny Chapman, rose and asked, “The Prime Minister gave the example of Canada and America as being a soft, frictionless border. Mr. Speaker, there are guns and armed customs guards on that border—surely that is not what she has in mind? Can she perhaps find another example?”

“What I said is that we are looking at the border arrangements in a number of countries around the world,” May replied, as if the infinite variety of border crossings around the world were a sign that someone must have a good trick, somewhere. Or maybe she was just trying to leverage the image of Canadians as harmless, cheerful neighbors. (Did she watch the Olympics? They are not as passive as all that.) She never did answer whether she’d seen anything, on any continent, that she liked—if she’d even looked very carefully.

Leo Varadkar, the Taoiseach, or Prime Minister, of Ireland, made it clear, in a statement to reporters, responding to May’s comments, that he had looked. “I visited the U.S.-Canada border. I visited it back in August, and I saw a hard border with physical infrastructure, with customs posts, people in uniforms, with arms and dogs, and that is definitely not a solution that is one that we can possibly entertain.” (At the time of the visit, he had tweeted out a picture of himself petting one of those dogs, with the note, “make no mistake—it’s a hard border.”) But then one of the central problems in all of this is that the English do not seem to be listening to the Irish, or even registering that their concerns and insights are valid. In the big televised debates before the Brexit vote, Ireland barely came up, and, when it did, the questions were effectively shooed away. The Irish, both in the Republic and in the North, noticed.

Johnson made his own chaotic contribution last week, during a BBC Radio interview, when he compared future controls at the Irish border to collecting traffic-congestion charges in London, which is accomplished with an E-ZPass-like system. “There’s no border between Islington or Camden and Westminster,” he said. “But when I was mayor of London we anesthetically and invisibly took hundreds of millions of pounds from the accounts of people travelling between those two boroughs.” All he managed to do was to offend people in a variety of ways. Was he saying that the Republic of Ireland was like a London borough? (“I lived in Camden for several years and was never stopped crossing the ‘border’ to Islington,” a spokesman for Fianna Fáil, an Irish political party, said, according to the BBC. “I have, however, had military rifles pointed at me when crossing into Northern Ireland in the nineties.”) Did Johnson not understand the complexity of moving people and goods across a continent? Or was he just being, as a Sinn Féin spokesman put it, “frankly ridiculous”?

Johnson further muddled matters by writing a memo, parts of which were leaked, in which he raised the possibility of a hard border—and then suggested that no one should worry, because technology would be helpful. At that, the Labour Party called on May to fire him, “before he can do any more damage.”

One complication is that, for important votes, May’s government relies on the Northern Irish Democratic Unionist Party, which is strongly opposed to any suggestion that the territory is anything but British. But many in Britain share that view. For example, last week, the European Union released a draft of a possible Brexit treaty that raised the possibility of what would, in effect, be a special deal for Northern Ireland, including it in a “common regulatory area” with the Republic. May said that she would not agree to “a customs and regulatory border down the Irish Sea”—that is, a line in the water between the island of Ireland and the rest of Britain—adding that “no U.K. Prime Minister could ever agree to it.” But then where will the border be?

The Brexiteers didn’t have much of an answer; instead, they used the draft as an opening to engage in one of their favored activities: railing against the supposed rottenness of the E.U. The charge now is that Europe is trying to steal or “annex” Northern Ireland. Jacob Rees-Mogg, one of the more theatrical Tory Brexiteers, likened the idea of a special deal for the North to a call for Britain to be “dismembered” in an “egregious act of aggression.” Rees-Mogg, who had earlier dismissed the whole Irish-border question as an “imaginary” problem, also chided Varadkar for what he deemed to be the Irish leader’s “immaturity.”

Worse, as Fintan O’Toole, the Irish critic, noted last week in the Guardian, some hard Brexiteers have taken to suggesting that the problem can be solved simply by ditching the Good Friday Agreement. One leading M.P., Owen Paterson, tweeted out an article saying that the deal might have “outlived its use.” And yet the Good Friday Agreement marked one of those rare moments when the parties in what had seemed an intractable conflict—with bombings and hunger strikes, civilians killed on all sides, and centuries-old grievances—found just enough common ground to build something lasting. It is also an achievement of the European Union, and an example of the ways in which free movement can increase, rather than diminish, security. What message are the Brexiteers sending now, with their failure to treat the Irish border question as a serious problem, worthy of their attention, and of their respect? The Troubles might not return, but a historic trust is being broken now.