Sherlock Holmes was fond of declaring that a tricky, seemingly impenetrable case was “a three-pipe problem,” demanding a lengthy period of quiet contemplation before the key to its unlocking could be found. Sometimes the solution to these cases would appear, intuitively, baffling or even absurd. But, as Holmes reminded Dr. Watson, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.” The great detective, however, was never tasked with solving a riddle as complex and apparently unresolvable as Brexit.

On Tuesday​, Theresa May endured a humiliation of the sort that in less extraordinary times would render the British prime minister’s position unsustainable. At long last, more than 2½ years after Britain voted to leave the European Union, she was prepared, and able, to present the withdrawal agreement reached with the 27 remaining E.U. members to the House of Commons. This was the “meaningful vote” that would determine whether a deal could be reached.

The answer was not in doubt, ​only the details​. The United Kingdom is stuck in the political equivalent of a Samuel Beckett play: Matters cannot go on like this, yet all alternatives are equally disagreeable. Waiting for Brexit has become an existential farce. The debate is not just an argument about leaving the European Union but, instead, a broader dispute about the kind of country Britain wishes to be. This week promises more of the same, only more so.

The details last week, of course, were ugly: ​No government has ever before been defeated by as many as 230 votes, ​and certainly not ​so comprehensively repudiated on the single biggest decision the country must make in nearly half a century.

Despite that, May struggles on. She is not for turning, even if comparisons between her position and Margaret Thatcher’s end there. Having survived internal rebellion and a confidence vote on her leadership last month, Conservative Party rules mean she is free from ​a ​challenge ​by her own side ​for a year. She will go, if she goes at all, only of her own volition or if the Labour Party successfully carries a vote of no confidence in Her Majesty’s government in the House of Commons.

Labour ​tried and failed ​that on Wednesday, however, so ​there is little sign ​the opposition can force a change in government or a general election that would at least allow for a resetting of the parliamentary arithmetic and, perhaps, hold out the prospect of finding a workable majority in the Commons for any kind of Brexit.

That is the nub of the problem. Parliament does not like May’s deal, nor can it agree on anything that might plausibly replace it. That in turn increases the possibility of leaving the E.U. without a deal by the March 29 deadline; the very outcome most members of Parliament think would be the worst of all possible Brexits. ​Dread of a “no deal Brexit” happens to be ​the one thing a majority in Parliament can agree upon.

Opinion has hardened on all sides. “Brexit means Brexit,” May says, failing to appreciate that there are as many different kinds of Brexit as there are kinds of British rain. ​With that truism, she’s mostly trying to threaten ardent leavers in her own party with the possibility that Parliament ​might ​decide against going ahead with Brexit at all. ​But at the same time, she’s also ​threatening remain-supporting MPs with the ​specter ​of a departure ​without a deal ​unless they support her cobbled-together, complex, unsatisfactory ​plan. The contradictory strategy has proved a dismal failure. MPs on all sides are holding out for their preferred options even if doing so risks leaving them with the result they fear and dislike most.

Notionally a referendum on ​the arcana of trade policy and border rules, ​Brexit was really an inquiry into a different, deeper, issue: What kind of country should Britain be? For 40 years, Britain had endured an uneasy relationship with the continent: part of the European club but never enthusiastically so.

Europe would suffice as a replacement for the long-gone empire. ​It was to ​be, at last, the answer to Dean Acheson’s quip that, having lost that empire, Britain was in desperate need of finding a new role in the world. Pivoting to the continent ​in ​1973​ ​was a means of arresting relative economic decline, but, as a matter of political psychology, Europe could offer only a pale imitation of past glories. The British were late to the party and even then only ambivalent participants. M​embership in a German-dominated E.U. ​reflected Britain’s reduced status, ​and it ​could not satisfy a yearning for something greater, something grander, than that. Brexit​, its proponents promised, ​would be a declaration that Britain was not just different but also, unavoidably, better.

Spared the worst of the 20th​ century’s wars, Britain never felt the urgency of European cooperation in the manner it was understood in France or Germany. There was no British equivalent of the symbolic, and deeply significant, meeting between François Mitterrand and Helmut Kohl, photographed holding hands at Verdun in 1984. That spoke to the essential poetry at the heart of the European project; Britain’s relationship, by contrast, has always been written in prose.

The positive vision for Brexit depended heavily upon the imagery of Britain as a newly liberated global trading house. While optimistic, this prospect still rested on a bedrock of implicit, and only rarely acknowledged, nostalgia: Freed from its Brussels captivity, Britain would be at the forefront of a new era of free trade. If this required a measure of wishful thinking, it still presented a picture many Britons instinctively find attractive. Brexit-supporting politicians indulged these flights of fancy, promising that trade agreements with other countries could be reached quickly and easily. Reality has not cooperated with these grandiose pledges, but reality only kicked in once the referendum votes had been counted.

No one enjoys being laughed at, but there is the unmistakable sense ​now ​of Britain becoming something close to an international laughingstock. Time and time again, Europe’s leaders have asked for guidance on what Britain hoped to achieve from Brexit, only to be left disappointed by the lack of any clear answer. Britain wanted the ball. ​But once Brexit seized it, the country belatedly ​discover​ed​ that it did not know what to do with it. “Taking back control” — the appealing and persuasive slogan coined by the leave campaign — has proved more complicated than expected.

That reflects the essential economic dilemma within Brexit: How do you maintain the economic advantages of E.U. membership without being a member of the E.U.? That is an unsquarable circle. Forced to choose between ​the nation’s ​economic self-interest and the political imperative issued by the electorate, May has opted for the latter.

So, too, has Jeremy Corbyn, ​the Labour ​leader and, unusually for a Labour politician, a veteran left-winger who has long been, at best, ambivalent about the E.U. Corbyn’s MPs, like Labour’s supporters, are overwhelmingly in favor of remain, but the leadership is more cautious, determined that the referendum result must be honored.

That means Labour will, as a matter of political expediency, continue to flirt with — but fail to commit to — a second referendum that might, at last, decide the issue once and for all. A fresh plebiscite would probably take at least six months to organize and require the E.U. to pause the withdrawal process while Britain, finally perhaps, made up its mind. Advocates of a so-called “People’s Vote” see Brexit as, in essence, a peaceful and British Vietnam, a project whose reverberations will last a generation.

Here, too, you may discern the signs of a political class crippled by dysfunction: a Parliament appalled by the road it finds itself on but equally unsure it can, or even wants to, take any other path. The result is a kind of political nervous breakdown. All the available alternatives are unpalatable but so, terribly so, is doing nothing. The meaning of Brexit is ​elementary​: When you have eliminated the impossible, whatever remains, however improbable, remains just as impossible.

Read more: