The impossible cannot have happened, therefore the impossible must be possible in spite of appearances.

The expression "The impossible cannot have happened, therefore the impossible must be possible in spite of appearances" is the epistemological cornerstone of Hercule Poirot's method in Murder on the Orient Express. It is spoken at a moment of maximum confusion, when the evidence seems to point in every direction at once and no single suspect can be logically accommodated. The phrase does not merely describe a clever trick; it announces a radical reorientation of the detective's thinking, one that ultimately leads to the novel's extraordinary solution.

Origin and Context

Poirot pronounces the maxim during the summary of the passengers' evidence, after M. Bouc has thrown up his hands in despair. Bouc declares, "But I understand nothing—but nothing, of all of this!" and asks Poirot to "show me how the impossible can be possible!" Poirot replies, "It is a good phrase that. The impossible cannot have happened, therefore the impossible must be possible in spite of appearances." The remark is not a casual witticism but a deliberate methodological statement. It comes after Poirot has heard the testimony of every passenger, examined the body, and reviewed the clues—and found that every conventional hypothesis collapses. The locked room, the multiple wounds, the conflicting alibis, the mysterious figures in the corridor: all seem to make the crime inexplicable. Poirot's response is to treat the apparent impossibility not as a dead end but as a sign that his own assumptions are wrong.

Logical Structure and Method

The phrase operates as a kind of logical inversion. Ordinarily, a detective faced with contradictory evidence tries to eliminate the impossible until only the truth remains. Poirot's maxim reverses this: if the evidence forces the conclusion that something impossible has happened, then the investigator must accept that the impossible is in fact possible—and therefore must find a new framework in which it becomes coherent. This is not mysticism but a rigorous refusal to let the mind be trapped by its own preconceptions. Poirot applies the principle by re-examining every piece of evidence not for what it seems to prove but for what it might conceal. The dented watch, the pipe-cleaner, the handkerchief, the scarlet kimono, the Wagon Lit uniform: each clue, taken separately, points to a different suspect. Taken together, they form a pattern that is "fantastically impossible"—which is exactly the impression the conspirators intended to create. Poirot's maxim allows him to see that the impossibility is itself the clue.

Application to the Case

The maxim directly enables Poirot's breakthrough insight: that the crime was committed not by one person but by twelve. He realizes that "the extraordinary difficulty of proving a case against any one person" and the fact that each alibi came from an "unlikely" person pointed to a single explanation: "They were all in it." The twelve stab wounds, the twelve passengers, the twelve members of a jury—the pattern becomes visible only when Poirot accepts that the impossible (a murder committed by a dozen people acting in concert) must be possible. The phrase thus functions as the pivot between the first, deliberately false solution (the "small dark man with a womanish voice" who escaped from the train) and the true solution (the self-appointed jury of the Armstrong household). It is the moment when the detective stops trying to fit the facts into a conventional murder scenario and instead constructs a new paradigm that accommodates all the evidence.

Thematic Significance

Beyond its role in the plot, the expression embodies the novel's deeper theme: that justice, when it fails in the official system, may create its own extraordinary forms. The impossibility Poirot confronts is not merely logical but moral—that twelve ordinary people, including a princess, a colonel, a governess, and a retired actress, could conspire to execute a man. By accepting that this impossibility is possible, Poirot also accepts the moral weight of their act. The maxim thus prepares the ground for the novel's famous ending, in which Poirot offers two solutions and allows M. Bouc and Dr. Constantine to choose the one that lets the conspirators go free. The phrase is not just a detective's tool; it is a philosophical justification for the suspension of ordinary justice in the face of a greater, if extralegal, equity.