When you have eliminated the impossible, whatever remains, however improbable, must be the truth.

The line is spoken by Sherlock Holmes in Arthur Conan Doyle’s early Holmes story “The Sign of Four” (1890). Holmes offers it as a maxim of reasoning while discussing how to reach a sound conclusion from limited or puzzling evidence. In the late-Victorian setting of Doyle’s detective fiction, Holmes’s method is presented as a quasi-scientific approach to crime: careful observation, the testing of hypotheses, and the disciplined rejection of explanations that cannot fit the facts. The aphorism became one of the most frequently quoted summaries of Holmes’s investigative persona and, by extension, Doyle’s popular image of deductive detection.

The statement frames truth as what survives rigorous elimination rather than what initially seems plausible. Holmes argues that investigators should discard explanations that are demonstrably impossible; once those are removed, the remaining account—no matter how unlikely it feels—should be accepted if it alone fits the evidence. The quote highlights a key tension in detective work (and reasoning generally): intuition about probability can mislead when the underlying assumptions are wrong or when rare events occur. It also underscores a methodological ideal: conclusions should be constrained by facts and logical consistency, not by comfort or conventional expectations.

“How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”

1) “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”
2) “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”
3) “When you have excluded the impossible, whatever remains, however improbable, must be the truth.”