“When you have eliminated the impossible whatever remains, however improbable, must be the truth.”
Holmes presents elimination as a reasoning discipline: once genuinely impossible explanations are removed, attention must turn to the remaining explanation even when it initially seems unlikely.
Source details
The Sign of the Four, Chapter VI, ‘Sherlock Holmes Gives a Demonstration,’ Project Gutenberg #2097. Holmes tells Watson that after eliminating impossible entry routes, ‘whatever remains, however improbable, must be the truth,’ then applies the precept to the locked-room investigation and the hole in the roof. It is fictional detective reasoning in a specific evidential setup, not a universal rule that any improbable remaining hypothesis is automatically true without sound premises or exhaustive elimination.