Holmesian deductionHolmes's primary intellectual detection method is induction, which Holmes rather inaccurately calls deduction. "From a drop of water", he writes, "a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other". Holmes stories often begin with a bravura display of his talent for "deduction". It is of some interest to logicians and those interested in logic to try to analyse just what Holmes is doing when he performs his induction. "Holmesian deduction" appears to consist primarily of drawing inferences based on either straightforward practical principles—which are the result of careful inductive study, such as Holmes's study of different kinds of cigar ashes—or inference to the best explanation. One quote often heard from Holmes is "When you have eliminated the impossible, whatever remains, however improbable, must be the truth".
Sherlock Holmes's straightforward practical principles are generally of the form, "If 'p', then 'q'," where 'p' is observed evidence and 'q' is what the evidence indicates. But there are also, as may be observed in the following example, intermediate principles. In "A Scandal in Bohemia" Holmes deduces that Watson had got very wet lately and that he had "a most clumsy and careless servant girl". When Watson, in amazement, asks how Holmes knows this, Holmes answers:
In this case, Holmes employed several connected principles:It is simplicity itself ... My eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts. Obviously they have been caused by someone who has very carelessly scraped round the edges of the sole in order to remove crusted mud from it. Hence, you see, my double deduction that you had been out in vile weather, and that you had a particularly malignant boot-slitting specimen of the London slavey.
- If leather on the side of a shoe is scored by several parallel cuts, it was caused by someone who scraped around the edges of the sole in order to remove crusted mud.
- If a London doctor's shoes are scraped to remove crusted mud, the person who so scraped them is the doctor's servant girl.
- If someone cuts a shoe while scraping it to remove encrusted mud, that person is clumsy and careless.
- If someone's shoes had encrusted mud on them, then they are likely to have been worn by him in the rain, when it is likely he became very wet.
"Watson's servant girl is clumsy and careless" and "Watson has been very wet lately and has been out in vile weather".
Deductive reasoning allows Holmes to impressively reveal a stranger's occupation, such as a Retired Sergeant of Marines in A Study in Scarlet; a former ship's carpenter turned pawnbroker in "The Red-Headed League"; and a billiard-marker and a retired artillery NCO in "The Adventure of the Greek Interpreter". Similarly, by studying inanimate objects, Holmes is able to make astonishingly detailed deductions about their owners, including Watson's pocket-watch in "The Sign of the Four" as well as a hat, a pipe, and a walking stick in other stories.
Yet Doyle is careful not to present Holmes as infallible—a central theme in "The Adventure of the Yellow Face". At the end of the tale a sobered Holmes tells Watson, “If it should ever strike you that I am getting a little over-confident in my powers, or giving less pains to a case than it deserves, kindly whisper ‘Norbury’ in my ear, and I shall be infinitely obliged to you”.