Sherlock-Holmes Fallacy

An alternative name for the fallacy of eliminative induction.

This name refers to Arthur Conan Doyle’s literary detective Sherlock Holmes, who used the following description of his truth-finding strategy:

“Once you have ruled out the impossible, then whatever remains, no matter how improbable, must be the truth.”¹⁾

This approach actually describes an abductive method which – except in certain very specific situations – at best leads to a probably correct result, but never a certain one.

The underlying fallacy here is a confusion of the abductive method (specifically a method called “eliminative induction”) with a deduction, and as a consequence, ignoring the level of uncertainty that this method entails.

The way that Sherlock-Homes’ method is stated, it can be paraphrased as follows:

Either A, or B, etc. … or N.
A is false.
B is false.
… and so on.
Therefore: N must be true.

This method, which can be a valid approach under certain circumstances, particularly within formal systems such as mathematics. However, comes up against its limits in more complex situations (such as in forensics), where the number of possible explanations is practically unlimited and no option can ever be ruled out with complete certainty.

And indeed, the hero of the aforementioned novels uses almost exclusively abductive reasoning to solve the cases, a form of reasoning that does not fulfil the formal requirements of such a rigid methodology.

However, as a fictional character in a novel, Sherlock Holmes has the advantage that his author can ensure that his findings always turn out to be true.

For more information, see: Fallacy of eliminative induction.