The neural computation of Sherlock Holmes' old maxim

Natural languages can express some logical propositions that humans, with similar cultural traditions, are able to immediately and correctly compute. We illustrate this fact with a famous text that Arthur Conan Doyle attributed to Sherlock Holmes: the “old maxim” mentioned in “The Adventure of the Beryl Coronet”, where Holmes said: “It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth”. This maxim is a subtle logical statement and the astonishing point is that the reader feels that it is an evident true. The problem we are trying to explain is the cognitive reason for such a feeling. We connect Holmes’ maxim with the modal logic of Aristotle, the symbolic methods developed by Boole, and the matrix algebra created by Cayley. We show how these theories converge in a class of neural network model, and we suggest that we accept as true Holmes’ maxim because our adult brains are equipped with neural modules that perform naturally modal logical computations.