Going through some of the back isssues of Inquiry has just turned up a publication from 1979 on the subject of Sherlock Holmes and Philosophy.
Redher, Wulf “Sherlock Holmes – Philosopher Detective” Inquiry 22 pp.441-457
Redher points out that in A Study in Scarlet Watson notes that Holmes’ knowledge of philosophy is ‘nil’ while in his later life Holmes devotes his time equally between philosophy and agriculture. Holmes is portrayed as employing Aristotle’s ‘induction by enumeration’ and Bacon’s ‘induction by elimination’ in the formulation of his law:
Eliminate all factors which in the face of the available facts are impossible; the one remaining possibility, even if improbable, must be the truth.
Rehder does a good job of attempting to draw some sort of consistent methodology out of the Holmes apocrophya. He suggest that Holmes employs the following techniques:
1.) The Method of Exclusion
3.) Inferential Reasoning
4.) Psychological Imagination