Josh Glenn reviews the BBC’s Sherlock, but really gives some insight into his thoughts on deduction, induction, and abduction:
Deduction, according to Peirce, proceeds from rule/guess (e.g., “All the beans from this bag are white”) to case (“These beans are from this bag”) to result/observation (“These beans are white”), whereas induction proceeds rather more tediously — from case to result to rule. …. Like the deductive reasoner, the abductive reasoner begins with a rule/guess: e.g., “All the beans from this bag are white.”
As for Holmes:
Though he insists that his method is a strictly deductive one, at various points in the Holmes canon, Conan Doyle’s detective advocates the use of “imagination,” “intuition,” and “speculation.” This explains why his so-called deductions so often lead Holmes to make revelations which appear almost magical; and this is why Holmes despairs of colorless, boring cases. He’s an obsessive, quasi-apophenic pattern-maker. When he finds a flaw in the pattern, he’s thrilled; when he doesn’t, he’s bored. He’s an obsessive-compulsive overjoyed and outraged to find reality out of order.