The Return of Sherlock Holmes
How we cite our quotes:
"Ah! my dear Watson, there we come into those realms of conjecture, where the most logical mind may be at fault. Each may form his own hypothesis upon the present evidence, and yours is as likely to be correct as mine." (Empty House.2.23)
Even when Holmes is departing from the "realm of logic" he still uses and relies on the scientific method, with his reference to a hypothesis. It's notable that Holmes is talking about determining human motives here. Human behavior often departs from logic.
"That it was written in a train. The good writing represents stations, the bad writing movement, and the very bad writing passing over points. A scientific expert would pronounce at once that this was drawn up on a suburban line [....]" (Norwood Builder.61)
Holmes's use of handwriting analysis points to how forensic science was evolving and becoming more widespread and accepted in this period.
"I am a practical man, Mr. Holmes, and when I have got my evidence I come to my conclusions." (Norwood Builder.143)
Though it seems like Holmes would be down with Lestrade's statement here, Holmes is actually a big fan of theory and of never taking evidence at face value. Evidence has to be picked apart and turned around before it can produce any sort of conclusion. And Holmes sometimes works backwards too, theorizing first and then proving or disproving the theory based on evidence.