What is Sherlock Holmes' outlook on life?

"The Red-Headed League" was one of the earliest Sherlock Holmes stories Sir Arthur Conan Doyle published. As such, it contains more direct characterization of Holmes than later stories. Direct characterization is when an author directly describes a character to the reader. Doyle also lets Holmes describe himself in this story; this is considered indirect characterization because the reader learns about the character from something the character does or says, or what others say to him or do in response to him.

The direct characterization gives us some hints about Holmes' view of life. When Watson is contemplating his friend's "dual nature," he states, "the swing of his nature took him from extreme languor to devouring energy." He attributes this to the battle between Holmes' exacting rational side and his "poetic and contemplative" side. We get a feeling that Holmes swings between dreaming and doing, between nourishing his inner life and making a difference in the outer world.

At the end of the story Watson compliments Holmes profusely. Holmes yawns and says it saved him from "ennui," or boredom. Then he states, "My life is spent in one long effort to escape from the commonplaces of existence. These little problems help me to do so." We get from this that Holmes thinks life is too drab, which seems like the view of someone who has no grounding beliefs about the purpose of life, perhaps no view of the ultimate flow of history toward good or evil, and no confidence in his role in that greater drama. Life overall seems boring and purposeless to him, and solving crimes is but a brief respite from the dullness of that rudderless boat ride he is taking on a sea of meaninglessness. 

Watson tries to encourage Holmes to take a more hopeful view by telling him he is a benefactor of mankind. Holmes accepts the compliment but demurs with the French aphorism, "The man is nothing; the work is all." Although this is a refreshingly humble admission from a man who can at times appear annoyingly arrogant, it nevertheless reflects an abdication of his personal responsibility to fully embrace his role in life. He does not seem to believe that he himself has been put on earth to benefit mankind, but he acknowledges that his work can be beneficial, can be "of some little use."