In Chapter 1, Doyle wastes no time introducing the reader to Holmes's penchant for deductive reasoning and obsession with rational decision-making. Holmes himself describes how he reaches his confounding conclusions with characteristic self-confidence, which he conveys through the use of hyperbole. Additionally, the moment is an example of logos and situational irony:
'It is simplicity itself,' he remarked, chuckling at my surprise—'so absurdly simple that an explanation is superfluous; and yet it may serve to define the limits of observation and of deduction.
Though observation such as this may be "simplicity itself" for Holmes, the reader—and Watson, who conveys his astonishment through his narration—is rarely able to piece together the reasoning for Holmes's conclusions until he explains himself.
Although he may not think them necessary, Holmes's explanations for his reasoning are essential for the reader's ability to understand his conclusions, and they are excellent examples of the use of logos as a rhetorical device. Logos the only skill that Holmes employs as he takes Watson from clue A to conclusion B is that of cool, logical reasoning, unencumbered by the distractions of estimation or emotion.
Although Holmes, through this reasoning, is a paragon of rationality in the novel, there is some irony to the fact that neither Watson nor the reader would be able to arrive at a similar conclusion without Holmes's help: what is clear to the detective is rarely clear to anyone else around him, and his insistence that his observations are pure "simplicity" frequently comes across as arrogance. It is ultimately up to the reader to determine whether such skills are worth this cold, unflinching attitude, or whether something more like Watson's emotional sensitivity is, in fact, more desirable. It is this sensitivity, after all, that leads Watson into the arms of Mary Morstan for their betrothal, which is the center of novel's happy ending.
In Chapter 6, Holmes must contend with the incompetent Athelney Jones, a local policeman whose shoddy intuition about Bartholomew's murder hinders Holmes's own investigation into the crime. As Holmes disparages Jones to Watson (and the reader), he lets loose two literary allusions—one in French, one in German:
'He can find something,' remarked Holmes, shurgging his shoulders; 'he has occasional glimmerings of reason. Il n'y a pas des sots si incommodes que ceux qui on de l'esprit?'
This first quotation is from Les Maximes, a collection of maxims published by the French aristocrat François de La Rochefoucauld in 1665. This particular maxim reads, "there are no fools so troublesome as those who have some wit." Evidently, Holmes finds Jones to be just bright enough to be irritating but not bright enough to draw any real conclusions about Bartholomew's death.
Holmes closes the chapter with another allusion, which is also an example of verbal irony:
Then I shall study the great Jones's methods and listen to his not too delicate sarcasms.
Wir sind gewohnt dass die Menschen werhöhnen was sie nicht verstehen.
'Goethe is always pithy.'
This second reference is from the first part of Johan Wolfgang von Goethe's legendary play, Faust: "We are used to seeing that man despises what he never comprehends." Evidently, Holmes does not find Jones to be "great" at all—this is an example of his withering verbal irony. Rather, Holmes sees Jones's suspicion about his detective work to be proof of Jones's own stupidity.
Holmes's penchant for such allusion and facile use of multiple languages underscore his fierce intelligence and his fierce belief in the power of knowledge and reason. Both of these quotes warn of the dangers brought by the uninformed.
