Character Analysis in The Canterville Ghost
Wilde calls the Minister and the twin boys "the only true republicans of the family" to emphasize that some members of the family identify more with the United States while others have a closer affinity for England and Europe.
That is, Washington is a very gifted athletic and natural diplomat, but he is susceptible to the influence of titles, the aristocracy, and has a particular love of gardenia flowers—which really isn't a weakness, but Wilde humorously suggests it to be out of character with Washington's other traits.
Mr. Otis establishes himself as a skeptic at the beginning of the story, preferring to rely on his practical, American sensibilities rather than listen to stories of ghosts. His attitude likely represents the perceived attitudes of Americans at the time, who valued items based on their ability to be purchased. He reasons that since no one has bought a ghost, they must not be real.
Notice that in recalling his "great achievements" and relishing in his artful performances as a ghost, Sir Simon doesn't express any sympathy or remorse for his victims. In addition to killing his wife, Sir Simon is responsible for several other deaths as well. He apparently has not sought atonement or forgiveness since his death.
Wilde reveals Sir Simon, the ghost, to be a true artist completely devoted to the aesthetics of his craft, which in this case is creating and spreading terror. The ghost has no reasons behind his art, and he seeks no objective over than perfecting the beauty of it. This approach to art and aesthetics was known as Decadence. Wilde shares these traits with his creation and was a leading member of the Decadent movement in the 19th century.
Similar to his son Washington's approach with the detergent, Mr. Otis also provides a chemical solution to the "problem" of the ghost. He fails to appreciate or recognize the ghost's efforts to scare him, highlighting the differences in how the ghost and the Otises value and understand aesthetics. For the ghost, rattling chains is part of the art of being a ghost, but for Mr. Otis, the rattling chains are problems meant to be solved.
Since pea-shooters are simple, small, and concealable, Wilde is pointing out that they have a strong association with classroom pranks and tricks that students often played on their teachers. This strongly suggests that the twins are mischievous children who delight in poking fun at others. They take particular pleasure in trying to prank the ghost.
Virginia fearlessly resolves to help Sir Simon. Her actions serve as point of reconciliation between American and British values because Virginia has accepted the aesthetics of the ghost and combined them with her own American practicality and hope for a better future. Wilde uses her as a character open to the past and present, one who can atone for ancient sins and represent a optimistic future.
This line reveals that Virginia, like Sir Simon, is an artist and more understanding of his understanding of aesthetics. Even as Sir Simon stole her paints, she continued her art, working with the materials she had available even if it compelled her to paint gloomy, depressing scenes.