The Name of the Rose is considered a detective story in that William of Baskerville and his disciple, Adso, pursue the mysterious death of Adelmo of Otranto. William does, in fact, solve a number of mysteries: for instance, he discovers how to navigate the library's labyrinthine structure, and he learns of the existence of a copy of Aristotle's lost second book of his Poetics. William is able to determine that a homosexual affair caused Adelmo to commit suicide because of guilt. He and Adso also are able to unearth a forbidden, secret room in the library that was used by Venantius of Salvemec, who was also murdered. They discover that he was studying a secret manuscript in this room.
William is able to discover that Jorge is the real power behind the abbey and is responsible for the murders that have occurred. Although Jorge manages to eat or burn most of the second book of the Poetics, William and Adso are able to salvage some bits of it.
The attempts to solve the mystery shake William, because he feels he discovered what he did by random chance, which suggests to him that the universe is chaotic and not ruled by a divine hand.
It should be noted that while detective stories usually involve the detective solving the mystery, this doesn't always happen. Sometimes, if rarely, detectives are defeated. William wasn't necessarily defeated—he does solve the mystery—but he was rattled, because the library burned and he realized that the universe might be a random place.
Detective stories traditionally reaffirm the idea that there is justice and order in the universe, because evil fails. Logic and rational thought allow good to triumph. Eco's novel undermines these orderly ideas.