Although the word "ratiocination" does not appear in "The Purloined Letter," Poe used it in other places to describe the mixture of rational, scientific inquiry and understanding of psychology/intuition that is necessary to solve crimes. As he does elsewhere, Dupin uses both to unravel the mystery of the stolen letter in this story.

Dupin learns from the police Prefect that a certain high government minister, called D, is suspected of stealing a compromising letter so that he can use it for blackmail. The police department tries to solve the case by completely dismantling every inch of the minister's apartment, but that yields nothing.

Dupin explains this method as illustrating the limitations of relying only on science: the police use all the most advanced techniques and have ample manpower, but they are not using ratiocination: they are not standing back and considering the psychological makeup of the thief.

Because Dupin does this, he is able to find the letter. As he explains, he knows Minister D and understands that this individual is "both mathematician and poet." In other words, the poetical side of the Minister allows him to think in creative ways. As a government insider, he is well aware that the police will find any secretive hideaway he devises, so the minister decides to hide the letter in plain sight, making it so obvious that the police will overlook it.

By understanding the psychology of the minister, Dupin is able to save the day.