The Parisian police, so much extolled for acumen, are cunning, but no more. There is no method in their proceedings, beyond the method of the moment.

Dupin makes this comment after reading all the newspaper articles on the murders. According to Dupin, the reason why the police are incapable of solving the murders is that despite their intelligence, the only strategy they know for crime-solving is “method of the moment,” their typical modern methods, applied indiscriminately to any crime regardless of its particulars. In this case, the police arrest Le Bon based on the semblance of a motive, despite these murders being motiveless. By focusing on motive where it doesn’t apply, they arrest an innocent man.

Now, brought to this conclusion in so unequivocal a manner as we are, it is not our part, as reasoners, to reject it on account of apparent impossibilities. It is only left for us to prove that these ‘impossibilities’ are not such.

Dupin makes this comment when he inspects the crime scene. As he explores the apartment, he methodically rules out impossibilities to determine how the murderer escaped the crime scene undetected. Having determined that the only ways to exit the apartment were either the stairs or the window, Dupin turns to the windows to prove that they were not as impossible an exit as they seemed. In addition to demonstrating Dupin’s analytical prowess, this quotation prefigures Sherlock Holmes’s famous statement about how the improbable must be true once the impossible has been eliminated.

If now, in addition to all these things, you have properly reflected upon the odd disorder of the chamber, we have gone so far as to combine the ideas of a strength superhuman, an agility astounding, a ferocity brutal, a butchery without motive…

Here Dupin lays out the list of known characteristics of the murderer to the narrator, as if inviting him to solve a logic puzzle. This moment demonstrates Dupin’s ability to see the big picture of the crime instead of focusing on the disturbing and upsetting details. He uses these details as puzzle pieces that build a larger picture of what happened. In this sense, Dupin organizes the violent chaos of crime.

The gigantic stature, the prodigious strength and activity, the wild ferocity, and the imitative propensities of these mammalia are sufficiently well known to all. I understood the full horrors of the murder at once.

The narrator here describes reading a description of orangutans in a book that Dupin presents to him. This moment reveals the key to the case that, as the narrator says, renders all its strange details simple. The orangutan’s strength, agility, temperament, and sound suddenly make the brutal murder scene, the strange voice, and the murderer’s difficult escape from the crime scene inevitable conclusions. Although some readers may find an animal as a murderer an unfair solution, this moment nevertheless establishes for future detective novels how the great reveal of the murderer must make the crime make sense and reestablish order.