In Chapter 7, Poirot and Sheppard examine the murder scene. Poirot uses logos to explain why he is interested in the odd positioning of a chair in the room, foreshadowing the way he will out-think Sheppard in the end:
“Raymond or Blunt must have pushed it back,” I suggested. “Surely it isn’t important?”
“It is completely unimportant,” said Poirot. “That is why it is so interesting,” he added softly.
The chair was reportedly pulled out from the desk at an odd angle. Sheppard insists that it must not be very important—after all, Ackroyd was murdered across the room from the chair. A reader who knows that Sheppard is the killer can see in retrospect that he is trying to use logos of his own to get Poirot to ignore the chair. Sheppard knows exactly why it was in a strange position. He pulled it out to block the dictaphone on the desk from sight. When he killed Ackroyd, he set up a dictaphone with a timer to make it sound as though Ackroyd was alive and speaking to someone after he was already dead. This way, Sheppard has given himself an alibi. He hid the dictaphone so that when people first arrived at the murder scene, he would have a chance to retrieve it before anyone saw it.
Poirot is one step ahead of Sheppard. His process as a detective involves gathering as much information as he can in order to piece together not the most obvious story, but the truest one. Poirot points out here that seemingly unimportant details often become important once they are contextualized by other unimportant details. Sheppard's attempt to steer Poirot away from the chair's significance backfires, instead making it more "interesting" to him.
In Chapter 13, Dr. Sheppard and Poirot discuss Ralph Paton's disappearance and his many motives for killing Roger Ackroyd. Poirot uses logos to challenge Sheppard's assertion that things are looking bad for Ralph:
“Dear me,” I said, rather taken aback. “The case does seem black against him.”
“Does it?” said Poirot. “That is where we disagree, you and I. Three motives—it is almost too much. I am inclined to believe that, after all, Ralph Paton is innocent.”
Sheppard, who is trying to frame Ralph, believes Poirot is almost convinced. He points out that although some of the circumstantial evidence against Ralph is iffy, Ralph stood to gain more money than anyone upon Ackroyd's death. With this comment, he leads Poirot to begin throwing out his own ideas about why Ralph might have killed Ackroyd. The more Poirot says, the more Sheppard must believe everything is going his way. But instead of accepting Sheppard's conclusion that Ralph is the simplest answer to the question of who the murderer is, Poirot throws a curveball into his logic. Three motives, he argues "is almost too much." If someone has an abundance of reasons to kill a person, they do not necessarily have a single, highly-motivating reason. Rather than suggesting that Ralph is guilty, Poirot is arguing, the multiple motives suggest that he is being set up.
The reader does not realize yet that Poirot is speaking to the killer himself. Nevertheless, this is one moment where Poirot demonstrates the quick thinking that makes him such a good detective. He is able to think not only like an investigator, but also like a killer who is trying to get away with murder. By trying so hard to frame Ralph, Sheppard has played right into Poirot's hand.
