Applied Logic Exercise

Crime Scene Investigation

This is a logic exercise which I have started doing with my students. I don’t begin this kind of exercise until after students have gained a sufficient understanding of the basic principles of syllogistic reasoning. I first heard the idea of using the book Crime and Puzzlement for logic exercises at a classical Christian school conference in Branson, MO. Since then I have developed my own approach. You are welcome to make use of, or modify, this exercise for your own classroom or homeschool. God bless and reason well!

In this exercise you will draw on all of your training in logic up to this point, applying it to a given crime scene, in order to make inductions, deductions, and reasonable inferences toward the purpose of determining “whodunnit.” Here is the procedure to follow in this exercise: 

1. Observe the image of the crime scene supplied to you and make as many observations as you can. Remember that even seemingly unimportant things might end up being important. 

2. After having made your visual observations, read the supplied statement and take down notes on any additional information supplied by the statement.

3. Make a list of suspects who might have perpetrated the crime. Even if it seems apparent to you that one of them is innocent, if they have something to do with the case then write them down. Also take note of any information about appearance, relationship to the victim, occupation, etc., given for each suspect.

4. Making use of all of the available information from your observations, and from the supplied statement, use syllogistic reasoning to draw conclusions. Make as many syllogistic arguments as come to mind (ten at minimum). What can you deduce as certain (undeniably true or false), probable (more likely the case than not), or plausible (within the realm of possibility)? Try to reason in terms of connecting the various suspects to the evidence or establishing that they did or did not have the means, motive, or opportunity to commit the crime.

5. Give an analysis of your various arguments how they affect your list of suspects, either towards their guilt or innocence. Keep in mind that it is possible for there to be multiple perpetrators in a crime. Also keep in mind that, in some cases, the apparent victim could be guilty of wrongdoing as well. You may find that some of the arguments you produce can help to establish the guilt or innocence of multiple people at the same time. Since you were producing arguments at a whim in the previous step, you may end up having some arguments with conflicting implications. If this is the case it may indicate an area where your final argument could be challenged. 

6. Write a narrative consistent with the facts and information above, making use of the conclusions from your arguments (or at least some of them), to imply the guilt of one or more of your suspects. Imagine yourself as a prosecuting attorney crafting a “closing argument” to be delivered in front of a jury in an attempt to gain a conviction of your suspect(s). Given that the information you are working with is limited, and you cannot interview witnesses or suspects, you may use your imagination to supply some additional details. What you must not do, however, is contradict the established facts and evidence. You should also be consistent with your own reasoning.

7. Exchange your case with another student and try to develop a counter case, poke holes in each other's reasoning and argumentation, and develop an alternative narrative.Write a defensive closing argument to present to the same jury to try to create reasonable doubt as to the guilt of their suspect.

“The Boudoir” 

“Amy LaTour’s body was found in her bedroom last night, as shown, with her pet canary strangled in its cage. Henry Willy and Joe Wonty, her boyfriends; Louis Spanker, a burglar known to have been in the vicinity; and Celeste, her maid, were questioned by the police.”¹

Step One: Making Visual Observations

1. The victim is lying on the floor.

2. The victim is wearing a scarf around her neck.

3. The victim’s right hand appears to be reaching toward her throat.

4. The victim’s left leg is bent and up off the floor.

5. The victim has a hair brush in her left hand.

6. The victim has her shoes on (high heels).

7. There are items of value (jewelry) clearly visible and accessible in the room and on the person of the victim.

8. One of the jewelry pieces appears to be an engagement ring.

9. A door is ajar and visible in the vanity mirror.

10. There is a picture of a man on the vanity with the message, “Love, Joe.”

11. There is a vase of fresh flowers with a message that says, “From Joe.”

12. The bird’s cage has been violently forced open.

13. The bird is dead.

14. The room seems to be largely undisturbed.

15. There is a butterfly in the room.

Step Two: Noting the Supplied Information

1. Amy (the victim) was found dead in her personal bedroom last night.

2. The canary’s death was caused by strangling.

3. Amy had two boyfriends, Henry Willy and Joe Wonty.

4. A burglar named Louis Spanker was known to be in the area last night.

5. Amy has a maid named Celeste.

6. All of those above named have been questioned by the police.

Step Three: List the Suspects

Henry Willy - Boyfriend of Amy LaTour

Joe Wonty - Boyfriend of Amy LaTour

Louis Spanker - Burglar known to be in the area.

Celeste - Maid employed by Amy LaTour

Amy LaTour - Victim

Step Four: Using Syllogistic Reasoning About the Available Information

Argument 1

1. If a burglar had killed Amy then the Jewelry would most likely have been taken.

2. The Jewelry was not taken.

3. Therefore it is unlikely that a burglar killed Amy. (Modus Tollens)

Argument 2

1. A woman with two boyfriends is likely to have a jealous man in her life.

2. Amy is a woman with two boyfriends.

3. Amy is likely to have a jealous man in her life. (AAA-1)

Argument 3

1. If someone has secured the affections of their lover then they have no motive to murder their lover.

2. Joe has evidently secured the affections of Amy (as demonstrated by the photo frame and fresh flowers and possibly an engagement ring).

3. Joe has no motive for murder.   (Modus Ponens)

Argument 4

1. If someone is jealous then they have a motive for murder.

2. It is apparent that Henry had reason to be jealous (because of Amy’s preference for Joe).

3. Henry had a motive for murder.   (Modus Ponens)

Argument 5

1. If Amy had felt threatened by an intruder then she would have resisted his approach.

2. The undisturbed scene suggests she did not resist the approach of the intruder.

3. Amy did not feel threatened by the intruder’s presence. (Modus Tollens)

Argument 6

1. If Amy didn’t feel threatened then it is reasonable to believe she knew the murderer.

2. It is already established that Amy did not feel threatened.

3. Amy probably knew the murderer.  (Modus Ponens)

Argument 7

1. If Louis Spanker was the murderer then it means Amy knew him.

2. Amy did not know Louis Spanker.

3. Therefore Louis Spanker is not the murderer.  (Modus Tollens)

Argument 8

1. If a murder victim is found with her hand reaching toward her throat then it is reasonable to suspect she has been strangled.

2. Amy’s hand was found reaching towards her throat.

3. It is reasonable to think Amy may have been strangled. (Modus Ponens)

Argument 9

1. If someone is known to have killed in a certain way in another instance then it is reasonable to suspect that they might kill that way again.

2. The assailant is known to have killed the bird by strangling.

3. Therefore it is reasonable to suspect the assailant also killed Amy by strangling. (Modus Ponens)

Argument 10

1. If Amy was strangled then it is more likely that a man killed her.

2. Amy was strangled.

3. It is more likely a man killed her. (Modus Ponens)

Argument 11

1. It must have either been Joe or Henry who killed Amy (since it was most likely a man who murdered her Louis was already eliminated as a suspect).

2. It doesn’t make sense for it to be Joe whom Amy obviously favored.

3. So it must have been Henry who killed Amy.   (Disjunctive Syllogism)

Argument 12

1. If someone killed Amy’s pet then it was just for the sake of spite.

2. Someone did kill Amy’s pet.

3. Therefore it was out of spite. (Modus Ponens)

Argument 13

1. If someone kills an animal out of spite then they likely have a personal connection to the victim.

2. Someone killed Amy’s bird out of spite.

3. That individual likely had a personal connection to Amy. (Modus Ponens)

Argument 14

1. If the engagement ring on the vanity is from Joe then Amy might have been about to break up with Henry.

2. If Amy was about to break up with Henry then that would give Henry a motive to kill Amy out of jealousy.

3. If the engagement ring on the vanity is from Joe then Henry would have a motive to kill Amy out of jealousy.    (Pure Hypothetical Syllogism)

Step Five: Analyze the total of your arguments to see who best fits the crime based upon means, motive, and opportunity. 

Argument 1: This argument works towards establishing doubt that Louis Spanker was present at the crime scene.

Argument 2: This argument suggests possible motives for murder for Henry Willy and Joe Wonty.

Arguments 3 & 4: These arguments attempt to clear Joe of suspicion while leaving Henry under suspicion as far as motive.

Arguments 5-7: These arguments are meant to demonstrate that Amy knew her murderer and thereby further aids in clearing Louis Spanker. This argument however would leave all other suspects still on the list.

Arguments 8-9: This argument attempts to show the means by which Amy was murdered.

Argument 10: This argument attempts to narrow down the killer to a certain sex, thereby eliminating Celeste as a probable suspect.

Argument 11: This argument works to establish that, in light of previous arguments, Henry Willy is the prime suspect.

Argument 12: This argument establishes the level of malice involved in the crime.

Argument 13: This argument implies a close personal connection between the murderer and Amy.

Argument 14: This argument further suggests motive for Henry WIlly to kill Amy.

Step Six: Pick a Suspect to Prosecute (Write a Narrative of Events)

Suspect Being Prosecuted: Henry Willy

Ladies and gentlemen of the jury, you have now seen and heard all that you need to convict the defendant, Henry Willy, as being guilty of murder. Let us review the facts. On the night Amy LaTour was murdered in her home a violent assailant entered into the privacy of her bedroom through the French doors. Those doors, which were directly behind the vanity, had a large mirror which would allow her to see whoever came through them. Amy had been sitting at her vanity, brushing her hair, getting ready for a night out on the town, full of life, full of hope for the future. She looked up as the doors behind her opened, and as she looked into the mirror she saw Henry Willy whom she was not at all surprised to see. Amy and Henry had been dating for some time, though casually and not exclusively. 

Recently, however, Henry had become aware that Amy’s affections were gradually slipping away from him and being redirected toward another man, Joe Wonty. The signs of Amy’s affections for Joe were everywhere, in the fresh cut flowers in her room, in the picture frame on her vanity, in the smile of her face when she spoke of him, and most recently in the engagement ring which she had just received from Joe. Amy was, in fact, about to go tell Joe, “Yes,” she would marry him. But being the good and decent kind of girl she was, she had asked Henry to stop by before her night out with Joe. She wanted to kindly tell him of her decision to exclusively date, and marry, Joe. Certainly she wished Henry well, she cared for him, but she did not love him. 

This news, along with all those signs of her love for Joe in the room, was more than Henry could bear. It caused him to lose control of his emotions and fly into a blind rage. He grabbed Amy by the throat and twisted her scarf like a tourniquet until all the life was drained from her body. She was so shocked to be hurt by a man whom she had trusted, and for whom she had wished good, that she hadn’t even time to think of resistance or to struggle against him. After the deed was done and Amy’s life and bright future had been destroyed by this man, Henry WIlly, he even went so far as to strangle Amy’s canary. Ask anyone who knew her, she loved that darling bird so very much. But that is just the kind of spiteful, jealous, and vindictive man that sits before you today. Henry willy is a murderer and you, ladies and gentlemen of the jury, know exactly how you should vote concerning such a man. 

I rest my case, your honor.

Step Seven: Defense of the Suspect being Prosecuted (Counter-Narrative)

Suspect being Defended: Henry Willy

Ladies and gentlemen of the jury, you have just heard a passionate story. A story that would make the blood of any good citizen boil for justice. Amy LaTour’s murder is tragic and the murderer deserves to be held to full account and punished! The problem with the prosecution’s story is not that they are seeking justice for Amy (bravo!) but that they are actually pressing you to create a second injustice rather than resolve the first one. For, you see, my client did not kill Amy LaTour! I, too, can tell stories. So here is another story to consider. On the night Amy was tragically murdered she was, just as you’ve been told, sitting at her vanity getting ready for a night out on the town. But she was not getting ready to go out with Joe, she was getting ready to go out with Henry.

Joe had been pursuing Amy with great passion for sometime but, lately, he had done so with increasing persistence and aggressiveness. The items found in her bedroom, the fresh flowers, the photo frame, and the engagement ring, were not examples of Amy’s love for Joe but of Joe’s overbearing attempts to win her affections. One might observe that the diamond ring in our photos of the crime scene is on her vanity, not upon her hand. Just as the prosecution has suggested, a man showed up that night to see Amy. It was not Henry, it was Joe. Amy was probably annoyed, but she didn’t know to be afraid. From this point on the story remains the same as what you have heard, only, it wasn’t my client who committed this atrocity. The man who murdered Amy LaTour was Joe Wonty. 

Now, perhaps you aren’t one hundred percent sure that this is true, but you must note that the evidence and information makes this account at least plausible. If indeed another account of the information can be given and said to be plausible, then it follows that there is reasonable doubt concerning the guilt of my client. You don’t have to be certain, right now, who killed Amy. Your job is to be certain whether or not my client, Henry Willy killed her, and that certainty has been far from demonstrated in this case. As such you must do the right thing and return with a verdict of not guilty.

1.  The text and Image are from Crime and Puzzlement, by Lawrence Treat.