Debunking Sherlock Holmes Myths: "Deductive Reasoning"

"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?"

     Sherlock Holmes, The Sign of the Four, ch. 6 (1890)

As with many Holmesian fanatics, the first time we heard the term "deduce" was while reading a Sherlock Holmes story. Prior to that, I had never heard the word before; so I quickly learned to associate the term "deduce" with Sherlock Holmes, as if it was something unique and central to him and his method.

It was many years later that I discovered that in fact there was an entire segment of Formal Logic devoted to studying "Deductive Reasoning". Being the Holmesian fanatic I was, (and being lured in by the image of a Holmes silhouette in the description) I embarked on a quest to master the skills of Deduction.

This image was placed in the description of "Deductive Reasoning".

However, to my dismay I realized something that shattered my reality; The "deduction" that I had always associated with Holmes wasn't utilized by the consulting detective at all!

Allow me to demonstrate what I mean.

Logic and Deductive Reasoning

Lets start by giving you a basic rundown of formal logic.

In logic, Deductive Reasoning is known as the "top-down" approach (as opposed to Inductive, which is a bottom- up approach). You basically start from general premises or categories, and you work your way down to a specific conclusion.

For instance, the most famous example is the "Socrates is a man" syllogism. It goes like this:

(P)All men are mortal

(P)Socrates is a man

-------------

(C)Socrates is mortal

You can think of it like this.We have a group of people called "men" and we know a variety of qualities that all people within that group share: they are mortal, they have a Y chromosome, etc. If we are told that Socrates is a person within that group, then we know that he shares the traits of the group- i.e. that he's mortal and has a Y chromosome.

(This method is different from Inductive Reasoning)

This method reasoning to a conclusion is actually very different from Holmesian Deduction

Holmesian Deduction

Holmesian Deduction is a bit different, and really draws from the word "deduce", which implies to subtract. In a way, Holmesian Deduction is all about shaving off the excess until you're left with the essential pieces.

The way that Holmes utilizes his deduction is quite simple: He prepares a number of possibilities in his head, and then tests them. The possibilities which are impossible or don't fit, are eliminated. The process continues until he is left with a single possibility that, no matter how improbable, must be the case.

Essentially, this is how Holmes solves his cases: He collects the facts from various sources, such as visiting the scene or talking to witnesses, and creates a list of possible solutions- and then he tests them one at a time using logic, visual simulation, or experiments. It is in fact, the scientific method as applied to crime solving.

Holmes' True Method

So what method does Holmes ACTUALLY use? Is there are formal logic version of his method. Well, essentially there are two major forms of formal reasoning in "Induction" and "Deduction". But there are somewhat less well known forms of logic as well. Such as Abduction.

Abductive Reasoning is a form of reasoning that goes from Observation to Hypothesis. It observes a situation, say a crime scene, and brings up several hypothesis that are sufficient for causing the crime. For instance, lets say we have this scenario:

Observation:

• There was a cookie place on the table in front of three sugar-loving children. Red, Blue, and Green. The cookie must be eaten if touched. 
• The cookie is now gone.

Hypothesis:

• You can abduce (create hypothesis) that:
• "Red may have eaten the cookie"
• "Blue may have eaten the cookie"
• "Green may have eaten the cookie"

To the many Holmesians out there, this might not look like the method of "deduction" that you have come to be aware of; It doesn't seem to have the "subtracting" of possibilities that I put down as core to Holmesian deduction. However, lets revisit it upon discovering some new information.

We return to the scene and find out some new information:

Red was asleep at the time of the cookie eating. 

In essence, we have added another point to our observations, and as such, the possible hypotheses have changed as well.

Here are the new hypothesies:

Observation: The cookie is missing. It could only have been eaten by one of the three children. Red was asleep at the time the cookie was eaten.

Hypotheses: "Blue may have eaten the cookie", "Green may have eaten the cookie".

As you can see, when we reevaluate the abduction with new information, we are essentially eliminating possibilities, just like how Holmes eliminates possibilities upon receiving new information. In essence "eliminating the impossible until only left with only one possibility".

Conclusion

Holmes' method doesn't resemble deductive reasoning at all. Instead, it's much more similar to a form of reasoning known as "Abductive Reasoning".

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5 minute Logic Tutorial: Deductive Reasoning and Inductive Reasoning

Alright, here's a 5 minute Logic tutorial on Deductive Reasoning and Inductive Reasoning. In formal Logic, these are the two main methods of reasoning.

1. Deduction- Top-down approach
2. Induction- Bottom-up approach

The "top" refers to a group or category
The "bottom" refers to an individual or particular instance

You should be able to pick it up as you read on.

Deductive Reasoning

In logic, Deductive Reasoning is known as the "top-down" approach. You go from general qualities of a group to say things about specific instances of that group.

For instance, the most famous example is the "Socrates is a man" syllogism. It goes like this:

(P)All men are mortal

(P)Socrates is a man

-------------

(C)Socrates is mortal

You can think of it like this. We have a group of people called "men" and we know a variety of qualities that all people within that group must share: they are mortal, they have a Y chromosome, etc. If we are told that Socrates is a person within that group, then we know that he must share the traits of the group- i.e. that he's mortal and has a Y chromosome.

This is different from Sherlock Holmes' Deduction (Abduction).

Inductive Reasoning

Inductive Reasoning is known as the "bottom-up" approach. It goes from a specific instance (or individual) to reaching grand conclusions about the group they belong to.

For instance, lets say we have Johan, who is a man from country XYZ. If Johan is a smoker and we say that all people from country XYZ are smokers, then we are using induction. Induction.

As you can see, very common use of this is in Stereotyping, where we take qualities from specific instances (in this case, Johan's smoking) , and assume that it applies to all the people of the group the person belongs to (assume that everyone from country XYZ are smokers).

Induction tends to be the riskier and more dangerous form of reasoning.

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Learn about Context and the Deductive Process

Imagine this:

You are waiting in a hospital waiting room, just looking through the magazines and observing the other patients as they wait to be seen by the doctor. When a man who had just entered tripped and fell over the leg of one of the chairs. He stands up and begins to gesture and yell loudly at the receptionist.

Assume this is all you know. What can you tell about the man? Well, your first inclination might be to try and look at the thing that makes him stand out: his gestures and yelling. Perhaps we assume that his actions are a result of anger, and that he has a nasty temper and is one who tries to blame others for his pain and suffering. In short:

He has an Outburst -> He has a nasty temper

But can we really?

It's a principle mistake to simply isolate a particular instance or action and assume that its indicative of all actions and inclinations that the person has. To deduce a person's thoughts and actions, one must be willing to be flexible and mold their deductions around all of a person's actions rather than just boxing them in with general frames.

The goal is to be as accurate with your deductions as possible,
 not to just to put people into a general category.

So what can we do? How can we make our deductions more accurate and more flexible? The answer lies in creating another layer or filter. You can't just think outburst -> temper. You have to consider Context.

Still not fully following? Let's use the same story we had earlier, but change the context.

New Context:On the alternate universe Htrae, the standard method of conversation is through wild gesturing and yelling. Any other method is considered rude. Whispering is used in angry fits.

 As you can see, if our original story had taken place on alternate universe Htrae, rather than Earth, our deduction of Outburst-> Nasty Temper would hold no weight at all.

From this, we see that context matters greatly in determining what actions have meaning, and which do not. Additionally we see that our deductions have to be keen to the context of the scenarios.

But lets return to Earth and see what the context might be able to tell us about the man.

Granted, the outburst may be telling of a nasty temper, but that is only one interpretation. The context may tell us more: The man is in a hospital, he is entering the waiting room of a hospital, he trips over the leg of a chair, he yells at the receptionist and only at the receptionist. He is also there at that time, as well as date.

What does this tell us? To understand it, we must break it down into parts:

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1. He is in a hospital. Who goes to a hospital? Everyone? Well, WHEN do people go to hospitals? Well, either they work there, are visiting, or are sick. The vast majority of the people who visit, are sick. And given the whole of his actions, it seems plausible that the man could be sick.
2. He is entering the waiting room. Not only that, but he is headed to the receptionist and not straight into the entrance of the door. So he is probably likely to be going to talk to the receptionist.
3. He trips over the leg of a chair. Is he clumsy? Is there something wrong with his leg? Was he distracted by something? And if so, by what?
4. Why does he yell at the receptionist? Is it because of his inclination to blame his pain on others? Why just the receptionist and not the other people there?

As you can see, the actual process of deduction using context is not as simple as the fixed deduction that we are inclined to use. However, we can learn a great deal more by formulating these questions, and then answering them by observing his actions.

The process of deduction requires a great deal of preparation, observation, and flexibility. Luckily it is also something we get better at through practice and time. As far as contexts go, it also can work well with many people within the same contexts- e.g. The hospital set applies to everyone in the waiting room, including you.

With a bit of practice and a little bit of work, understanding the context can go a long way.

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