Sunday, April 13, 2014

Debunking Sherlock Holmes Myths: "Deductive Reasoning"

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"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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  4. 1) The term Abduction was coined in the 20th century - after Holmes' time.

    2) The term deduction as used in philosophy/logic does not necessarily have the same meaning/connotation as it does in criminology or colloquially.
    If you look at the standard definition of the term deduce ((in 19th cent. England)) it is perfectly applicable to what Sherlock Holmes does.

    http://dictionary.cambridge.org/dictionary/english/deduction
    http://dictionary.cambridge.org/us/dictionary/english/deduce
    http://webstersdictionary1828.com/Dictionary/deduction
    https://books.google.com/books?id=z3kKAAAAIAAJ&pg=PP5
    https://books.google.com/books?id=bXsCAAAAQAAJ&pg=PT7
    https://books.google.com/books?id=L0gXAAAAIAAJ

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