Tag Archives: logic

The Logic of Sherlock Holmes

The Reminiscenses of Jon

Over the past few years, I’ve become a Sherlockian so to speak, though not in the traditional sense. I’ve watched the Robert Downey, Jr. films and both Series 1 and 2 of BBC’s Sherlock (hopefully Series 3 will be up on Netflix relatively soon!). I have also become an avid viewer of CBS’s Elementary adaptation. Until very recently, however, my interest in Holmes’ and Watson’s adventures had nothing to do with Sir Arthur Conan Doyle’s novels and short stories. That I neglected to read about the original Holmes is likely a mistake on my part, but one that I am attempting to quickly correct.

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Three modern day Sherlocks. From left to right: Jonny Lee Miller, Robert Downey, Jr., and Benedict Cumberbatch.

Seeing that my spring semester just concluded, I’ve found myself with a good deal of free time—free time perfectly suited for some pleasure reading. Now, when I do have time to read for pleasure—which certainly does not occur frequently during school semesters—I almost always choose to read nonfiction (in my mind, I’d rather learn something about a topic of interest to me than read something that is made up (this is a topic for another day)). This time, however, I decided to give Sir Arthur Conan Doyle a chance and, so far, am very happy I did.

I’ve read A Study in Scarlet, The Sign of Four, and a couple of short stories so far. I think another reason why I hesitated to dive into the old readings is, well, because they are old. For reference, A Study in Scarlet was published in 1887 and The Sign of Four in 1890. I’ve never particularly enjoyed reading books published prior to the 20th century because of the antiquated language and style, but, again, Holmes has not disappointed, which prompted me to write this post.

Back to the stories themselves though.  What has impressed me about the literary Sherlock is the logic that he uses to make his deductions. On a screen, it is easy to convey how Holmes deduces something about a person. I thought it would be difficult to replicate this precise process through writing, but Sir Arthur Conan Doyle does exactly this in very succinct fashion. While there are more involved deductions in the novels, take this brief passage, from The Sign of Four, for example,

Observation tells me that you have a little reddish mold adhering to your instep. Just opposite the Wigmore Street Office they have taken up the pavement and thrown up some earth, which lies in such a way that it is difficult to avoid treading in it entering. The earth is of this particular reddish tint which is found, as far as I know, nowhere else in the neighborhood. So much is observation. The rest is deduction.

Now it is possible for one to argue that there are flaws in Holmes’ logic every so often, but I think that much of the logic is rather sound for the purpose of storytelling.

What I really wanted to get into with regard to the Holmes books, however, is some of the logic which literary Sherlock employs to crack cases and its robustness in real-world applications. Namely, in A Study in Scarlet, I read, “It is a capital mistake to theorize before you have all the evidence.  It biases the judgment.” While in The Sign of Four, I encountered the famous line, “when you have eliminated the impossible, whatever remains, however improbable, must be the truth.” Let me address both in turn.

“It is a capital mistake to theorize before you have all the evidence. It biases the judgment.”

I entirely agree that evidence should always come before theory, else we run into the issue of manipulating evidence to suit a theory. Though I question, do we need all evidence in order to craft a strong theory? I tend to think not. Bayesian inference techniques rely on using new information to update probabilities and, ultimately, theories. Take the sunrise for instance. I am pretty darned sure that the sun will rise tomorrow. But am I certain? The answer is no. Each day that I see it rise I get more evidence that it rises every day, but I will never be 100% sure. Imagine living eons ago and witnessing the sunrise for the first time. Would you think it would follow the same pattern day-in and day-out? If in that position I know I wouldn’t bet on that with 100% certainty. But each day I witnessed the sun rise, I would up the probability of it following the pattern.

Verdict: While it is ideal to have all of the data before making a decision or crafting a theory (whatever the discipline may be), this is rarely feasible. Sherlock Holmes himself never has access to all of the data related to a case. I think that it is best to craft a theory once an ample amount of evidence is obtained and to constantly update that theory when new evidence becomes available. Also, I believe that it is important to be transparent and to let your audience know of the limitations of your theory (limited data, missing data, etc.) so that they may judge the validity and merit of your theory on their own).

“when you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

I think that this logic is intuitively appealing.  I think that, similar to the other quote which I discussed above, it fundamentally speaks to the dangers of biased judgment. I think one ought to delve into a problem with a hypothesis about what is true, but should be prepared for that hypothesis to fail. If too attached to a hypothesis, one runs the risk of manipulating the data/evidence to fit that hypothesis.

Verdict: I’d take Sherlock’s advice. If the data proves a hypothesis wrong in favor of a seemingly improbable result, admit that the data proved you wrong. Be open. Now, I certainly find it acceptable to dig deeper and try to reveal why your hypothesis was wrong. This leads to even more knowledge creation and understanding. Replication, meta-analyses, and peer-reviews are all valuable in this regard.

While Sherlock Holmes is fun and entertaining, I think that practical lessons can be drawn from his adventures. I always like to get something that I can apply in the real-world out of a book or movie, and from Sherlock Holmes, I take away lessons in logic.