Elementary, my dear, but not deduction
What Sherlock Holmes can teach us about human reasoning
There are many myths about the nature of human reasoning and knowledge. It is hard enough to think clearly and attempt to truly know things, let alone also trying to pay careful attention to what we are doing when we are thinking clearly. And once we think we know how thinking works, it’s hard to see how our ideas could be wrong. A good example is the curious case of Sherlock Holmes.
Arthur Conan Doyle, in writing his many Sherlock Holmes stories and novels, sought to explain and promote an approach to reason that he referred to as "The Science of Deduction".1 In A Study in Scarlet, Holmes writes an article about “how much an observant man might learn by an accurate and systematic examination of all that came in his way” and that if properly trained in this way, his “conclusions were as infallible as so many propositions of Euclid.” Mathematical geometry, which was first established by Euclid, is considered to be a paradigmatic example of deduction as a method of reasoning.
Neither deduction nor induction
Conan Doyle repeatedly referred to Holmes’ methods as deduction. To pick one example from the story “The Adventure of the Speckled Band”, he wrote that Dr Watson always admired "the rapid deductions, as swift as intuitions, and yet always founded on a logical basis with which [Holmes] unravelled the problems which were submitted to him." Please note, there will be spoilers in this article about that story, so feel free to read it first.
For a logician, however, Conan Doyle’s insistence is more of a hope than fact. Deduction is the form of reasoning by which you start with particular assumptions, facts or premises, and follow the logic to identify what necessarily follows from them. The following example is one that everyone who has ever studied this will have seen:
1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.
It is not possible for 1 & 2 to be true and 3 be false, so we can deduce the truth of 3 as a conclusion from the truth of 1 & 2. However, if it is at all possible that 1 & 2 are true and 3 is false, then this argument is not a logical deduction.
The stories about Sherlock Holmes are, however, full of 'deductions' where Holmes' conclusion does not necessarily (in a strictly logical sense) follow from the facts at hand. Let’s pick a simple example from “The Adventure of the Speckled Band”. At the start of the story, a young lady visits Holmes in a state of considerable agitation. In observing her appearance, he concluded correctly that his visitor had had "a good drive in a dog cart, along heavy roads" that morning, with the evidence being the particular spatters of mud on the sleeves of her jacket.
This reasoning cannot be a strict deduction as it is very possible, and not entirely implausible, that the visitor had the particular spatters of mud on her coat without having been in a dog cart. For example, she might have borrowed the jacket from someone else with the mud already in place. Despite Conan Doyle’s ambition, Holmes’ reasoning can never be as infallible as Euclidean geometry as it is almost always possible for another conclusion to be reached.
Historically, the type of reasoning that was contrasted to deduction was induction. This type of reasoning is where you take a series of observations and reason to a general conclusion. So you might observe that everything you see that can fly has wings, so therefore conclude that a thing needs wings to fly. Or you could flip coins and notice that the result is pretty evenly scattered between heads and tails and so you identify that the chance of either result is 50%. This also does not describe Sherlock Holmes' style of reasoning. He is always trying to figure out a particular truth and a particular situation. He is not trying to build general rules or facts.
Abduction and theory building
As I have noted before, there is a third category of reasoning that was first identified in the 19th century by CS Peirce: abduction. This mode of reasoning is often referred to as 'inference to the best explanation'. We observe a number of things going on in the world and figure out the most likely explanation for them, which we then take as true (or likely true). This style of reasoning can be seen clearly and repeatedly in any Sherlock Holmes story.2 To go back to the example above, given the time of day and the situation, the most likely explanation for the mud spatters on the visitor’s jacket was that she had been in a dog cart that morning.
One challenge with thinking about abduction is that it often feels like a rather vague concept. What ‘inference to the best explanation’ is and how it works is not obvious and it isn’t clear why we can or should rely on it. However, the two different reasoning functions that I wrote about in my previous post provide a useful framework for understanding it. As a reminder, there is one reasoning function that is focused on building theories or representations of the world (which is identified with left hemisphere brain functions). The other function, by contrast, pays attention to the world and compares what we know to what is out there (which is identified with the right hemisphere).
The central case of the “Adventure of the Speckled Band” offers a useful case study for how this reasoning process works. To summarise it briefly, the young lady’s twin sister died a few years previously from unknown causes inside a locked bedroom after a series of strange events. Now the young lady was sleeping in the same room and similar things were happening.
To begin his investigation, Holmes ensures that the young lady provides as much detail as she can and he pays close attention to all the information about the case that he can gather - using the second reasoning function. Then there “was a long silence, during which Holmes leaned his chin upon his hands and stared into the crackling fire.” This period of deep thought relied on the first reasoning as he tried to construct a theory that would explain the facts he had been told. This silence was broken when he decided to act and needed to visit the house the lady lived in with her step-father. To quote: “There are a thousand details which I should desire to know before I decide upon our course of action.”
Holmes had built a theory of what was happening but (in line with good scientific practice) he wasn’t happy to trust it yet. He needed switch back to the second reasoning function and compare his theory with the world again. As noted by Holmes at the end of the story, at this stage of the case he had “come to an entirely erroneous conclusion”. Upon examining the relevant bedroom, Holmes noted a strange bell rope and odd ventilation vent to a neighbouring room, where the step-father slept. He was paying close attention to the world again and rapidly formed a new theory: the new information “instantly gave rise to the suspicion that the rope was there as a bridge for something passing through the hole and coming to the bed.”
Given the step father had been a doctor in India and had some strange pets, he immediately suspected a poisonous snake and new theory took shape. However, yet again, Holmes did not trust his updated theory until he had gathered more evidence. In this case, the next stage of evidence gathering involved hiding in the bedroom to see what happened - which proved his theory correct. If we put it in terms of science, he made a prediction (the stepfather would send a snake into the room and down the bell rope) which he then verified by observation.
The process of abductive reasoning, inferring the best explanation, involved Holmes repeatedly trying to formulate, and then testing, theories that both explained the facts of the case and were consistent with a wide range of background knowledge and information. The ‘best explanation’ was the one that both fitted the facts and was the simplest, or most likely, given everything else that he knew to be true about the world and the people involved.
This pattern of (i) pay attention to the world (observe), (ii) build the best theory we can that explains what we have observed, and (iii) apply the theory to the world to use it and test if the theory is true, is the core engine of scientific practice and of good detective work. It uses both of the reasoning functions identified and repeats the cross-hemispheric dynamics in the brain that Iain McGilchrist - the neuroscientist summarised in my previous post - argues is essential to good brain functioning. There needs to be a move from the right hemisphere of the brain to the left hemisphere and then back to the right again.
Pure deduction is relevant to this process - theory building and making predictions on the basis of a theory involve significant deductive thinking - but the overall process is abductive rather than deductive. Critically, this means that much of our knowledge consists in theories (or other representations) that could turn out to be wrong, if later contradicted by observations or experiments. This interplay between paying attention to the world and theory building builds our knowledge but means we need to remain humble about what we know.
This is the title of Chapter 2 of A Study in Scarlet - the first Sherlock Holmes novel. All quotes in this paragraph are from this chapter. You can read it at: https://www.gutenberg.org/files/244/244-h/244-h.htm#link2HCH0002
This is not a new observation. Holmes' reasoning is sufficiently well known as an example of abduction is that it is cited on the Wikipedia entry for Abductive Reasoning.