Investigating the Investigator’s Investigations

by Kevin Lux

“It may seem very foolish in your eyes”, [Watson] added, “but really I don’t know how you deduced it.” Holmes chuckled to himself.

The investigator hinted at in the title is indeed the great consulting detective Sherlock Holmes. Not that we will question his approach to solving crime though; his outstanding series of successes, after all, is rather hard to argue with. What we will question is what he claims his reasoning process to be. Throughout the stories, Holmes frequently announces to have determined the identity of the culprit(s) using deductive reasoning. But can what Holmes does really be called deduction?

One key characteristic of deduction is that there is a move from the general to the particular. For example, from the fact that all human beings are mortal and the fact that Socrates is a human being, we can infer that Socrates is mortal. Is this kind of argumentative structure in any way comparable to how Holmes reaches his conclusions? To answer this question I think there can be no better way but to take a look at one of Holmes’s supposed deductions:

Sherlock Holmes’s quick eye took in my occupation, and he shook his head with a smile as he noticed my questioning glances. “Beyond the obvious facts that he has at some time done manual labour, that he takes snuff, that he is a Freemason, that he has been in China, and that he has done a considerable amount of writing lately, I can deduce nothing else.”

Mr. Jabez Wilson started up in his chair, with his forefinger upon the paper, but his eyes upon my companion.

“How, in the name of good-fortune, did you know all that, Mr. Holmes?” he asked. “How did you know, for example, that I did manual labour? It’s as true as gospel, for I began as a ship’s carpenter.”

“Your hands, my dear sir. Your right hand is quite a size larger than your left. You have worked with it, and the muscles are more developed.”

Let us focus on the manual labour argument. Holmes, upon seeing Mr Wilson’s disproportionately muscular right hand, inferred that he must have done a fair amount of manual labour. Now how exactly did Holmes reach this conclusion? Clearly, a crucial element in his reasoning process was general knowledge. Holmes has found a pattern, namely that people who do manual labour often develop muscular asymmetry because of the particular chore they have been assigned. Since Mr Wilson has asymmetrical muscles, Holmes came to the conclusion that Wilson has done manual labour. That Holmes’ reasoning is ingenious is indisputable, but is the method he used deduction? The answer is no and the reason is the following: Deductive arguments require that one of the premises be a universal, such as ‘All human beings are mortal’. Holmes, however, makes no such claim. He may claim that a lot of people who have done manual labour developed muscular asymmetry, but he does not claim that this applies to all manual labourers. In other words, Wilson’s disproportionately large right hand could very well have been caused by something other than manual labour (more on this later). It just so happened that Holmes was right. So while we may credit Holmes’ impressive reasoning skills we must acknowledge that an element of luck was still involved.

If Holmes’ argument is not a deductive one, what is it? Well, this is where things get complicated. As it turns out, people disagree on this matter. Essentially, there are those who claim that Holmes uses induction and those who claim he uses something called inference to the best explanation (IBE). Induction refers to the act of reasoning from a set of observations to a generalisation, and IBE amounts to choosing from a set of hypotheses that which is the most reasonable in a particular context. In order to pick a side in this debate, it is integral that the difference between these two types of reasoning becomes clear. Let us begin by giving an example of an inductive argument.

Suppose we have a very large collection of empirical data according to which every swan that has ever been spotted was white. From this we infer that all swans are white. This move from observations to generalisation is typical of (but not essential to!) induction. Arguably the most important thing to be noted about induction is that, contrary to deductive arguments, we are not entitled to assume that our conclusion is necessarily true. When we make use of induction, we are always limited to probability. After all, there is no law of nature that prevents swans from being black. And indeed we have found swans that are black, meaning that the theory that all swans are white has been proven false. Now to IBE.

What exactly is inference to the best explanation? To find out, let us consider a scene from the 2001 French romantic comedy Amélie, in which the eponymous protagonist has invited Nino—her love interest—to meet her at a café. It is crucial to emphasise that this was not a regular kind of invitation. The way Amélie invited Nino to meet her was by taking a photo of herself in a photo booth wearing a mask—they do not know each other’s identity at this time—and holding up a sign that read “Café les 2 moulins. I’m often there after 4pm”. She then ripped the photo apart and shoved the bits underneath the photo booth, knowing that Nino—who has a somewhat unconventional hobby, the details of which I will leave unspecified—will find them, reassemble the photo and go meet Amélie at the café. Unfortunately, on the big day, Nino is late. After waiting for some time, Amélie, understandably, begins to wonder why Nino has not yet shown up:

Amélie can only think of two possible explanations: firstly, that he didn’t find the photo; secondly, before he could assemble it, a gang of bank robbers took him hostage. The cops gave chase. They got away, but he caused a crash. When he came to he’d lost his memory. An ex-con picked him up, mistook him for a fugitive and shipped him to Istanbul. In Istanbul he met some Afghan raiders, who took him to steal some Russian warheads. But their truck hit a mine at the border with Tajikistan. He survived, took to the hills, and became a Mujaheddin.

I think we can all see that one of the two explanations for Nino’s being late is much more reasonable than the other, in the sense that we believe one is much more likely to be true than the other. Those who have seen the film will remember that Amélie’s mind chose to dwell on the latter, less reasonable assumption, but to explain that particular decision is a problem of psychology, not philosophy. The matter that is of main interest to us is to determine what exactly makes Amélie’s first hypothesis more reasonable than the latter. In doing so, we will be explaining what it means for us to infer to the best explanation.

Four key criteria in determining which hypothesis in a given set is the most reasonable are the following:

  1. Simplicity
  2. Coherence
  3. Testability
  4. Comprehensiveness

Instead of going into great detail about each of these criteria, we may also just sum the idea up in a single sentence: „Choose the explanation characterised by features closest to those of an open and shut case“. With this new information in mind, let us reconsider Amélie’s two hypotheses. Her first hypothesis assumes one thing and one thing only, namely that Nino did not find the photo (and therefore could not have shown up). The second assumption, on the other hand, comprises an awful lot of assumptions. Moreover, the assumptions that the second hypothesis is built on are rather outlandish, and for the second hypothesis to be true, there would have to be an impressive series of unlikely occurrences within a very short time frame. Given this very reasoning, I don’t think anyone would doubt that it is more reasonable to assume that Amélie’s first explanation is far more reasonable than her second one. And this is exactly what IBE is about.

After this rather long digression, we can finally return to Sherlock Holmes. Which of the two methods just outlined describes Holmes’ reasoning habits more accurately? In their book Plato and a Platypus Walk into a Bar… Thomas Cathcart and Daniel Klein confidently argue that Holmes go-to reasoning mechanism is induction. While I do not categorically disagree with them, I believe that the example Cathcart and Klein used is rather unfortunate, because rather than proving that Holmes uses the inductive method, I think it actually proves that he uses IBE.

Let us then have a look at Cathcart and Klein’s example. The scenario is the following: Holmes and Watson have gone camping only to realise, in the middle of the night, that their tent has mysteriously disappeared. Holmes reasons:

  1. I went to sleep in a tent, but now I can see the stars.
  2. My intuitive working hypothesis, based on analogies to similar experiences I have had in the past, is that someone has stolen our tent.
  3. In testing that hypothesis, let’s rule out alternative hypotheses: a) Perhaps the tent is still there, but someone is projecting a picture of stars on the roof of our tent. This is unlikely, based on my past experience of human behavior and the equipment that experience tells me would have to be present in the tent and obviously isn’t. b) Perhaps the tent blew away. This is unlikely, as my past experiences lead me to conclude that that amount of wind would have awakened me, though perhaps not Watson. c) Etc., etc., etc.
  4. No, I think my original hypothesis is probably correct. Someone has stolen our tent.

Does this argument bear a stronger resemblance to the white swan example or the Amélie example? I definitely lean towards the latter, my motivation being that in inductive reasoning we do not compare competing hypotheses. Yet that is precisely what Holmes did in this case. He compared his hypothesis that the tent was stolen with hypotheses a) and b). In our example case of induction, we did no such thing. Our extensive empirical data of swans justified us in inducing one thing and one thing only, namely that, probably, all swans are white. In the case of IBE, however, the data at our disposal does not necessarily lead us one way more than another, which is why we conjure up alternative explanations which we then weigh against each other to see which one is most likely to be true.

Approaching the matter from a slightly different angle, we can see that induction is not really concerned with finding an explanation for a particular state of affairs. When we induce that all swans are white, we are not looking to explain why all the swans we have seen were white. The only thing that is relevant to us in this context is the empirical data that tells us that, so far, every swan that has ever been spotted was white and that therefore all swans we are probably white. If we reconsider Sherlock Holmes and the case of the vanished tent, we can see that the detective goes beyond the information that is available to him. The tent could have disappeared in a variety of ways, which, naturally, Holmes acknowledges. But when he weighs his alternative explanations against one another, he finds that, the most reasonable thing to assume is that the tent has been stolen.

What about Mr Wilson’s hand though? Was Holmes’ claim that Wilson has done manual labour the result of an induction or of an IBE? Well, that is a tough question. And unfortunately the answer seems to be that it depends on how you look at it. Holmes’ observation, let us remember, was the following: “Your right hand is quite a size larger than your left. You have worked with it, and the muscles are more developed.If we construe this as an inductive argument, we might end up with something like this: “Mr Wilson has a disproportionately large right hand. A lot of people with muscular asymmetry that I have encountered have done manual labour. This leads me to believe that Mr Wilson has done manual labour.” (Some may question whether this is really an induction, since there is no move from the specific to the general. But, as I mentioned earlier, induction does not need to conform to this structure. For instance, we may well induce that, since the world record for holding one’s breath underwater is 22 minutes, my brother was probably lying when he said he achieved 25 minutes. Despite consisting in a move from a general proposition to a specific one, and despite having the appearance of a deductive argument, this is still an induction, for the fact that the world record for holding one’s breath underwater is 22 minutes may make it extremely likely that my brother lied, but it does not make it necessarily true.)

If we construe the same thing as an inference to the best explanation, we get something along the lines of: “Mr Wilson has a disproportionately large right hand. A lot of people with muscular asymmetry that I have encountered have done manual labour. On the other hand, Wilson’s disproportionately large right hand could be due to something else (perhaps some genetic disorder). But I believe that, all things considered, my first hypothesis is the most likely to be true.” The problem with this IBE is of course that Holmes did not articulate any alternative explanations for the state of Wilson’s right hand. Given the situation, it is not unreasonable to suppose that Holmes had a set of potential explanations that he compared, but we cannot know if he actually did.

What is the upshot of these considerations? Sadly, it is that, in the case of Mr Wilson’s right hand at least, we cannot tell whether Holmes reasoned by induction or IBE. What we can tell is that he definitely did not deduce.

Having dealt with the matter of determining Holmes’ reasoning method(s), the question remains of how we make sense of Sir Arthur Conan Doyle’s use of the word ‘deduction’ where in fact he meant ‘inference to the best explanation’ or ‘induction’. My first suspicion is simply that ‘I deduce that the murderer was…!’ conveys a lot more conviction than ‘I think it is most likely that the murderer was…!’. My second thought is that, again quite simply, people do not always use ‘deduce’ in the strict sense that philosophers expect it to be used. Indeed, in the dictionary we find two different uses of ‘deduce’; the first one is ‘to arrive at (a fact or conclusion) by reasoning’, the second one is ‘to draw as a logical conclusion’. Accordingly, Doyle’s use of ‘deduce’ is not necessarily wrong, so long as what he had in mind was the former rather than the latter meaning. But the point still stands that, as far as philosophers are concerned, Holmes’ go-to reasoning method is definitely not deduction.


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