Sherlock Holmes and Philosophy

by Josef Steiff

  In “The Adventure of the Yellow Face,” Holmes believes that the anonymous person living in a cottage near his client is the first husband of his client’s wife. But he later discovers that the mysterious person was instead the daughter of the client’s wife and her first husband. Holmes had not even considered such a hypothesis.

  Many criticisms have been raised against this method. According to philosopher and mathematician Gottfried Leibniz, this analytic method does not tell us how to come up with hypotheses, but only how to test hypotheses once we have thought of them. John Alan Robinson states that this analytic method is based on a procedure which is not rational, insofar as it requires intuition and divination.

  Still, Cellucci observes, the situation is similar to that of the axiomatic method, as used in geometry. The latter defines a certain method of proof but it does not provide any indication as how to find a proof for a given proposition from given axioms. Similarly, the analytic method defines a certain notion of proof, but it does not provide any indication as how we could find hypotheses to solve a given problem.

  This quest for the solution of a problem is an endless exercise and characterizes the method used by Plato. Many of his dialogues are not conclusive for this reason. In the Republic Plato states that the process of reasoning backwards arrives at what is no more than hypothetical. The Republic describes “the idea of a perfect Town, that—like every idea, according to Plato—can never be fully realized in this world. Only in the perfect City can the principle of everything be reached. Hence, in this imperfect world the search for hypotheses is a potentially infinite process” (Cellucci). And this long tradition of analysis is the method which Sherlock Holmes referred to.

  We can observe that the difference between the analytic process executed inside an investigative context and within a theoretical context is that in the first case the quest has an end: when we caught the murderer (and know the reasons for the killing), we are satisfied. We do not need—for instance—to find the reasons why she had such and such feelings that led her to kill. When we establish that Mr. X had revenge reasons for a murder, it’s enough. We don’t ask why he could not forgive the victim’s past actions. We can stop there.

  According to what we have just specified, we should better express Holmes’s being a genius in terms of capability of finding the right path upwards. We can agree with this opinion of Holmes’s methods:

  Holmes’s success at his brand of “deduction” is well described as a mastery of both a huge body of particular knowledge of things like footprints, cigar ashes, and poisons, which he uses to make relatively simple deductive inferences, and the fine art of ordering and weighing different competing explanations of a body of evidence. Holmes is also particularly good at gathering evidence by observation, as well locating and tracking the movements of criminals through the streets of London and environs (in order to produce more evidence)—skills that have little to do with deduction per se, but everything to do with providing the premises for particular Holmesian inferences. (www.wordiq.com/definition/Sherlock_Holmes)

  Still, it should be stressed that mastering the paths upwards requires also mastering the paths downwards. In other words, the “right” hypothesis for a certain conclusion must be one that can be shown to lead to that conclusion. So, declaring that a hypothesis is right presupposes in any case the verification that that hypothesis leads to that conclusion, verification that consists of a deduction.

  Emotional Rescue

  At the same time that Andrea Nye was writing her book challenging our ways of considering logic, investigations of the psychology of reasoning looked at why we so often make errors. The role of emotions has been re-examined, and the results are that the role of emotions is at least ambivalent: sometimes emotions drive us away from the right path, but sometimes they help.

  For instance, the Wason (Wason, not Watson!) test is one of the standard examples of how most people don’t think logically. In the most talked-about version of this test, the experimenter places four cards on a table which have a letter or a number visible to the participant (“A”, “D”, “4”, “7”). The participants are told that each card has a number on one side and a letter on the other side.

  The problem for the subject is to choose which cards to turn over to determine whether the following rule is true or false about the four cards: “If a card has a vowel on one side, then it has an even number on the other side.”

  The correct answer would be “A” and “7” (and only “A” and “7”), because the only situations that do not obey the above rule occur when a vowel on one side is accompanied by an odd number on the other side. So, the only relevant evidence is whether “A” has an even number on the other side and whether “7” has a consonant on the other side. Most people get this wrong.

  However, that’s not the end of the matter, because it was later found that the percentage of subjects getting this problem right goes up dramatically if it is cast in terms of a real problem from everyday life, especially one involving social obligations.

  For instance the same logical principle can be presented as follows. There are four boys at summer camp, respectively aged 14 and 21, drinking beer and drinking water; the rule is “If a person is drinking beer then he must be over 18.” In this case, if we put the question “Which of them should be checked out to establish if the rule is respected,” then most people easily get the correct answer. It now seems obvious that the two examples to check up on are the boy aged fourteen and the boy drinking beer. Apparently the risk of being punished or deceived stimulates our capability for thinking logically. So it seems that some emotional involvement may sometimes help us to reason correctly.

  Still, there are also reasons in favour of a strict symbolicformal expression of reasoning. Gottlob Frege, who tried to design a new and purely logical language, understood that in everyday life, logic is all bound up with feelings and images, but that it can be helpful to identify the purely logical by stripping away these non-logical associations. According to Frege, “language does not simply express thoughts; it also imparts a certain tone or colouring to them. And this can be different even where the thought is the same.” “In human beings it is natural for thinking to be intermingled with having images and feeling. Logic has the task of isolating what is logical . . . so that we should consciously distinguish the logical from what is attached to it in the way of ideas and feelings.”

  This Way Lies Madness

  Logicomix by Apostolos Doxiadis and Christos Papandropoulos sheds some light on this desire of avoiding feelings inside logic. The authors consider the biographies of important logicians like Frege, Bertrand Russell, Ludwig Wittgenstein, and Kurt Gödel, claiming a link between logic and madness: some people devote their life to logic because they are incapable of managing their emotions. They’re afraid of becoming mad, use logic as a way to live in a solid and sure world, but then their inability to manage their emotions results in the very thing they’re afraid of: their madness—or that of their relatives. Russell’s character says of Wittgenstein: “Like me, he constantly analyzed everything, a habit that annihilates emotions” and then the authors remark: “Russell’s childhood had given him good reasons for annihilating emotions. Character, uncertainty, neurosis led him to logic” (p. 236). We’re also informed that Russell’s son suffered from schizophrenia, and that the same was true for Hilbert’s son. The authors speculate that the fear of emotions which impels some people to study logic may make them bad parents.

  Holmes has often been described as neurotic. Some diagnose Holmes as suffering from bipolar disorder. This can be inferred from the fact that he alternates between days or weeks of listless lassitude and periods of intense engagement with a challenging case or with his hobby, experimental chemistry. Some websites have instead diagnosed Holmes with Asperger syndrome, a light form of autism .

  Uta Frith, in her essay on “Autism: Explaining the Enigma,” identifies the clues of Holme
s’s Asperger syndrome in Holmes’s oddness, his socially detached mind, and his circumscribed but deep interests (as testified by his little monograph on the ashes of 140 different varieties of pipe, cigar and cigarette tobacco), that Frith describes as still vital ingredients “in all creations in art or science”. Both the novel and film The Seven-Percent Solution give a psychoanalytic explanation for Holmes’s behavior.

  Logic can be a harbor for people escaping from emotions. In this case it represents a false harbor, since psychological problems should be faced and not simply put aside; otherwise they come back to bite us somewhere else. Strong emotions can also motivate us to concentrate better and become more logical.

  Sherlock Holmes declares that he has to refrain from loving to keep his mind clear, but perhaps if he were open to love, he might even find his powers of analysis and deduction enhanced.

  Chapter 23

  What Mycroft Knows that Sherlock Doesn’t

  Andrew Terjesen

  Sherlock Holmes is the master of the science of deduction, a consulting detective with no equal. Everyone seems to think so. But is he really?

  By Sherlock’s own admission, his older brother is the true master at solving puzzles and problems. He tells Watson, “When I say, therefore, that Mycroft has better powers of observation than I, you may take it that I am speaking the exact and literal truth” (“The Adventure of the Greek Interpreter”). Sherlock makes it very clear that he considers Mycroft to be his superior in both observation and deduction.

  We see this superiority of Mycroft on display in his first appearance. At the Diogenes Club, Mycroft and Sherlock engage in a series of deductions very reminiscent of Sherlock’s skillful conclusion in A Study in Scarlet that Watson was recently discharged from Afghanistan. Sherlock and Mycroft engage in a series of deductions about someone who has recently served in India. In this instance, Mycroft picks up on a particular detail (that the man had more than one child) that Sherlock seems to have missed.

  But what is it that makes Mycroft better than Sherlock?

  Is it that Mycroft has a photographic memory that enables him to function as a living computer for the British government? Possibly. After all, Watson tells us the limits of Sherlock’s knowledge, and there seems to be a lot he doesn’t know about. If that were the issue though, it’s unlikely that Sherlock would have called Mycroft better at observation and deduction.

  Is it simply that Mycroft has had seven more years of practice than Sherlock? Again, that might be a viable explanation, but I imagine that Sherlock’s pride and his dogged adherence to the facts would have caused him to mention that simple difference.

  Instead, Mycroft’s superior skills arise out of the one major difference between the brothers that Sherlock remarks on when he first mentions his brother to Watson: Mycroft has no interest in detective work.

  Mycroft’s Unique Insight

  It’s tempting to think that Mycroft’s lack of interest is a result of laziness and not the product of some special insight into “the science of deduction.” In both of the major appearances of Mycroft in the canon, Sherlock makes a point of telling Watson that his brother is lacking in ambition and energy.

  Certainly the reason Mycroft gives for passing a case on to Holmes seems to back up this view. When he asks Sherlock to look into the case of stolen submarine plans, he is emphatic that he won’t take care of it himself (even though it is a matter of national security). As he explains to Sherlock, “Give me your details, and from an armchair I will return you an excellent expert opinion. But to run here and run there, to cross-question railway guards, and lie on my face with a lens to my eye—it is not my métier” (“The Adventure of the Bruce-Partington Plans”). However, a lazy person would not bear the burden of running the British government (as Sherlock mentions that his brother is the government at times).

  Of course, this could be a very specific form of laziness, like Sherlock’s own aversion to spending time learning about philosophy or astronomy. As Sherlock points out, his brother

  will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right. Again and again I have taken a problem to him, and have received an explanation which has afterwards proved to be the correct one. (“The Greek Interpreter”)

  Mycroft is especially useless as a consulting detective because he will not take the time to work out the “practical points” that must be worked out before the case can be put before a jury. But it seems to me that it’s quite likely that Mycroft sees no point in such endeavors because he appreciates the “Problem of Induction” in a way that his brother does not.

  Lock and Key

  “Induction” is the name logicians prefer to give to what Sherlock calls “The Science of Deduction.” In everyday speech, we tend not to distinguish between induction and deduction and often use the terms interchangeably. Logicians think it is very important to differentiate between these two types of reasoning because each has its own problems that must be considered when evaluating an argument.

  Deduction, as used by logicians, refers only to arguments that are constructed in such a way that their premises guarantee the truth of the conclusion. A classic example of a deductive argument is the process of elimination, in which one eliminates every other possibility and whatever remains (no matter how improbable) must be the truth. Holmes gives an example of this when investigating the theft of the Bruce-Partington plans as he reasons about how the suspect, Cadogan West, could have gotten the plans from the safe.

  Holmes considers three possibilities: West used the clerk’s keys, West used Sir James’ keys or West had a copy made of one of those sets of keys. Holmes eliminates the clerk because he had only a key to the safe, he lacked the keys needed to open the building and the office. Sir James has all three keys, but they are always with Sir James who was in London at the time of the theft. The only possibility remaining is that West had a copy made and that must be what happened given the original premises of the argument. If there are only three possibilities and two are impossible then the one that is left must be what happened.

  While most of Holmes’ deductions end with a real bit of deductive reasoning, like this process of elimination, they almost always rely on quite a bit of inductive reasoning to establish the premises. Unlike the conclusions of a deductive argument, the conclusion of an inductive argument can only be known to be probably true. The conclusion of an inductive argument is never guaranteed to be true, even if all the premises supplied are true.

  In the Bruce-Partington example, Holmes’s process of elimination depends on there being only three possibilities. Holmes relies on inductive reasoning (in this case a bit of observation as to who had the keys and an inference from experience that keys can be copied) to establish these possibilities. When reasoning inductively there is always the possibility that we have missed some important bit of observation or that the experiences one is making inferences from are incomplete. In this case, Holmes had not considered the possibility that Sir James’s brother Colonel Valentine had made copies of Sir James’s keys so that he could steal the plans and sell them in order to pay off his debts.

  This is the nature of induction, but it is not “The Problem of Induction” with a capital “P.” Sherlock is very aware of the limits of reasoning from experience and observation. As he tells Watson at one point, “It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts” (“A Scandal in Bohemia”).

  Holmes knows full well that insufficient data can lead to wrong-headed conclusions and so he usually plays things close to the chest until he has a critical mass of information. Scientists often rely on inductive reasoning in their experiments, so the scientific method strives to make sure that the sample size is sufficient and to test hypotheses. Holmes does the same thing before wrapping up a case. Although he suspected that West was not the culprit, he had to draw out the
real thief and even he was surprised when it was Colonel Valentine. However, a simple awareness of the limits of probability and the possibility of missing an important clue are not the real problems of induction.

  Billiard Balls that Don’t Move

  The philosopher David Hume is among the first to clearly identify what has become known as the Problem of Induction. In his Enquiry Concerning Human Understanding, Hume lays out the Problem as follows:

  When I see, for instance, a Billiard-ball moving in a straight line towards another; even suppose motion in the second ball should by accident be suggested to me, as the result of their contact or impulse; may I not conceive, that a hundred different events might as well follow from that cause? May not both these balls remain at absolute rest? May not the first ball return in a straight line, or leap off from the second in any line or direction? All these suppositions are consistent and conceivable. Why then should we give the preference to one, which is no more consistent or conceivable than the rest? All our reasonings a priori will never be able to show us any foundation for this preference. (Section IV, Part 1)

  Hume’s point is that when we see someone hitting one billiard ball so that it rolls straight towards another, we anticipate that the motion of the first billiard ball will be transferred to the second when they collide. After the collision, the first ball will stop and the second ball will move in the direction that the original ball was traveling. We would be astounded if the second billiard ball was not set into motion after the first had collided with it. If it did happen, we would begin to look for a logical explanation. For example, did the original billiard ball run out of momentum before getting to the second ball and only appeared to make contact? Or was it the case that the second billiard ball had been glued to the table or nailed down?