# Posts Tagged ‘Sherlock Holmes’

## When You Have Eliminated the Impossible…

Posted by allzermalmer on March 20, 2013

Sherlock Holmes is written to have said “when you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

The full quote is found in the book The Sign of Four: “You will not apply my precept,” he said, shaking his head. “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth? We know that he did not come through the door, the window, or the chimney. We also know that he could not have been concealed in the room, as there is no concealment possible. When, then, did he come?”

The method that Holmes is using is an Eliminative Method, or a form of Eliminative Inference. This form of reasoning has at least two forms of inference. They are the Disjunctive Syllogism and Modus Tollens.

Disjunctive Syllogism: Because at least one disjunct must be true, by knowing one is false we can infer that the other is true.
Premise 1: Either A or B
Premise 2: ~A
Conclusion: Therefore, B

Premise 1: Either they Came through the Door, or Came through the Window, or Came through the Chimney, or Came through the hole in the roof.
Premise 2: Didn’t come through the door and Didn’t come through the window and didn’t come through the chimney.
Conclusion:Therefore, they Came through the hole in the roof.

This is an eliminative inference. We have some possible solutions to the mystery that Holmes is investigating. Holmes has also made some observations that are inconsistent with some of those possible solutions. These observations contradict the possible solutions, and this makes them impossible. Holmes rejects some of the conjectured solutions and has now limited possible solutions that are still consistent with his observations.

Suppose Holmes were to list alternative hypothesis. Suppose that Holmes ordered them in preference, and those that he preferred the most were considered to be the most probable. For example: Come through the Window (65%) > Come through the Door (20%) > come through the Chimney (10%) > Came through the hole in the roof (5%).

Here are four alternative hypothesis, and each one of them is graded on their probability of being true and his preference going from most probable to improbable. Holmes collects some observations. Some of the hypothesis are inconsistent with the observations. The more probable hypothesis are eliminated by the observations collected. To hold to the observations collected and hypothesis that are inconsistent with those observations, would be equivalent to holding to what is impossible. The hypothesis are contradicted by the observations. No matter how probable the impossible is, it still isn’t possibly true. And once we have eliminated the impossible, whatever remains, however improbable, must be the truth.

## Sherlock-Holmesian Reasoning

Posted by allzermalmer on September 22, 2012

Sherlock Holmes is the “[t]he only unofficial consulting detective”, and he had a certain method of reasoning in his “detecting”. This is laid out in the “The Sign of Four” by Sir Arthur Conan Doyle. One chapter is called “The Science of Deduction“, which goes over Holmes basic outline of reasoning. I have altered the format of The Science of Deduction reproduced here by trying to put it more into a Dialectical format.

Those portions that are italicized are not done so in the story itself. I have italicized them myself in order to show important features of Sherlock Holmes method of detection, or method of reasoning. These help to form the basic outlines, or characteristics, of his method propounded here. These are what I shall call Holmesian Reasoning, or Holmesian Thinking.

“Sherlock Holmes took his bottle from the corner of the mantel piece, and his hypodermic syringe from its neat morocco case. With his long, white, nervous fingers he adjusted the delicate needle and rolled back his left shirtcuff. For some little time his eyes rested thoughtfully upon the sinewy forearm and wrist, all dotted and scarred with innumerable puncture marks. Finally, he thrust the sharp point home, pressed down the tiny piston, and sank back into the velvet lined armchair with a long sigh of satisfaction.

Three times a day for many months Watson had witnessed this performance, but custom had not reconciled his mind to it. On the contrary, from day to day he had become more irritable at the sight, and his conscience swelled nightly within him at the thought that he had lacked the courage to protest. Again and again he had registered a vow that he should deliver his soul upon the subject; but there was that in the cool, nonchalant air of his companion which made him the last man with whom one would care to take anything approaching to a liberty. Sherlock Holmes great powers, his masterly manner, and the experience which Watson had had of his many extraordinary qualities, all made Watson diffident and backward in crossing him.

Yet upon that afternoon, whether it was the Beaune which Watson had taken with his lunch or the additional exasperation produced by the extreme deliberation of his manner, he suddenly felt that he could hold out no longer.

Watson: “Which is it today? Morphine or cocaine?”

Holes raised his eyes languidly from the old black letter volume which he had opened.

Holmes: “It is cocaine, a seven-per-cent solution. Would you care to try it?”

Watson : “No, indeed. My constitution has not got over the Afghan campaign yet. I cannot afford to throw any extra strain upon it.”

Holes smiled at Watson’s vehemence.

Holmes: “Perhaps you are right, Watson, I suppose that its influence is physically a bad one. I find it, however, so transcendently stimulating and clarifying to the mind that its secondary action is a matter of small moment.”

Watson: “But consider! Count the cost! Your brain may, as you say, be roused and excited, but it is a pathological and morbid process which involves increased tissue change and may at least leave a permanent weakness. You know, too, what a black reaction comes upon you. Surely the game is hardly worth the candle. Why should you, for a mere passing pleasure, risk the loss of those great powers with which you have been endowed? Remember that I speak not only as one comrade to another but as a medical man to one for whose constitution he is to some extent answerable.”

Holmes’s did not seem offended. On the contrary, he put his fingertips together, and leaned his elbows on the arms of his chair, like one who has a relish for conversation.

Holmes: “My mind rebels at stagnation. Give me problems, give me work, give me the most abstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere. I can dispense then with artificial stimulants. But I abhor the dull routine of existence. I crave for mental exaltation. That is why I have chosen my own particular profession, or rather created it, for I am the only one in the world.”

Watson: “The only unofficial detective?”  said while raising his eyebrows.

Holmes: “The only unofficial consulting detective, I am the last and highest court of appeal in detection. When Gregson, or Lestrade, or Athelney Jones are out of their depths–which, by the way, is their normal state–the matter is laid before me. I examine the data, as an expert, and pronounce a specialist’s opinion. I claim no credit in such cases. My name figures in no newspaper. The work itself, the pleasure of finding a field for my peculiar powers, is my highest reward. But you have yourself had some experience of my methods of work in the Jefferson Hope case.”

Watson: “Yes, indeed, I was never so struck by anything in my life. I even embodied it in a small brochure, with the somewhat fantastic title of ‘A Study in Scarlet.’ ”

Holmes: “I glanced over it. Honestly, I cannot congratulate you upon it. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner. You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love story or an elopement into the fifth proposition of Euclid.”

Watson: “But the romance was there. I could not tamper with the facts.”

Holmes: “Some facts should be suppressed, or, at least, a just sense of proportion should be observed in treating them. The only point in the case which deserved mention was the curious analytical reasoning from effects to causes, by which I succeeded in unravelling it.

Watson  was annoyed at Holmes criticism of a work which had been specially designed to please him. Watson confess, too, that he was irritated by the egotism which seemed to demand that every line of his pamphlet should be devoted to Holmes own special doings. More than once during the years that Watson had lived with Holmes in Baker Street Watson had observed that a small vanity underlay his companion’s quiet and didactic manner. He made no remark however, but sat nursing his wounded leg. Watson had had a Jezaii bullet through it some time before, and though it did not prevent him from walking it ached wearily at every change of the weather.

Holmes: “My practice has extended recently to the Continent,” said Holmes after a while, filling up his old brier-root pipe. “I was consulted last week by Francois le Villard, who, as you probably know, has come rather to the front lately in the French detective service. He has all the Celtic power of quick intuition but he is deficient in the wide range of exact knowledge which is essential to the higher developments of his art. The case was concerned with a will and possessed some features of interest. I was able to refer him to two parallel cases, the one at Riga in 1857, and the other at St. Louis in 1871, which have suggested to him the true solution. Here is the letter which I had this morning acknowledging my assistance.”

Holmes tossed over, as he spoke, a crumpled sheet of foreign notepaper. Watson glanced his eyes down it, catching a profusion of notes of admiration, with stray magnifiques, coup-de-maitres and tours-de-force, all testifying to the ardent admiration of the Frenchman.

Watson: “He speaks as a pupil to his master.”

Holmes: “Oh, he rates my assistance too highly. He has considerable gifts himself. He possesses two out of the three qualities necessary for the ideal detective. He has the power of observation and that of deduction. He is only wanting in knowledge, and that may come in time. He is now translating my small works into French.”

Holmes: “Oh, didn’t you know?” he cried, laughing. “Yes, I have been guilty of several monographs. They are all upon technical subjects. Here, for example, is one ‘Upon the Distinction between the Ashes of the Various Tobaccos.’ In it I enumerate a hundred and forty forms of cigar, cigarette, and pipe tobacco, with coloured plates illustrating the difference in the ash. It is a point which is continually turning up in criminal trials, and which is sometimes of supreme importance as a clue. If you can say definitely, for example, that some murder had been done by a man who was smoking an Indian lunkah, it obviously narrows your field of search. To the trained eye there is as much difference between the black ash of a Trichinopoly and the white fluff of bird’s-eye as there is between a cabbage and a potato.

Watson: “You have an extraordinary genius for minutiae.”

Holmes: “I appreciate their importance. Here is my monograph upon the tracing of footsteps, with some remarks upon the uses of plaster of Paris as a preserver of impresses. Here, too, is a curious little work upon the influence of a trade upon the form of the hand, with lithotypes of the hands of slaters, sailors, cork cutters, compositors, weavers, and diamond-polishers. That is a matter of great practical

interest to the scientific detective–especially in cases of unclaimed bodies, or in discovering the antecedents of criminals. But I weary you with my hobby.”

Watson: “Not at all. It is of the greatest interest to me, especially since I have had the opportunity of observing your practical application of it. But you spoke just now of observation and deduction. Surely the one to some extent implies the other.”

Holmes: “Why, hardly,” he answered, leaning back luxuriously in his armchair and sending up thick blue wreaths from his pipe. “For example, observation shows me that you have been to the Wigmore Street Post Office this morning, but deduction lets me know that when there you dispatched a telegram.”

Watson: “Right! Right on both points! But I confess that I don’t see how you arrived at it. It was a sudden impulse upon my part, and I have mentioned it to no one.”

Holmes: “It is simplicity itself,” he remarked, chuckling at my surprise–“so absurdly simple that an explanation is superfluous; and yet it may serve to define the limits of observation and of deduction. Observation tells me that you have a little reddish mould 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 in entering. The earth is of this peculiar reddish tint which is found, as far as I know, nowhere else in the neighbourhood. So much is observation. The rest is deduction.”

Watson: “How, then, did you deduce the telegram?”

Holmes: “Why, of course I knew that you had not written a letter, since I sat opposite to you all morning. I see also in your open desk there that you have a sheet of stamps and a thick bundle of postcards. What could you go into the post office for, then, but to send a wire? Eliminate all other factors, and the one which remains must be the truth.

Watson: “In this case it certainly is so,” he replied after a little thought. “The thing, however, is, as you say, of the simplest. Would you think me impertinent if I were to put your theories to a more severe test?”

Holmes: “On the contrary,” he answered, “it would prevent me from taking a second dose of cocaine. I should be delighted to look into any problem which you might submit to me.”

Watson: “I have heard you say it is difficult for a man to have any object in daily use without leaving the impress of his individuality upon it in such a way that a trained observer might read it. Now, I have here a watch which has recently come into my possession. Would you have the kindness to let me have an opinion upon the character or habits of the late owner?”

Watson handed Holmes over the watch with some slight feeling of amusement in his heart, for the test was, as he thought, an impossible one, and he intended it as a lesson against the somewhat dogmatic tone which Holmes occasionally assumed. Holmes balanced the watch in his hand, gazed hard at the dial, opened the back, and examined the works, first with his naked eyes and then with a powerful convex lens. Watson could hardly keep from smiling at Holmes crestfallen face when he finally snapped the case to and handed it back.

Holmes: “There are hardly any data,” he remarked. “The watch has been recently cleaned, which robs me of my most suggestive facts.”

Watson: “You are right,” he answered. “It was cleaned before being sent to me.”

In Holmes heart he accused his companion of putting forward a most lame and impotent excuse to cover Watson’ s failure. What data could he expect from an uncleaned watch?

Holmes: “Though unsatisfactory, my research has not been entirely barren,” he observed, staring up at the ceiling with dreamy, lacklustre eyes. “Subject to your correction, I should judge that the watch belonged to your elder brother, who inherited it from your father.”

Watson: “That you gather, no doubt, from the H. W. upon the back?”

Holmes: “Quite so. The W. suggests your own name. The date of the watch is nearly fifty years back, and the initials are as old as the watch: so it was made for the last generation. Jewellery usually descends to the eldest son, and he is most likely to have the same name as the father. Your father has, if I remember right, been dead many years. It has, therefore, been in the hands of your eldest brother.”

Watson: “Right, so far,” said I. “Anything else?”

Holmes: “He was a man of untidy habits–very untidy and careless. He was left with good prospects, but he threw away his chances, lived for some time in poverty with occasional short intervals of prosperity, and finally, taking to drink, he died. That is all I can gather.”

Watson sprang from his chair and limped impatiently about the room with considerable bitterness in his heart.

Watson:  “This is unworthy of you, Holmes,” he said. “I could not have believed that you would have descended to this. You have made inquiries into the history of my unhappy brother, and you now pretend to deduce this knowledge in some fanciful way. You cannot expect me to believe that you have read all this from his old watch! It is unkind and, to speak plainly, has a touch of charlatanism in it.

Holmes: “My dear doctor,” said he kindly, “pray accept my apologies. Viewing the matter as an abstract problem, I had forgotten how personal and painful a thing it might be to you. I assure you, however, that I never even knew that you had a brother until you handed me the watch.”

Watson: “Then how in the name of all that is wonderful did you get these facts? They are absolutely correct in every particular.”

Holmes: “Ah, that is good luck. I could only say what was the balance of probability. I did not at all expect to be so accurate.”

Watsons: “But it was not mere guesswork?”

Holmes: “No, no: I never guess. It is a shocking habit–destructive to the logical faculty. What seems strange to you is only so because you do not follow my train of thought or observe the small facts upon which large inferences may depend. For example, I began by stating that your brother was careless. When you observe the lower part of that watch case you notice that it is not only dinted in two places but it is cut and marked all over from the habit of keeping other hard objects, such as coins or keys, in the same pocket. Surely it is no great feat to assume that a man who treats a fifty-guinea watch so cavalierly must be a careless man. Neither is it a very far fetched inference that a man who inherits one article of such value is pretty well provided for in other respects.

Watson nodded to show that he followed his reasoning.

Holmes: “It is very customary for pawnbrokers in England, when they take a watch, to scratch the numbers of the ticket with a pinpoint upon the inside of the case. It is more handy than a label as there is no risk of the number being lost or transposed. There are no less than four such numbers visible to my lens on the inside of this case. Inference–that your brother was often at low water. Secondary inference–that he had occasional bursts of prosperity, or he could not have redeemed the pledge. Finally, I ask you to look at the inner plate, which contains the keyhole. Look at the thousands of scratches all round the hole–marks where the key has slipped. What sober man’s key could have scored those grooves? But you will never see a drunkard’s watch without them. He winds it at night, and he leaves these traces of his unsteady hand. Where is the mystery in all this?”

Watson: “It is as clear as daylight,” he answered. “I regret the injustice which I did you. I should have had more faith in your marvellous faculty. May I ask whether you have any professional inquiry on foot at present?”

Holmes: “None. Hence the cocaine. I cannot live without brainwork. What else is there to live for? Stand at the window here. Was ever such a dreary, dismal, unprofitable world? See how the yellow fog swirls down the street and drifts across the dun coloured houses. What could be more hopelessly prosaic and material? What is the use of having powers, Doctor, when one has no field upon which to exert them? Crime is commonplacc, existence is commonplace, and no qualities save those which are commonplace have any function upon earth.

Watson had opened his mouth to reply to this tirade when, with a crisp knock, our landlady entered, bearing a card upon the brass salver.

Holmes: “Miss Mary Morstan,” he read. “Hum! I have no recollection of the name. Ask the young lady to step up, Mrs. Hudson. Don’t go, Doctor Watson. I should prefer that you remain.”

1. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner.

Sherlock Holmes does not allow for emotions to come into his method of detection, or his method of reasoning. He tries to keep feelings and emotions outside of he considers to be how detection is actually done or how detection actually ought to be done. Now Holmes is either guided by what detection actually is or what detection ought to be, or both what detection is and what detection ought to be. This appears to be open to being derived from  Is v. Ought and Descriptive v. Normative, or Is and Ought are one and the same and Descriptive and Normative are one and the same. As Joe Friday use to say, “Just the facts, ma’am.”. The Facts, for Holmes, are, or ought to be, treated in a cold and unemotional manner.

2.  Analytical reasoning from effects to causes, by which succeeded in unravelling a fact.

Sherlock will argue from an observation to a cause of that observation. From a single fact, Holmes argues to another, which is what produced the fact before him, what is the facts cause. From the fact that there is smoke, by analytical reasoning, Holmes concludes that there is fire. From the fact that there is red mud on Dr. Watson’s pants, he argues to a cause of the red mud on Dr. Watson’s pants. This fact was noticed by observation. From the facts of scratches and writing, and a certain functional characteristic on the watch that he observed, Holmes reaches a certain cause of those scratches and writing, and certain functional characteristics of the watch.

In the examples that are given in the dialogue, inductive reasoning is being used. Holmes moves from what is known to what is unknown. Holmes moves from the known to the unknown. Holmes moves from the effect, from the known, to the unknown cause. Holmes knows there is red mud on Watson’s pants, but Holmes did does not know where Watson went when Holmes was not with Watson. Holmes, also, did not see Watson walk into any red mud in the time that they were together.

3. The power of observation,  deduction, and a wide range of exact knowledge, (and intuition(?)).

You must be able to use your senses. You must be able to observe in order to notice things. You must have a wide base of exact knowledge. The example of Watson’s clock is one. Holmes notices some scratches on it, and he notices some writing on it, and he also knows the type of watch. The type of watch is based on Holmes wide range of exact knowledge. This wide range of exact knowledge also includes Holmes notices some scratches on it, and he notices some writing on it,  feels the watch in his hand, he focuses his attention to the dials of the clock, he opens the back of the watch and looks at the internal functionings of the watch with his naked eye and than with a magnifying instrument in front of his naked eye. These are the facts of observation that is shown to Holmes by observation.

Holmes have a wide range of exact knowledge, which either comes from his personal experience or from those that he has read in books or other people have said. He knows that jewelry is passed down to the eldest son, the eldest son usually has the same first name as the father, and he knows what  50 years old watches look like. From this exact knowledge he could deduce that the watch is Watson’s brothers. From that wide range of exact knowledge is previous knowledge brought to the situation when make the observations, which is how certain things can stand out to garner ones attention.

Holmes has a wide range of knowledge that is known to be true, and he has these particular observation, data, before him, and these together allow him to deduce something that is not known by the observations, or  data, itself or the wide range of knowledge itself. He does not know that the watch was owned by Watson’s brother and that Watson cleaned the watch before showing it to Holmes. But he knows a certain general principle that was established by enumeration of particular observations by himself or others, and the observations before Holmes now are consistent with those general principles themselves, and so it is another enumeration of that general principle.

All men are mortal (part of Holmes wide range of knowledge). Socrates is a man (observation made by Holmes). So Holems concludes that Socrates is mortal, even though Holmes has not made the observation itself that Socrates is mortal. Holmes concludes this through logical deduction from these known things. But the conclusion that Holmes draws is one that is not known itself by observation. He has not observed that Socrates has died, and so does not know that Socrates is mortal.

4. Eliminate all other factors, and the one which remains must be the truth.

Holmes will eliminate other factors that can lead to different conclusions of the observations before him. Take the example of the ash that comes from different cigars. Holmes had enumerated many experiments with a hundred and forty forms of cigar, cigarette, and pipe tobacco. He noticed that each type of cigar, cigarette, and pipe tobacco, left their own distinct ash. This became a wide range of exact knowledge he obtained.If Holmes did not know all these different possible cigars, cigarettes, and pipe tobacco, and the ash they leave behind, then he would not know what else would be consistent with the ash that Holmes observes. But knowing these things, he can eliminate certain possible types of cigars, cigarettes, and pipe tobacco, because the observation eliminates those causes of the ash. The observation is not consistent with those possible causes, or source, of the ash that is left behind.

Knowing all the possible factors involved in the situation, would allow Holmes to eliminate certain possible causes for what is being observed. Holmes would eliminate what is impossible, because the observation contradicts a cause that is possible in and of itself. Like eliminating that the ash belongs to cigar type x because cigar type x ash is not similar to the ash observed. So whatever else is left would be the truth if it is the only factor left, like cigar y is the only source consistent with the observed ash, and if it is not the only factor left then at least know what is not the possible source of the ash. Cigar types a,b, and c have been eliminated. It narrows the search down further to the cigar, cigarette, and pipe tobacco to be the source, the cause, of the ash observed.

Holmes eliminates possible causes of the effect that is observed, and only one possible cause is correct. The murder smoked a particular type of tobacco product, and that particular tobacco product left behind a certain kind of ash. He eliminated particular tobacco products as the cause of the ash because those causes product different effects than the one observed. So the murder did not smoke those tobacco products. But Holmes himself did not observe what particular tobacco product itself that the murder smoked. He is eliminating a possible unknown cause by a known effect, and how the possible unknown cause is not consistent with the known effect.

5. Some facts ought be suppressed, or not given much attention.

Some observations ought not to be taken attention or pay much attention to. This appears to follow from Holmes saying that emotions that are found to go along with observations ought to be ignored. This is because emotions are not cold and unemotional. There are also other factors that do not play into a possible cause for the observation, which appears to come from ones wide range of exact knowledge, or intuition. The shoes that Watson has on appear to have no causal relation with the watch the Watson presented for Holmes to observe. So Holmes ought to suppress the observation of what shoes Watson has on, or Holmes emotional state in making the observation of the watch.

(This blog post will go through alteration and addition at a later date.)