Sherlock Holmes - The Watch Deduction

Have you ever wondered how Sherlock Holmes reaches his conclusions? In the story, The Sign of Four, Holmes is sitting on a couch and is as listless as a person possibly could be. He wants a new case, a problem to occupy his idle mind. "My mind," he said, "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...But I abhor the dull routine of existence. I crave for mental exaltation."

Watson, annoyed at Sherlocks arrogance and lack of appreciation for a compliment he just gave him, hands him a watch. Sherlock then makes a deduction that wows us as readers and Watson. Let's read.

I handed him over the watch with some slight feeling of amusement in my heart, for the test was, as I thought, an impossible one, and I intended it as a lesson against the somewhat dogmatic tone which he occasionally assumed. He 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. I could hardly keep from smiling at his crestfallen face when he finally snapped the case to and handed it back.

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

"You are right," I answered. "It was cleaned before being sent to me." In my heart I accused my companion of putting forward a most lame and impotent excuse to cover his failure. What data could he expect from an uncleaned watch?

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

"That you gather, no doubt, from the H. W. upon the back?"

"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. Jewelry 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."

"Right, so far," said I. "Anything else?"

"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."

The story continues.

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."

I nodded, to show that I followed his reasoning.

"It is very customary for pawnbrokers in England, when they take a watch, to scratch the number of the ticket with a pin-point 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 key-hole. 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?"

The deductions of Sherlock are a combination of deductive, inductive and abductive reasoning. Many of his "deductions" are a chain of these logic models. Let's review some of them.

Deductive Logic (Syllogism Model)

Major Premise: Every A is B

Minor Premise: C is A

Conclusion: Therefore C is B

Example: All men are mortal (Major Premise), Socrates is a man (Minor Premise), Therefore (Conclusion) Socrates is a mortal

Inductive Logic

Specific Observation: I observe (A)

Another Specific Observation: I observe (A)

Another Specific Observation: I observe (A)

Theory: Based on my observations, I suspect I will see (A) again.

Example: I pulled a quarter from my pocket, I pulled another quarter from my pocket, I pulled another quarter from my pocket. I theorize that I have a lot of quarters in my pocket.

Abductive Reasoning

This is type of reasoning/logic is useful for forming hypotheses to test against. It requires you to think of possible reasons for an event with the current evidence. Basically you are making an educated guess.

Example: It is 102 degrees outside and I have been running around in it. I feel light headed. I am dehydrated and need to sit down and drink some water. This sounds like the most reasonable explanation, but perhaps I have some other underlying medical condition that is causing me to feel that way.

The Watch Deduction

Let's ignore the obvious conclusions of 'the watch has recently been cleaned' and 'it belonged to your elder brother'. Sherlock does a pretty good job of explaining himself about that. Let's explore some of the other inferences and conclusions he reaches.

Syllogism 1:

Major Premise: New watches are made and polished to show no scratches.

Minor Premise: This watch has scratches.

Conclusion: Therefore this watch is not new.

Comment: The argument is valid and the logic is valid because the premises are true. No watchmakers in Sherlocks time would make a watch riddled with scratches.

Syllogism 2:

Major Premise: People that allow their items to be scratched are careless

Minor Premise: This watch is scratched.

Conclusion: Therefore the owner of the watch is careless.

Comment: This argument is valid but the major premise is false so the conclusion is false. Just because an item has scratches on it, doesn't mean a person is careless. A person may have had an accident and dropped the watch. Or perhaps the watch was purchased second hand with scratches already on it. But considering that the watch is old, over 50 years, you also might suspect that the watch goes through wear and tear.

Inductive Reasoning:

I own a watch and I make sure that i don't scratch it by putting it into my pocket with things like keys because I am careful with expensive items.

I have seen Watson take care of his pocket watch by avoiding putting it into his pocket along with keys and coins.

I have observed a man that kept his watch in a separate pocket than his keys and coins.

Discerned pattern: People that want to keep their watches safe, keep their watches in pockets that don't have coins or keys in them to scratch them. People that do keep their watch in pockets with keys and coins are careless.