Sir Arthur Conan Doyle’s fictional Sherlock Holmes is supposedly the best detective in the world. What’s the secret behind his astonishing ability to gather clues from the crime scene that the police always seem to be missing? The answer is quite elementary, my dear reader.

While typical police detectives might use deductive reasoning to solve crimes, Sherlock on the other hand is a master of inductive reasoning. But what’s the difference?

What is deductive reasoning

Deductive reasoning involves drawing a conclusion based on premises that are generally assumed to be true. If all the premises are true, then it holds that the conclusion has to be true.

Deduction always starts with a general statement and ends with a narrower, specific conclusion, which is why it’s also called “top-down” logic.

The initial assumption presumes that if something is true, then it must be true in all cases. A second premise is made in relation to the first statement, and since the initial premise is supposed to be true, so must be the second statement as well. The association between two statements — a major and a minor statement — to form a logical conclusion is called a syllogism.

In math terms, you can think of it this way: A=B, B=C, therefore A=C.

We use deduction often in our day-to-day lives, but this reasoning method is most widely used in research, where it forms the bedrock of the scientific method that tests the validity of a hypothesis.

Here are some examples:

Premise A: All people are mortal.

Premise B: Socrates is a person.

Conclusion: Therefore, Socrates is mortal.

Premise A: All mammals have a backbone.

Premise B: Dogs are mammals.

Conclusion: Dogs have backbones.

Premise A: Multiplication is done before addition.

Premise B: Addition is done before subtraction.

Conclusion: Multiplication is done before subtraction.

Premise A: Oppositely charged particles attract one another.

Premise B: These two molecules repel each other.

Conclusion: The two molecules are either both positively or negatively charged.

What is inductive reasoning

Inductive reasoning is the opposite of deductive reasoning, in the sense that we start with specific arguments to form a general conclusion, rather than making specific conclusions starting from general arguments.

For this reason, inductive reasoning is often used to formulate a hypothesis from limited data rather than supporting an existing hypothesis. Also, the accuracy of a conclusion inferred through induction is typically lower than through deduction, even if the starting statements themselves are true.

For instance, take these examples of inductive logic:

• The first marble from the bag is black, so is the second, and so is the third. Therefore, all the marbles in the bag must be black.
• Every cat I meet has fur. All cats then must have fur.
• Whenever I get a cold, people around me get sick. Therefore, colds are infectious.

Deductive versus inductive reasoning: which one is better?

Deductive inference goes from the general to the specific, while inductive inference goes from the specific to the general. Deductive reasoning cannot be false if its premises are true, whereas inductive reasoning can still be false due to the fact that you cannot account for those instances where you are not correct. In deduction, the conclusion either follows or it doesn’t. There is no in-between like there are degrees of strength or weakness in induction.

In science, neither deduction nor induction is necessarily superior to one another. Instead, there’s a constant interplay between the two, depending on whether we’re making predictions based on observations or on theory.

Sometimes, it makes sense to start with a theory to form a new hypothesis, then use observation to confirm it. Other times, we can form a hypothesis from observations that seem to form a pattern, which can turn into a theory.

Both methods allow us to get closer and closer to the truth, depending on how much or how little information we have at hand. However, we can never prove something with absolute certainty, which is why science is a tool of approximation — the best there is, but still an approximation.

That being said, each method is far from perfect and has its drawbacks. A deductive argument might be based on non-factual information (the premise is wrong), while an inductive statement might lack sufficient data to form a reliable conclusion, for instance.

As an example of when deduction can go hilariously wrong, look no further than Diogenes and his naked chicken. Diogenes was an ancient Greek philosopher who was contemporary with the honorable Plato — and the two couldn’t be more different. Diogenes slept in a large jar in the marketplace and begged for a living. He was famous for his philosophical stunts, such as carrying a lit lamp in the daytime, claiming to be looking for an honest man.

When the opportunity presented itself, Diogenes would always try to embarrass Plato. He would, for instance, distract attendees during Plato’s lectures and bring food and eat loudly when Plato would speak. But one day, he really outdid himself.

Plato would often quote and interpret the teachings of his old mentor, Socrates. On one occasion, Plato held a talk about Socrates’ definition of a man as a “featherless biped”. Diogenes cleverly plucked a chicken and with a wide grin on his face proclaimed “Behold! I’ve brought you a man.”

The implication is that a deductive conclusion is only as good as its premise.

Meanwhile, inductive reasoning leads to a logical conclusion only when the available data is robust. For instance, penguins are birds. Penguins can’t fly. Therefore, all birds can’t fly, which is obviously wrong if you know more birds than just penguins or weird plucked chickens.

Abductive reasoning: the educated guess

There’s another widely used form of reasoning — in fact, it is the one that we most use most often in our day-to-day lives. Abductive reasoning combines aspects of deductive and inductive reasoning to determine the likeliest outcome from limited available information.

For instance, if you see a person sitting idly on her phone at a table with two glasses of wine in front of her, you can use abduction to conclude her company is away and will likely return soon. Seeing a dog on a leash in front of a store makes us infer that the owner is likely shopping for a brief while and will soon return to join their pet.

In abductive reasoning, the major premise is evident, but the minor premise and therefore the conclusion are only probable. Abduction is also often called “Inference to the Best Explanation” for this very reason.

Abductive and inductive reasoning are very similar to each other, although the former is more at ease with reasoning with probable premises that may or may not be true.

This excerpt from Conan Doyle’s The Adventure of the Dancing Men provides a great example of Sherlock’s inductive and abductive mind:

Holmes had been seated for some hours in silence with his long, thin back curved over a chemical vessel in which he was brewing a particularly malodorous product. His head was sunk upon his breast, and he looked from my point of view like a strange, lank bird, with dull gray plumage and a black top-knot.

“So, Watson,” said he, suddenly, “you do not propose to invest in South African securities?”

I gave a start of astonishment. Accustomed as I was to Holmes’s curious faculties, this sudden intrusion into my most intimate thoughts was utterly inexplicable.

“How on earth do you know that?” I asked.

He wheeled round upon his stool, with a steaming test-tube in his hand, and a gleam of amusement in his deep-set eyes.

“Now, Watson, confess yourself utterly taken aback,” said he.

“I am.”

“I ought to make you sign a paper to that effect.”

“Why?”

“Because in five minutes you will say that it is all so absurdly simple.”

“I am sure that I shall say nothing of the kind.”

“You see, my dear Watson”–he propped his test-tube in the rack, and began to lecture with the air of a professor addressing his class–“it is not really difficult to construct a series of inferences, each dependent upon its predecessor and each simple in itself. If, after doing so, one simply knocks out all the central inferences and presents one’s audience with the starting-point and the conclusion, one may produce a startling, though possibly a meretricious, effect. Now, it was not really difficult, by an inspection of the groove between your left forefinger and thumb, to feel sure that you did NOT propose to invest your small capital in the gold fields.”

“I see no connection.”

“Very likely not; but I can quickly show you a close connection. Here are the missing links of the very simple chain. 1. You had chalk between your left finger and thumb when you returned from the club last night. 2. You put chalk there when you play billiards, to steady the cue. 3. You never play billiards except with Thurston. 4. You told me, four weeks ago, that Thurston had an option on some South African property which would expire in a month, and which he desired you to share with him. 5. Your check book is locked in my drawer, and you have not asked for the key. 6. You do not propose to invest your money in this manner.”

“How absurdly simple!” I cried.

“Quite so!” said he, a little nettled.

In laying out his arguments that led to his conclusion, Holmes can be seen reasoning by elimination (“By the method of exclusion, I had arrived at this result, for no other hypothesis would meet the facts,” A Study in Scarlet) and reasoning backward, i.e. imagining several hypotheses for explaining the given facts and selecting the best one. But he does this always with consideration of probabilities of hypotheses and the probabilistic connections between hypotheses and data.

This makes Holmes a very good logician, which is the perfect skill to have as a criminal investigator, as well as a scientist.

All of these reasoning techniques are important tools in any critical thinking arsenal, with each having its own time and place. Whether starting from the general or the specific, you have everything you need to win your next argument in style.