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Through deductive reasoning and inductive reasoning, you can get closer to the facts.

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Editor’s note: In today’s era of being surrounded by information, logical reasoning plays a crucial role in the development of individual comprehensive capabilities. When it comes to logical reasoning, it is necessary to mention two classical methods of reasoning, inductive reasoning and deductive reasoning. This article is from Farnam Street and was originally titled Deductive vs Inductive Reasoning: Make Smarter Arguments, Better Decisions, and Stronger Conclusions. The main comparison of the article is about inductive reasoning and deductive reasoning. I hope to inspire you.

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Although it sounds a bit strange, in science, law, and other areas, there is no proof that something is a fact. Conclusions drawn from facts and observations.

Although scientists cannot prove the authenticity of a hypothesis, they can prove their authenticity as much as possible by collecting evidence. Similarly, although lawyers can’t prove whether something happened, they can provide irrefutable evidence.

In today’s era of all kinds of false news, the question “What is real?” is becoming more and more important. This article explores what exactly is truth and how to build truth. Specifically, we will be divided into two methods: Inductive Reasoning and Deductive Reasoning.

“Reversely,” Tweedledee went on to say, “There are people who say is true, that may be true; if that isReally, it may be true; but in fact it is not true, it must not be true. This is the logic.

——Alice in the World of Mirrors, Lewis Carroll

The essence of reasoning lies in finding truth. However, truth is not as simple as we think.

A long time ago, philosophers discussed the topic “Is there any absolute truth in the world?” Although there is no clear answer at the moment, this should not stop us from improving our way of thinking by learning more.

In general, if we can prove something based on existing evidence, then we can infer that it is true. EvidenceThe more the conclusion, the more convincing the conclusion. Sample size is also a very critical factor when it comes to samples.

In some areas, it is necessary to accept very subjective truths. For example, ethicists believe that because with the development of the times, standards will change, and the standards of the same thing may vary from place to place around the world. Therefore, it is not easy to establish absolute truth and determine whether something is right or wrong. .

When talking about reasoning, a well-worded statement can be seen as having objective truth. And some statements with objective truth may not be judged specifically. For example, for the saying that “there are no aliens in the world”, although there is evidence in other places to prove its existence, we currently have no evidence to prove whether they exist or not.

Either deductive reasoning or inductive reasoning, they all belong to evidence-based reasoning.

In the process of reasoning, there are usually the following kinds of evidence:

• Direct evidence or experimental evidence. This type of evidence relies primarily on observation and experimentation, and should be consistent after multiple observations and experiments.

• Anecdote evidence or indirect evidence. The anecdotal evidence is based on the assumption that there is some correlation between the two coexisting factors before they are found. Excessive reliance on anecdotal evidence can lead to logical fallacy. The anecdotal evidence is mainly used to draw hypotheses and then to be verified by experimental evidence.

• Disputing evidence. Sometimes, we will draw conclusions based on facts. howeverIf the facts are not verified directly by assumptions, then the evidence is not reliable. For example, when you see light in the sky, you come to the conclusion that it is an alien spaceship. This is evidence of controversy.

• Speech evidence. When a person makes a statement, his point of view is a verbal evidence. Similarly, because many people may be biased and may not have direct evidence to support their views, such evidence is not reliable.

For an extraordinary claim, the weight of the evidence must be commensurate with its unusual degree.

——Théorie analytique des probabilités, French probabilist and physicist Laplace

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Inductive reasoning

Introduction to inductive reasoning, I have to mention the fictional detective Sherlock Holmes by the famous British detective novelist Arthur Conan Doyle.

Sherlock Holmes observes everything in every detail, and in certain circumstances, the most probable conclusion can be drawn from his observations. Although he often pretends that his knowledge is black and white, it is not true. That is true reasoning and a very convincing explanation based on his observations.

Take his first meeting with Watson as an example to see how he reasoned to judge that Huasheng had just returned from Afghanistan.

“Observation is my second nature. When we first met, I told you that you just came back from Afghanistan, and you seem to be very surprised.”

“No doubt, someone told you.”

“Impossible. I know at a glance that you have just returned from Afghanistan. Due to the habits that have been developed for a long time, a series of thoughts will pass through in my mind, so when it comes to conclusions, it seems that there is no thought. In the middle, there are rigorous steps of reasoning. I reasoned like this: ‘This gentleman, who has the characteristics of a medical worker, is a military man. SoIt is obviously a military doctor. In addition, his face is dark, according to his wrist skin, this is not his original skin color, so he may return from the tropics. His face is stunned and he must have experienced hardships and hardships. The movement of his left arm seems to be stiff and unnatural, and the left arm must have been injured. Therefore, a British military doctor has experienced hardships in the tropics and his arm has been injured. Where did he go? It is obviously Afghanistan. This series of thoughts lasted less than a second, then I blurted out and said that you were from Afghanistan, and then you were very surprised.

——A Study in Scarlet, Arthur Conan Doyle

The process of inductive reasoning needs to combine facts and use logic to draw conclusions. We use inductive reasoning all the time. If a friend with a good literary taste recommends a book for you, you might assume that the book must be very interesting.

Of course, inductive reasoning is strong and weak. If the induction argument is very strong, the conclusions reached are more likely to be true; conversely, the logic between the hypothesis and the actual conclusion may not be correct.

In terms of inductive reasoning, there are mainly six ways of reasoning:

• General reasoning: Conclusions drawn from generalization. For example, “The swan I have seen is white. Therefore, all swan may be white.”

• Statistical reasoning: is a conclusion based on statistics. For example, “95% of swan is white. Therefore, randomly selected swan may be white.”

• Sample reasoning: A conclusion drawn about a sample based on a different sample. For example: “There are 10 white swan in this pond. Therefore, the swan in the next pond may be white.”

• Essential reasoning: A conclusion based on the same characteristics of two different sample populations. For example: “All Aylesbury ducks are white. Swan and Aylesbury ducks are very similar. Therefore, all swan may be white.”

• Predictive reasoning: A prediction based on past samples. For example: “I came to this pond last year, when all the swans were white. So when I go to the pond again, all the swans in the pond may be white.”

• Causal reasoning: A conclusion based on causal associations. For example: “All the swan in the pond is white. I saw a white bird at the pond. This bird may also be a swan.”

Our entire legal system is also designed based on reasonable reasoning. Therefore, it must also be based on evidence. For lawyers, they usually use inductive reasoning to find connections between different facts, to find the corresponding evidence, and to draw conclusions.

Generally, the initial conclusions are based on general reasoning or statistical reasoning. Even if this conclusion is not 100% certain, it can basically reveal his authenticity. For this reason, the evidence is rarely taken as a fact.

For example, if a fingerprint is found at the crime scene, then it will say “this fingerprint matches the fingerprint of the suspect” instead of “this is the fingerprint of the suspect.” What is implied in such a description is that, from a statistical point of view, this is basically not the fingerprint of the suspect.

In addition, inductive reasoning also involves Bayesian updating. The so-called Bayesian update, that is, at a certain stage, a hypothesis can be regarded as true, but if new evidence emerges, it must be adjusted to update this hypothesis again.

The Bayesian update is actually a way of adjusting the likelihood that a hypothesis is true as new evidence emerges.

Image source: Mattbuck

If inductive reasoning is used in a legal context, with the help of Bayesian updates, the possibility of the defendant being guilty under reasonable suspicion can be constantly adjusted in the context of constant evidence.

If we envision a simple, purely hypothetical criminal case, then we can imagine a situation in which Bayesian inference is combined in the inductive reasoning process.

For example, in a house, one person was murdered, and five other adults were present. One of them was the main suspect and there was no evidence that other people had entered the house.

In this case, the initial probability of the main suspect being murdered was only 20%. But as other evidence emerges, it will affect the proportion of this possibility.

If the other four people testified that they saw the criminal act of the main criminal suspect’s murder, the fingerprint of the suspect was also consistent with the fingerprint on the weapon, and the suspect’s clothes also contained the victim’s blood, then the jury The group may be close to 100%, thinking that the suspect is the murderer of the murder.

Of course, the reality is probably more complicated than this example. But the conclusion is never 100% certain, only infinitely close to 100%.

One of the main differences between deductive reasoning and inductive reasoning is that the latter can conclude that a conclusion is uncertain and may change in the future. This conclusion is neither strong nor weak; neither right nor good. In daily life, we also use inductive reasoning all the time, according to what we have seen and heard, and then we may adjust our views.

However, inductive reasoning in our daily lives is not always correct, but it usually helps.

For example, the concept of superstition is usually derived from inductive reasoning. If the athletes are particularly good at the day when the socks are reversed, they may think that the socks may bring good luck to them.

This idea may be further enhanced if the next time they re-wear the socks and just succeed again. On the contrary, they may constantly adjust this concept until they think that this concept is wrong.

Another example (for the time being, do not consider whether the turkey has subjective initiative): the farmer feeds the turkey every day, so the turkey believes that the farmer will be responsible for its “clothing, food and shelter”. But until Thanksgiving Day, this assumption was overthrown.

If you abuse inductive reasoning, cognitive shortcuts and biases may emerge in your conclusions. The world we live in is not as predictive as inductive reasoning. We may selectively determine our beliefs based on past experience.

If you abuse the inductive reasoning, a person may only recall the bad luck experience in the past when he is not lucky, to support his hypothesis, while ignoring the experiences that have been lucky.

In the book “The 12 Secrets of Persuasive Argument,” the author wrote:

In the induction argument, attention should be paid to the conclusion. When reasoning relies on a certain inference and contains new information that does not exist in the premises, this reasoning is inductive reasoning. For example, according to the premise, the defendant’s speech is vague, walking, bumping, and alcoholic, then you have reason to infer that the defendant is drunk. This isInductive reasoning. In the process of inductive argumentation, the conclusion is at most very likely. Prerequisites In the real case, the conclusions are not necessarily true. Conclusion The possibility of being true needs to be determined based on the strength of the premise-based inference. Therefore, in inductive reasoning, pay special attention to the “Inductive Leap” from the premise to the conclusion.

……

With regard to deductive reasoning and inductive reasoning, there are some common misconceptions. The reasoning that Holmes makes based on different factual observations is usually inductive reasoning, not deductive reasoning.

In the book Inductive Reasoning, the author wrote:

…We use inductive reasoning every day. We will infer what behavior a person might take, what the weather might be like, how the taste of lunch will wait, etc. These are common inductive inferences.

…Inductive reasoning is a cognitive activity that is presented at multiple angles. It can be to present cartoon pictures to children and ask simple questions, or to provide a series of complex oral arguments to adults and let them make probabilistic judgments.

…Inductive reasoning is also related to a range of other cognitive activities, such as classification, similarity judgment, probability judgment, and decision making. Most of the research on induction is related to the induction based on classification. For example, based on the premise that your neighbor is a human being, even if you have never seen a neighbor sleep, you can infer that he sleeps every day.

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Deductive reasoning

Deductive reasoning starts with a broad set of facts, the premise. For example, people are inherently dead. Next, there will be another small premise, a more specific statement. For example, Socrates is a human being. Thus, I came to the conclusion that Socrates would not live forever.

If both the premise and the minor premise are true, then the result cannot be false.

Deductive reasoning is non-black and white reasoning, and the conclusion is either true or false; it is impossible to have a situation that may be true or possible. Determining whether or not deductive reasoning is true, the main evaluation is the strength of the correlation between the premise and the conclusion. If a person is inherently dead and Socrates is also a human being, then he cannot be eternal. If the premise is notIn fact, the conclusion is even less likely to be true.

In the field of science, scientists often use deductive reasoning to prove the truth of the conclusion. The hypothesis is first proposed and then supported by evidence collection. If the evidence can support its authenticity, then the hypothesis can be confirmed.

The structure of deductive reasoning is usually: If A is equal to B and C is A, then C is B. If A is not equal to B, then C cannot be equal to B.

In the field of science, when broad conclusions are drawn from specific observations (through data to draw conclusions), inductive reasoning is also involved. If you can see a solid model through the data, it can also be used to support the hypothesis.

For example, after seeing ten white swans, we can use inductive reasoning to infer that all the swans are white. For such assumptions, it is easier for us to overthrow rather than confirm. In addition, the premise is not necessarily true, but based on the available evidence, and the researchers can not find it is not true, then these premises have to be identified as true.

By combining deductive reasoning and inductive reasoning, science can be brought closer to reality. In general, the more strange a statement is, the stronger the evidence supporting it is.

At the same time, we need to be wary that deductive reasoning sometimes seems reasonable, but in fact it may not lead to facts. For example, a dog has four claws and my pet has four claws. So my pet is a dog. This conclusion, on the surface, seems to be logical, but it is not, because the original premise is too specific.

Image source: Benjamin Frisch

written at the end…

In the book “How to Deliver a TED Talk,” author Jeremey Donovan wrote:

Discussion logic will inevitably involve the difference between inductive reasoning and deductive reasoning. According to strict definitions, inductive reasoning is to prove a general conclusion, that is, a viewpoint worthy of dissemination, through a specific set of events, trends or observations. In contrast, deductive reasoning is to narrow down the scope and draw a concrete conclusion through general conclusions. This is also a viewpoint worthy of dissemination.

OneLogic is a very important skill. Because we use it every day, we can benefit a lot by understanding the specific methods we use to draw conclusions.

Understanding how to present arguments, whether it’s making choices for us or understanding how the world works, has valuable value. It can also help us identify behaviors that deliberately mislead us through fallacy arguments. In addition, understanding and learning the way of reasoning can also help us avoid falling into logical fallacy and better communicate and negotiate with others.

Translator: Ishii Junichi