Logical errors. Training course. Solutions to the problems from chapter 1

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

The rule here is this: I offer my reference solutions for all problems, sometimes I accompany them with my thoughts, where it will be in the topic. I am not claiming that my decisions are correct, and therefore you may well discuss with me in the comments. Due to the careful attitude to my time, I will only respond to comments that deserve attention and my answer, I ask the others not to be offended, just try to think for yourself. Even if I'm wrong.

Problem 1

Two arguments are given: “all the coins in my pocket are gold” and “I put a coin in my pocket”. Does it follow from this that "the coin put in the pocket will become gold"?

Yes and no. Here we have a misunderstanding related to the perception of natural language. From the point of view of strict logic, the answer is “no”, because if, say, I have 2 coins in my pocket, and both are gold, then the first statement is true. I put, for example, a copper coin in my pocket, making the second statement also true. However, as life practice shows, it does not have to become gold. We gave an example that refutes the expressed situation, from the point of view of mathematics, this is enough.

On the other hand, the first statement “all the coins in my pocket are gold” in some cases may mean that the coins are become gold in my pocket. Why is this possible in natural language? Imagine a school teacher says: "All my graduates are smart." It is clear what he means: all kinds of students come to him, and he makes them smart by the end of the training. The same is with the magic pocket: all coins that fall into it become gold. This may well be understood in such a categorical form in which the original statement was made. In this case, the answer to the problem will be "yes".

Be careful with the logic expressed in natural language, because it is very insidious, behind the seeming obviousness of the statements, there may be some subtext that you could not grasp right away. And this is what happens most often in life.

A detailed analysis of this problem and the linguistic tricks in its formulation is a preface to the next chapter.

Task 2

Consider a typical example of an unsuccessful student returning home from school, parents start scolding their son.

Act I

- You got a deuce again?

- But there was a difficult job, everyone did a bad job!

- We are not interested in what everyone has, we are interested in what you have! Take responsibility for yourself!

Act II

- Well, what is the control?

- "Three".

- Why “three”, everyone got “four” and “five”, and you - “three” ?!

Both acts took place in the same family with the same child. Find the logical error of the parents and try to explain the reason for its occurrence, which is the most probable, in your opinion.

The error here, I think, is obvious. At first, parents argue that there is no need to equalize with others, and then they contradict themselves, trying to compare their son with others.

The reason for the error, in my opinion, is deeply rooted in psychology. Personally, I see in this example a lack of parenting culture and a lack of understanding of the processes taking place in the world. The following text is the result of my many years of communication with schoolchildren and students, they often shared the problem of the parents' position on educational issues, so I had the opportunity to collect a lot of data and draw conclusions.

Parents mistakenly want their son to be the best at everything, and they measure this “everything” by such a narrow and almost insignificant indicator as “grade”. They know that the assessment depends on how easily their child will be able to take one or another stable position in the future, and that competition, other things being equal, will be based on these digital indicators. They do not want their son to look like losers who do not do well in school, and therefore forbid comparing themselves to them (Act I). They do not want their son to be worse than those who "beat" him according to estimates, and therefore compare him with them (Act II). It would be more correct for parents to immediately indicate their position to the child: “you should be the best, and therefore do not equalon those who do something bad, and level up on those who do something better than you. " Then the correct dialogue would be like this:

Act I

- You got a deuce again?

- But there was a difficult job, everyone did a bad job!

- You must be better than these losers!

Act II

- Well, what is the control?

- "Three".

- Why “three”, everyone got “four” and “five” ?! You should be no worse than these successful students!

Then there is no contradiction: the parents clearly propose to level themselves only with the successful (estimated) students.

By the way, it should be said here that in the educational process, parents often violate logic and common sense when they do not have reasonable arguments in favor of their position, or when the child cannot understand these arguments due to, for example, age. When, in childhood, a child was scared that if he did not wash his face, Moidodyr would come, then why not at a more conscious age begin to come up with something similar, but more believable? For example: "you will be like this your Kolka the dolt, collect bulls in the trash heaps." This mistake is called “after, therefore, for a reason” (Kolka did not study well, and therefore, after studying, he began to collect bulls - there is no direct connection here). Or: "if you study badly, you will not enter a university, and then you will go to the army, there you will be beaten or forced to dig potatoes from morning to evening." The error is called an "inclined plane": a series of likely following one of the other events is presented as fatal, that is, with a completely inevitable consequence.

A child, accustomed to obey such logic due to the authority of his parents, begins to subconsciously accept it and uses it himself in life. And then we wonder: why do people make the simplest mistakes in life over and over again?

However, we will talk about these errors later. These examples were also the announcement of the next chapter.

Problem 3

A moderate alcohol drinker's argument might be:

"Wine is made from grapes, and grapes are good for the heart, so drinking wine is good." What is the error and what is its cause? Do you think the moderate drinker himself knows about this mistake?

An analogy can be used to expose this logic. “Hydrogen can be obtained from water, but water does not burn. Therefore, hydrogen also does not burn. But in fact it burns.

“Meat cutlets are made from a pig, and a pig grunts. Therefore, the cutlets grunt too."

“An adult grows out of a baby, and a baby cannot talk. Consequently, an adult cannot speak."

The mistake is that some property of one object is transferred to another object, which is somehow related to the first. There are a lot of similar mistakes in our life: attributing to children the properties of parents (you are as hot-tempered as your father), attributing the same properties to similar objects (a whale looks like a fish, which means it can breathe under water), speculating for a person his intentions (he looks at me strangely, this is usually the view of those who know something bad, but do not want to say), etc. At the same time NOTit is important whether wine is actually good for the heart or not, it is important that the logic of this conclusion is erroneous. In a similar way of "proving" with the proper imagination, you can "prove" anything you want.

I have experience of sobering people up and weaning them off alcohol, so I can share my observations. Almost all drinkers or drank people I know KNOW that this argument is false and know that grape juice also has the property of "made from grapes", but they drink alcohol for another reason, and this argument is presented for self-persuasion (cognitive distortion "tendency to confirmation”) and due to the lack of other arguments (usually drinkers know that any dose of alcohol brings significant harm, and therefore try to dodge). There are very powerful social mechanisms that prevent a person from resisting the pressure of society. A classic example is given in the famous popular science film "Me and Others" (1971), the experiment with pyramids is especially interesting. Communicating with drinking people, I noticed that they most often cannot resist the culture of drinking on holidays precisely because of the pressure of tradition and the mood that other participants in the drink set, this is what makes them look for plausible excuses for their behavior. Everything written in this paragraph is my personal experience, it may not coincide with yours.

By the way, there are studies that disprove the benefits of wine for the heart. If possible, I will touch on this topic and show an example of scientific falsification of statistical data, which doctors often refer to, now this topic is out of this course.

Problem 4

One person on a forum on the Internet proves his point of view to another, there is a long exchange of views, but at some point the interlocutor stopped responding. “I won,” the first thinks, “I wrote everything to him so clearly that he cannot object, so I’m right!” The question is the same: what is the error and what is its cause?

The mistake is that silence can mean a variety of reasons, and admission of defeat is probably the rarest of them. There are two logical mistakes at once: premature conclusion and attribution of properties convenient for oneself to another person (the so-called dispute with a dummy). We will discuss all this in more detail later.

The "logic of the last word" is firmly entrenched in our culture. Whoever has the last word is right. Have you noticed this? In a quarrel, everyone wants to call the other with impunity so that he does not answer. In a dispute, everyone wants to have the final say. Where does this cultural feature originate?

There are various considerations in this regard. Here is one of them. A. Belov “Anthropological detective. Gods, people, monkeys … :

For example, in saimiri monkeys, which were observed by zoologists D. Ploog and P. McLean, the demonstration of an erect penis to another male is a gesture of aggression and challenge. If the male, to whom such a gesture is addressed, does not assume the posture of submission, he will immediately be attacked. In the herd, there is a rigid hierarchy of who can show the penis to whom.

Another similar example from a book on Sufficient General Management Theory:

So in a herd of baboons, a hierarchy of their "personalities" is built on the basis of identifying who is showing a penis to whom with impunity.

Apparently, to leave the last word for oneself is just a cultural shell of the described ancient behavioral traditions that passed to man in the course of the evolution of man from ape.

An analogy now suggests itself. What do you think, these beautiful rituals of initiation into knights, which can be seen in films, when a certain hierarch lays a sword on the shoulder of a kneeling future knight … Does this not look like a cultural shell of the same monkey ritual? And the word “dagger”, as if not by chance, has at least two meanings: “sword” and one more from the list of taboo vocabulary. Well, you get the idea. To be honest, I don't know the answer to the question in this paragraph.

Of course, the fact that the person doesn't answer you can mean different things. One of them looks like this: "I am so tired of explaining to this stupid interlocutor his delusions that I would rather go and teach a dozen more capable people something good." And silence can also mean that a person has problems, and because of them he cannot write a message, or he simply does not want to further explain something, because he believes that he has said everything necessary, and everything further is no longer his concern. … But no, in most cases known to me, the one who left the last message “with impunity” is considered the winner, as outside observers usually think so. Strange, but this is quite clearly manifested even in debates on various talk shows, where smart people seem to be gathering.

On the contrary, in the place of people who left the last word for themselves, I would consider silence as a bad sign, first of all for myself. For example, when I do not answer an arrogant interlocutor, it means that he himself has already written so many nonsense that his further exposure on my part is not required. Regardless of what outside observers think of me.

Problem 5

The person blames the other for something that he is not really to blame. However, the second cannot prove his innocence and blushes. "Yeah, an honest man will not blush when he is scolded, then you are to blame!" The question is still the same …

This is a very common misconception of many people. They often assume that others will behave exactly like them in similar situations. If, for example, a person is inclined to make excuses and prove something to an erring opponent, then he believes that others in his place should do the same. There is also another logical error mentioned in the previous task: premature inference (based on insufficient data set).

When I was there, I often found myself in situations in which it was impossible to prove that I was right, but at the same time you know that you are not guilty, they just misunderstood you, you ended up in the wrong place at the wrong time, etc. A little later I started get into situations where my phrase is misinterpreted. For example, I, a convinced teetotaler, can say in the circle of other teetotalers this: Prohibition must not be introduced, alcohol must be distributed freely. They immediately attack me, they say, I am for "alcoholics" and encourage cultural drunkenness. Making excuses is useless, so I usually keep quiet. But why am I silent? Rave because I reject my statement and give in against the pressure of a half dozen teetotal fanatics?

No. The reason is different. If a person does not understand the elementary foundations of management and makes the simplest logical mistakes, it is useless for him to prove anything, this will only lead to even greater misunderstanding of each other and to even greater problems. Therefore, it is better to simply remain silent, for the sake of everyone's safety.

Thus, if the interlocutor does not justify himself, then it does not follow from this that he pleads guilty or defeated. He may simply be aware that you will not understand him anyway. Or a situation may arise like in spy films: a person cannot reveal a secret and it is beneficial for him to be thought about in a different way than in reality. Learn to rapport!

Another funny example: if you do not drink, then in some companies drinking people will immediately assume that you do not respect them, and if you do, you should drink. A similar logic once occurred to one of my teachers. Oh, it would be better if he kept silent …

This logical error of premature conclusion and projection of one's qualities on the qualities of the interlocutor leads to even more sad consequences. Some time ago I was accused of one malicious act, mean and base. The motivation of the accusing party was based on the fact that he, the prosecutor, in my place would have done exactly this, and other people known to him would have done the same: in order to revenge for humiliation, he would have ruined the thing behind the back of another person while he does not see. As for me, as a well-mannered person, I did not perform the specified action, and the owner himself ruined the product, not noticing the marriage during the marriage, and the breakdown accidentally manifested itself in my presence. It is impossible to prove your case: the labels have already been hung, and the conclusions have been drawn. This incredible combination of circumstances then led to the fact that they had to use force in self-defense …

Outcome

When solving any problems, it is also useful to think about how the problem arising in the problem manifests itself in life, what other signs and consequences it still have. The point of my training course is to show the manifestation of mistakes in life and the possible options for how to avoid them. All the tasks that I will give further will also have this property: the problem described in them occupies a very significant place in the lives of many people and manifests itself much more strongly than it seems.