Logical errors. Training course. Chapter 2. Types of logical errors - 1

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

Repetition

In the first chapter, you learned about where logic errors can come from. These can be a wide variety of reasons: from intent to imperfection of the mind, from artistic techniques to linguistic reasons. You have learned that logical mistakes, and mistakes in general, do not always play a bad role, since, for example, in art it is sometimes appropriate to replace truth with plausibility, and when speaking in public it is not always appropriate to strictly prove something, it is enough to speak convincingly (honestly or dishonestly is another question).

A more attentive reader could draw some philosophical conclusions from the previous chapter. It turns out that living by strictly logical laws is not always possible. Any everyday conversation in natural language can literally be full of errors from the point of view of formal logic, nevertheless, people understand each other and their final conclusions may well be correct. For example, I can say: "people are mortal, therefore Socrates is mortal." This is a logical error! However, the conclusion is correct. I just missed the self-evident and out-of-context statement that "Socrates is a man." Imagine if any person who wants to be logically flawless had to state ALL basic premises that would tire the interlocutors before making a conclusion. Often times, people leave out the obvious or leave something in silence to make the conversation simpler and easier to understand. Such abbreviated reasoning, in which one of the logical elements is missed, is called enthyme. ema, they are perfectly acceptable to use in ordinary natural communication. The main thing is that this does not lead to a situation, as in the well-known anecdote:

Vasily Ivanovich and Petka are maneuvering a tank in the middle of the battlefield, the situation is extremely tense. Vasily Ivanovich briefly asks:

- Petka, devices!

- Twenty!

- What twenty? - Vasily Ivanovich clarifies.

- And what about the instruments? - Petka is perplexed.

However, the perniciousness of logical errors is that sometimes a person still draws completely wrong conclusions, since he does not notice mistakes or makes them deliberately for selfish purposes. And sometimes people just don't understand each other. So, for example, the seemingly correct example

may be erroneous from the point of view of logic. And there may be a number of reasons for this. For example, it may turn out that not every person belongs to the category of people. In our usual classification of people from a biological point of view, “people” is the plural of the word “person”. However, in a number of cases, the word man is understood as a particular representative of humanity, endowed with, say, a number of moral characteristics. Remember the saying: “all people, but not all are“human”? Or you can remember Diogenes, who walked during the day with a lantern and said “I am looking for a man”, although there were many people around. So, what am I doing?

If Socrates is a man, and only people are mortal, then Socrates does not have to be mortal at all, which means that the judgment is already logically incorrect. It was also necessary to add the argument “all“people”are people, then everything would fall into place.

Another point in the above example with Socrates is that in the second statement ("Socrates is a man") Socrates can be a man, and in the final conclusion ("Socrates is mortal") we are talking about the "Socrates" computer. It does not matter whether such a machine actually exists. This feature of the language is called "substitution of concepts", and it is not always deliberate.

The reader might have thought that I had gone into demagoguery, but no. The point is that these examples are closely related to our topic today. The reasoning given in two paragraphs above tells about the so-called “informal” logical errors, which, unlike “formal” ones, can bring much more problems to modern people precisely because of their informality.

Chapter 2. Types of logical errors (part 1)

The chapter is presented according to the following sources:

• A certain page (without a title) with examples for almost all existing errors. If you have a "crooked" encoding when opening the page, manually specify "Unicode".
• Evolution and logical errors. This article illustrates well the informal logical fallacies that arise in the creationist versus evolutionary debate. The article is written from a creationist perspective (which does not diminish the value of the material).
• Logical error - An article in RatioWiki listing errors.
• Logical Fallacies - Part of the article on logical fallacies from the English-language Wikipedia.
• Fallacies: Formal and Informal Fallacies - A video in English that explains the difference between formal and informal mistakes. There is another video on the site with the analysis of errors.

Mainly, all logical errors are divided into formaland informal … The first are associated with the violation of formal logical rules. They violate the correctness of inferences, which, in principle, can be expressed mathematically. The latter are associated with the perception of the person himself, with how he understands the content of the initial premises or conclusions. Formally speaking, informal logical reasoning can be logically and mathematically flawless, but it can still contain errors. Formal mistakes have a mistake in the form of thought. Informal - in the content of thoughts.

An example of a formal error: If a person is allergic to bananas, then he does not eat bananas. Vasya doesn't eat bananas. So he's allergic to bananas.

This is the classic mistake of rearranging cause and effect. We say If P, then Q, but this does not follow If Q, then P. As you can see, formal logic comes to the rescue and explains the error.

An example of an informal mistake: Practice is the path to excellence. The teacher has a lot of practice. Hence, the instructor is perfect.

Here the word "practice" is used in two different senses, and therefore, despite the sufficient logical accuracy, there is a substitution of concepts, and, consequently, there is no direct connection between the premises and the effect (we are talking about different things). In other words, this is a kind of linguistic gimmick.

You should not use this division of errors into formal and informal too actively, because, as the example with Socrates showed above, the same situation can be viewed from both formal and informal positions. Formal and informal errors can transform one into another depending on the angle of view, and can also be combined in a variety of ways.

However, there is another classification of logical errors: according to the nature of the technique inherent in them. The whole variety of logical errors can be broken down into a relatively small number of similar techniques, with the help of which a consequence is obtained from the premises. This is the classification we will follow.

Classification of logical errors

False (unreasonable, hasty) generalization (Dicto simpliciter, Hasty Generalization)

There are two main options for this error. In the first, a certain private property inherent in a member of the group is generalized to the entire group.

Example: All officials are bribe-takers. All men are goats.

Another example: (on the road the car has a punctured wheel)

- Honey, I do not know how to change the wheels in the car myself.

- What do you guys know how?

In another version, the special case is not taken into account and the law is generalized to it too.

Example: It is easy and pleasant to tell the truth. You were taken prisoner. You must easily and pleasantly tell your enemies the truth about your strategic plans and the location of your military units.

Another example: Cutting a person with a knife is a crime, and the surgeon does just that. So the surgeon is a criminal.

Any reader might think that this version of a logical error is so simple that no one actually commits it. But, alas, simple examples do not mean that the error is just as simple. Let's move on to some more sophisticated options for false generalization.

One of such complex options appears when a person, from one particular projection, tries to draw conclusions about the object as a whole.

In addition to the picture, the above error is well shown in the Indian parable "The Blind Men and the Elephant", described in poetic form by D. Sachs (19th century) and then translated into Russian by S. Marshak. It is called "Scientific Controversy". I am sure you are familiar with this poem and understand it well.

It is also clear to the reader that it is quite possible to restore the whole from a set of projections, as, for example, a master of carving does, cutting out an object from a series of projections and sketches. But what am I leading to then?

Take grades at school and university. These are just very condensed projections of the logic of social behavior of schoolchildren or students in the learning process, reflecting also a certain subjective opinion of the teacher about the nature of the student's knowledge. All the variety of talents and characteristics of a person, his character and propensity for a certain job is expressed in four numbers (from 2 to 5). Then, based on the set of these numbers, characterizing different areas of thinking, a certain potential employer makes his own conclusions about the relationship of a potential subordinate. And even more often they look only at the color of the diploma: red or blue. Just look at how diploma color and GPA affect job opportunities, and you’ll see that many employers make the mistake of false generalization when they try to measure a person’s ability by estimates. Fortunately, this tendency is gradually subsiding, and only the backward bureaucratic community still looks at the GPA as an objective indicator of what they call the word “knowledge”.

Next, take the ratings. For example, the rating of cities in terms of quality of life. There are a lot of such ratings, and they include a typical set of purely consumer characteristics: the number of schools, kindergartens, shops, air purity, life expectancy of people, tourist attraction, the presence of a cafe with Free Wi-Fi, etc. rating - and concluded that he wants to live in a city that is in the first place. And what will he get in the end? A city in which it is impossible to live for some other reason that is not reflected in the rating. For example, the congestion of kindergartens, traffic jams, population density - all these factors can dramatically worsen the situation of "the best city in the opinion of the magazine" Shish, but not shisha "", but this is no longer a concern. It's just that people's consciousness generalizes the ratings to other characteristics that are out of the question. The same happens in social networks, by the way (and indeed everywhere). The "Popular" tab reflects only the fact that people gave the most votes to such and such articles. This tab has nothing to do with the meaning of the word "popular". Whether someone actually reads them is unknown. It is also a mistake to reward popularity itself for the fact of popularity, which I wrote about in the semi-humorous article "The Popularity Paradox".

In other words, to ascribe various broad properties to a certain object, which turned out to be higher in the rating according to particular criteria - this is a variant of a false generalization. And he really rules this world.

Another example from the scientific community. At the end of the last century, articles were written on the so-called "meta-analysis", on the basis of which the benefits of moderate alcohol consumption were "proven". The articles were published in peer-reviewed scientific journals and the conclusion was that moderate consumption reduces the risk of coronary heart disease compared to avoiding alcohol and drinking too much. The research was carried out in this way: three groups of people were taken - teetotalers, moderate drinkers and alcoholics (excessive drinking). A medical study was carried out, which showed a clear dependence and revealed that moderate drinkers are least likely to suffer from this disease. It would seem that the scientific method, prestigious journals, indisputable facts … All this is enough to convince even a learned person to believe in the benefit of moderate drinking.

It turned out, however, a false generalization of the word "teetotaler". Who was included in the group of teetotalers in the study? It turned out that among the teetotalers there were those who had previously consumed alcohol and undermined their health so much that they had to become a teetotaler, as well as those who already had health problems, because of which they could not even start drinking. There were few healthy and sober people in this group, and therefore they practically did not affect the statistics of morbidity. With the same success, it was possible to recruit only people with heart pathologies in the group of teetotalers, and to recruit different athletes to the group of moderate drinkers, and then say that alcohol reduces the risks of heart disease. Such nonsense in "science" is exposed in scientific publications:

1. J. Hietala, “Novel Use of Biomarkers and their Combinations for Detecting Excessive Drinking” (2007).
2. K. Fillmore, T. Stockwell, T. Chikritzhs, et al. “Moderate Alcohol Use and Reduced Mortality Risk - Systematic Error in Prospective Studies and New Hypotheses” (2007).
3. T. Chikritzhs, K. Fillmore, T. Stockwell, “A healthy dose of skepticism - Four good reasons to think again” (2009).
4. R. Harriss et al. “Alcohol consumption and cardiovascular mortality accounting for possible misclassification of intake: 11-year follow-up of the Melbourne Collaborative Cohort Study” (2007).

By the way, belief in science is one of the fairly common logical mistakes, and we will probably talk about it later.

Another variant of statistical false generalization is called "false statistics", that is, when the sample is not representative or when the experiment itself is carried out under such conditions in order to obtain the desired result. There are two anecdotes on this topic. First: "Internet poll showed that 100% of people have the Internet." The second is expressed in this picture:

For a more cunning example of false generalization, see my article Why Fortune Tellers and Fortunetellers Don't Win the Lottery? I ask readers not to make false generalizations and attribute to me the desire to defend all sorts of charlatans, this article is only about a logical error, regardless of my attitude to the problem of fortune-tellers and fortune-tellers.

Irrelevant judgment (Ignoratio elenchi, Missing the Point)

It is also a common mistake where a given argument may be true, but it has nothing to do with what is being discussed.

Example 1: (in debate)

- Does the law protect unemployed citizens?

- The law should protect unemployed citizens, because they are the same citizens, but found themselves in a difficult situation, they need help to find work.

The mistake is that the question sounded like "does it protect?" and not "should I protect?" It can be seen that the interlocutor is trying to evade the answer, giving the correct argument, but not related to the topic.

Example 2

- I would like to buy a house by the sea.

- How can you dream of a house by the sea when people die every day in Africa?

The mistake is that while the horrific argument is not wrong, it is not relevant to the topic under discussion. In addition, people die every day, not only in Africa, and this is by no means always tragic for someone (including the dying).

Example 3

- I advise you to run in the morning, it gives such and such advantages.

- It has long been proven that running has a bad effect on the knee joints, they are destroyed.

The mistake is that a particular thesis, true in some cases (onlywith improper running or joint pathologies), acts as a refutation of the main thesis about the benefits of running. Let me give an analogy, brought to the point of absurdity: it is harmful for a person to drink water, because if he drinks 14 liters of it in 3 hours, irreversible processes will begin in his body, leading to death. But you must admit that with this thesis I did not prove that drinking water is harmful. Likewise, the thesis that running destroys the knee joints does not disprove the benefits of running, but only demonstrates a person's sports illiteracy. With proper running, a healthy person will not ruin their legs. In any case, my two coaches and I are not aware of such cases.

A more complex example: "How can you believe the Bible, which says that God created the Earth in 6 days, science has proven that by the time the Earth appeared, about 10 billion years had passed?"

Let the reader not try to understand my personal attitude to the Bible, it is impossible to do this from the materials that I publish. Here, in the given example, we have a whole bunch of logical errors, one of which refers to irrelevant judgments. The scientific substantiation of the age of the universe and the Earth as a whole cannot be compared with the biblical 6 days. These are different things, if only because these "days" in the Bible are acts of creation, the duration of which in our earthly years is not indicated anywhere at all. And the assessments of scientists are time intervals, translated into the relatively-frequency methods of measuring time adopted on the already existing Earth. There is no connection between one and the other, which means that there is no indicated contradiction between science and words from the Bible (but this does not mean that it cannot be in another place).

Generally speaking, non-judgmental judgment is one way to change the topic of conversation. Example:

- Alcohol is harmful in any dose, and people who consume it simply do not want to understand the situation.

- My grandfather Innokenty has been drinking for 70 years, and nothing, he lived a long life. Anyway, during the war, combat 50 grams could save lives.

As a result, the interlocutor, instead of explaining his thesis about the dangers of alcohol, will be forced to spend time explaining the typical myths about grandfather Innokenty and the fighting 50 grams (you can dig up a hundred such stories). In the meantime, he does this, time is running out, and the desire to listen to a person, too. Therefore, a person who is armed with a number of pre-prepared arguments that are not related to the topic can be guaranteed to chatter you with them to such an extent that instead of the topic of the report, you will say all sorts of nonsense. And it doesn't matter whether you succeed or not: the interlocutor achieved his goal, he did not allow you to say what you wanted. One of the options for this behavior is typical for debates: you need to force a person to prove that he is not a camel, simply by hanging deliberately ridiculous labels on him and forcing him to spend time denying the obvious.

A less obvious example is indirectly related to the error of non-relative judgment. It is called " dispute with a dummy". Instead of the thesis being discussed, the opponent begins to argue with another thesis, which he himself ascribes to the interlocutor, thus leaving the topic and the original subject of the conversation. A person argues not with a person, but with a dummy, for which he himself is responsible.

For example, among some overly ardent opponents of the religious worldview, one can find an argument: “Tertullian said: 'I believe, for it is absurd.' That is, you believers believe in absurdity. " The problem is that Tertullian didn't say that. He said another phrase, which can be interpreted, including the following words: "there are things that a person can hardly understand, and he can only believe in them." Of course, I have given one of the simplest interpretations. In our time, it would be appropriate to give an example: when physicists first saw what was happening in an experiment with two slits, they, of course, already partly understood what was happening:

However, to an unprepared person, the result would seem absurd: “how is it, an electron flies by simultaneouslythrough both slots? And he stops doing it when you just watch him ?? Are you crazy ?! Absurd! . But a fact is a fact, and therefore it remains only to believe in it, until the picture of the world in the head is formed in the right way and everything falls into place. Then there will be no absurdity, and no belief in it.

So, having attributed to the interlocutor a point of view that is obviously convenient for yourself, you easily refute it, and then you say that you have refuted his initial thesis. Unfortunately, this kind of logic is loved by both creationists and the scientific method.

Homework

Let me remind you that tasks notshould be discussed in the comments (unless you find an error in the wording).

Problem 1

One person says to another: “The conspiracy theory is nonsense, because you yourself imagine that a certain group of persons conspired and controls all world processes in politics … do you yourself believe that this is possible? So they gathered for cognac, sat down at the table and plan to kill someone else and make whom president. What's the point?.

Try to list all the logical errors here and explain in more detail the ones that we covered in this part of the second chapter.

Task 2

Before you is a common argument, with the help of which they are trying to prove intent in the actions of another: "a person with your character and could not have acted otherwise." Where is the mistake?

Problem 3

Here is an anecdote.

Three scientists - a biologist, a physicist and a mathematician - were traveling across Scotland in the same compartment of a train. Through the window they saw a black sheep grazing on one of the hills. The biologist said, “Wow, you! There are black sheep in Scotland. " The physicist replied: "No, we can only say that there is at least one black sheep in Scotland." The mathematician concluded: "There is at least one sheep in Scotland, black on at least one side!"

Consider the anecdote from the perspective of the material covered. What mistake is he dedicated to? What is the cultural value of its content?

Problem 4

One historian once said that the ancient pyramids of Egypt could not have been built by those who lived at that time, because even today no modern method of stone processing can cut such huge blocks so flawlessly evenly. He also said about the impossibility of constructing some of Baalbek's buildings, since even modern technology does not allow lifting stones of such a huge size.

Is there a false generalization error here? If so, what is it? Are there any other bugs you know about here?

Problem 5

One person once asked: "How to choose high-quality alcohol for the New Year, so that I don't get poisoned like last time?"

The answer was: “why drink at all for the New Year? Don't drink alcohol and there will be no problems."

This is not an easy task: in this answer you need not only to find a logical error, but to suggest situations in which you cannot get away from it. That is, when it is impossible to answer without error.