Here are examples of sophisms that became famous in ancient times: “What you have not lost, you have; You didn’t lose your horns; it means you have horns,” “The one sitting stood up; whoever stands up stands; therefore, the one sitting is standing,” “This dog is yours; he is a father; that means he is your father.” The sophism "Liar", attributed to the ancient Greek philosopher Eubulides of Miletus, is associated with the question: "If a person says that he is lying, is he lying or telling the truth?" Assuming that he is telling the truth will mean that the truth is that he is lying (this is what he is saying), which means that he is lying. If he is lying, then this is precisely what he openly admits. It turns out that he is telling the truth.

In Ancient Greece, sophists, for a fee, taught the art of winning an argument, no matter what the argument was about. Such a teacher, for example, was the philosopher Protagoras. He is discussed in the famous sophism “Evatl”. Euathlus learned from Protagoras the art of argument. According to the agreement between the teacher and the student, Evatl had to pay his tuition after the first lawsuit he won. A year has passed since graduation. Evatl did not participate in any trials during this year. Protagoras began to show impatience. He invited Evatlu to pay the tuition fee. Evatl refused. Then Protagoras said: “If you do not pay the fee, I will go to court. If the court decides that you must pay, then you will pay for the tuition according to the court's decision. If the court decides “not to pay,” then you will win your first case and pay for training under the contract.” Since Euathlus had already mastered the art of argument, he objected to Protagoras: “You are wrong, teacher. If the court rules “not to pay”, then I will not pay according to the court decision. If he decides to “pay”, then I will lose the process and will not pay under the contract.” Puzzled by this turn of events, Protagoras devoted a special essay to this dispute with Euathlus, “The Litigation of Payment.” Unfortunately, it did not reach us. Nevertheless, we must pay tribute to Protagoras, who immediately sensed a problem behind a simple judicial incident that deserved special study.

Examples of sophistry

Even and odd.

5 is 2+3 (“two and three”). Two is an even number, three is an odd number, it turns out that five is both an even and odd number.

You don't know what you know.

“Do you know what I want to ask you?” - "No". - “Do you know that virtue is good?” - "I know". - “This is what I wanted to ask you about. But it turns out you don’t know what you know.”

Medicines.

“Medicine taken by a sick person is good. The more good you do, the better. This means you need to take as many medications as possible.”

“The thief does not want to acquire anything bad. Acquiring something good is a good thing. Therefore, the thief means well."

Father is a dog.

“This dog has children, which means she is the father. But it's your dog. So she is your father. You beat her, which means you beat your father and you are the puppies’ brother.”

“What you haven’t lost, you have. You didn't lose your horns. So you have horns."

Hello!

Today I would like to bring to the attention of the respected community what is, in my opinion, very interesting.

The topic is completely non-poker, but very interesting, so I decided to bring it closer to the theme of the site.

So, Sophism (from the Greek σόφισμα, “skill, skill, cunning invention, trick, wisdom”) is a false conclusion, which, nevertheless, upon superficial examination seems correct. Sophistry is based on a deliberate, conscious violation of the rules of logic (thanks wiki).

Historically, the concept of “sophism” has invariably been associated with the idea of ​​deliberate falsification, guided by Protagoras’ recognition that the sophist’s task is to present the worst argument as the best through cunning tricks in speech, in reasoning, caring not about the truth, but about success in the argument or practical benefit.

Have you ever had this happen where a person proves to you, for example, that the sky is green? It would seem that there is nothing easier than to prove the opposite, and you try, but your opponent brings up quite logical arguments, gradually tipping the scales in his favor. Then he already has supporters from the listeners and help him. And the situation turns out: there are 10 people opposite you, one of them is an opponent, who claim and convincingly prove that the sky is green. And the fact that the sky is blue becomes rather precarious.

Why does this happen? The sky did not turn green from the opponent’s arguments, but this is not necessary, because the measure of truth for a sophist is the opinion of people. A statement becomes true when it is accepted by the majority, regardless of its absurdity. And the sophist gets the most important thing from this: the support of people, which allows him to please his pride, earn money on people’s trust, etc.

Public people and government officials often resort to the tricks of sophistry. A poker player, by and large, does not need this - his profit does not depend in any way on whether he knows how to defend his point of view in discussions in all possible ways. But one bright member of the community, in my opinion, quite often resorts to various tricks and scams in the discussion. Probably, many guessed that we would talk about Max, whose last name does not need to be mentioned.

I will try to analyze excerpts from his posts and comments from the point of view of sophism.

From the post Reasons for my conflicts with colleagues:

This is nonsense, well, think for yourself - a normal person in his right mind would not think of arguing with someone for the sake of popularity. I am sure that such maneuvers are done only out of conviction, and never out of calculation. I don’t believe that anyone makes them thinking “well, tomorrow everyone will read this scandal and I will be popular.”

This is a technique called narrowing the choice: you can quarrel with someone only out of conviction; the option of quarreling with someone for popularity is not considered, since this is nonsense (an unproven statement that creates the appearance of logic in all subsequent ones)

Another example of narrowing down choices from Max's discussion with Bizi:

I consider the sale of shares from IU without potential shares from getting on TV table chaos. This is only possible because the buyers do not have the right to vote with the players and it’s like everything will go away.

On the controversial thesis “selling shares from IU without potential shares from getting on the TV table is lawlessness.” the idea of ​​anarchy in the sphere of sale of shares and the terrible lack of rights of buyers of shares is based. The main idea of ​​the above excerpt: to scare potential buyers so that they do not buy until it becomes exactly what Max needs. In addition to narrowing the choice, there is also a substitution of concepts. Max is trying to portray his private conflict as a crisis of the entire market for the sale of shares in order to expand the circle of his supporters.

Lika's question from the comments:

Lika: What kind of attitude do you expect towards yourself if you directly write “I don’t care about everything!”, “I don’t care about everyone!”, even if you haven’t even read many of the thoughts and constructive criticism on the forum?

Max:I don’t care about the opinions of people who write it publicly. I enjoyed chatting with everyone who wrote to me personally or talked to me; I don’t give a damn about them at all. No one expressed any negative attitude in a personal conversation. Those who wrote publicly, in my opinion, did it only to quarrel, and not at all because I somehow offended them, not because they want to change something, and generally not in order to deal with constructive dialogue with me. Just make a scandal. Therefore, neither they nor their opinions interest me at all, I don’t read them, I don’t even know who wrote there.

And again the choice is narrowed: only those who communicate with him personally have the right to criticize Max. Criticism from others is not accepted. Although it is precisely because of Max’s rejection of criticism that these people do not want to communicate with Max personally. Here Max depicted an insurmountable logical construction, according to which he will no longer accept criticism.

Of course, I buy packages for satellites with very good discounts, and the lessons I offer are not cheap, but I am confident in buying lessons from John and watching the WOD at the price at which I offer it + EV for the user.

Here is an equivocation. Juggling meanings. It is clear that watching WODs and learning is always +EV. Therefore, in theory, any price will sooner or later pay off due to +EV.

About “playing out” the finals:

Gypsy:A thing that is officially recognized as fraud - you justify it, you do it. And when you were asked, “Do you think that the fact that you finish the finals for other people causes a loss to the other player?” You simply replied, "No." Explain your position.

Max:There was a provocative topic... Probably, damage is being done to these people. But again, this is my position that for now there is a fair game of cards and people there do not know additional information. The fact that another person sat down and played is insignificant.

Petitio principi - anticipation of the foundation. Here the entire argument is built around an unproven thesis (on which the argument cannot be built): “the fact that another person sat down to play is insignificant”

About the community:

Question:Max, how do you feel without the community, and what will you do without us?!

Do you remember what this forum gave you?! There is a proverb: “don’t spit in the well, you’ll need to drink the water!”...

Answer:I really love pokeroff and my audience (seriously). I try to write a lot of complex posts with all sorts of thoughts, about poker, about business and in general. There are more than 1200 posts on the blog, at least 400 of which are stories about issues that I thought a lot about and tried to write in simple and understandable language.

The fact that there are characters running around is, firstly, natural, and secondly, I often provoke them myself. They don't interest me at all :). In general, I really love the audience and don’t even think about giving a damn about them.

Here non sequitur, literally – “does not fit.” A way of saying a lot without saying anything. The question of attitude towards the community is difficult for Max - after all, Max considers 95% of people not very interesting. But you can’t write about it. Therefore, he began to write something about love for his audience and emotional posts from the bottom of his heart, without answering anything specific.

About trading:I sold everything, and never in my life did I allow myself to tell a client the wrong thing about what I was thinking about buying. When I thought that he didn’t need it, I simply didn’t offer it.

So, in my opinion, it’s much easier to sell only what you think is right to sell.

There were times when I was mistaken and convinced people of what I thought was good, but in the end it didn’t work - yes. But to know that this is nonsense and sell it anyway? It seems to me that you can lose respect for yourself this way.

This technique is called eristics from a fool - Max pretends to be not very smart in order to remove responsibility for unsuccessful endeavors: Of course, I told people when I was selling it that it would work. But he didn’t deceive them, he was simply mistaken.

About Mikhail Semin

And Mikhail Semin expressed a very serious defense of this position, and then he generally wrote that thieves are being imprisoned all over the world, but there are not fewer of them, and then an honest guy stumbled and you all attacked him. To me, this position seems to be either the position of a stupid person, or the position of a fraudster, or the position of a friend of a fraudster. I don’t understand how a person with brains can take such a position on such an issue, so I wrote what I wrote.

"Dirty" method of discussion - ad personam. Insulting the opponent, rather than challenging his arguments, implicated in the unproven thesis “only a fraudster or his friend can have such a position”

About complaints about high topics for training:

So, this desire to constantly destroy everything, to find the most expensive price and start sucking on it, or to make verdicts just because you want it to be so without even knowing the player, it infuriates me. And now it’s still an evening philosophical mood, and so it is. I don’t like these people who gossip on benches in the entrances and wash everyone’s bones (I’m not talking about pensioners), and all they do is drink beer and watch TV. But they know better than anyone what the price is for what, and how to do what.

They then raise poor children, create poor life values, and whole crowds of people grow up who, instead of thinking about how to develop themselves or do something good, think about how to destroy something. *****.

Another “dirty” trick: ad hitlerum: little people cannot discuss and criticize what I do.

And finally, the dialogue:

Soul: When one of Max’s acquaintances wins a major tournament, that’s a skill, and a guy who wins a tournament for 2k online is a lacker. Please clarify

Max:the discrepancy that you pointed out was due to the fact that I am a lying, inconsistent scoundrel Jew, thirsting exclusively for profit - presenting the facts in a way that suits my interests.

Soul: You have always done and are doing exactly the same. For example, selling shares and training from yourself and your friends. If you do not agree that the situations are identical, then what is the difference? Please, an exact logical criterion, without personal assessments.

Max:Well, I can, I’m a scoundrel.

Not everything that is possible for me is possible for others. Since when did we have equality in the world? Someone works at the factory, and someone manipulates the facts. But how can we allow someone else to do this?! Especially the red-haired representative of a respected honest site, and not a lying, self-serving Jew manipulator with the last name Katz.

Ignoratio elenchi - substitution of the thesis. Max, instead of answering questions, attributed a bunch of accusations and insults to his opponent and thereby avoided answering.

Look like that's it.

Thank you for your attention! Don't give in to provocations!

Sophism

But here is a modern sophism that substantiates that with age, “years of life” not only seem, but are actually shorter: “Every year of your life is a part of it, where is the number of years you have lived. But . Hence, ".

Historically, the concept of “sophism” is invariably associated with the idea of ​​deliberate falsification, guided by Protagoras’s recognition that the task of a sophist is to present the worst argument as the best through cunning tricks in speech, in reasoning, caring not about truth, but about success in argument or benefit. (It is known that Protagoras himself was a victim of the “sophism of Euathlus”). The “criterion of foundation” formulated by Protagoras is usually associated with the same idea: a person’s opinion is the measure of truth. Plato already noted that the basis should not lie in the subjective will of a person, otherwise one will have to recognize the legitimacy of contradictions (which, by the way, was what the sophists argued), and therefore any judgments will be considered justified. This thought of Plato was developed in Aristotle’s “principle of non-contradiction” (see Logical Law) and, already in modern logic, in interpretations and the requirement for evidence of “absolute” consistency. Transferred from the realm of pure logic to the realm of “factual truths,” it gave rise to a special “style of thinking” that ignores the dialectics of “interval situations,” that is, situations in which the Protagoras criterion, understood, however, more broadly, as the relativity of truth to conditions and means of its knowledge turns out to be very significant. That is why many reasonings that lead to paradoxes and are otherwise impeccable are qualified as sophisms, although in essence they only demonstrate the interval nature of the epistemological situations associated with them. Thus, the sophism “heap” (“One grain is not a heap. If there are not a heap of grains, then the grain is also not a heap. Therefore, any number of grains is not a heap”) is just one of the “paradoxes of transitivity” that arise in the situation “ indistinguishability." The latter serves as a typical example of an interval situation in which the property of transitivity of equality when moving from one “interval of indistinguishability” to another, generally speaking, is not preserved, and therefore the principle of mathematical induction is not applicable in such situations. The desire to see in this an “intolerable contradiction” inherent in experience, which mathematical thought “overcomes” in the abstract concept of a numerical continuum (A. Poincaré), is not justified, however, by a general proof of the removability of this kind of situations in the sphere of mathematical thinking and experience. Suffice it to say that the description and practice of applying the “laws of identity” (equality) that are so important in this area, just as, generally speaking, as in the empirical sciences, depends on what meaning is given to the expression “same object”, what means or criteria for identification are used. In other words, whether we are talking about mathematical objects or, for example, about objects of quantum mechanics, answers to the question of identity are irreducibly related to interval situations. At the same time, it is not always possible to oppose one or another solution to this question “within” the interval of indiscernibility with a solution “above this interval,” that is, to replace the abstraction of indistinguishability with the abstraction of identification. And only in this last case can we talk about “overcoming” the contradiction.

Apparently, the first to understand the importance of the semiotic analysis of sophisms were the sophists themselves. Prodicus considered the doctrine of speech and the correct use of names to be the most important. Analysis and examples of sophisms are often found in Plato's dialogues. Aristotle wrote a special book “On Sophistic Refutations”, and the mathematician Euclid wrote “Pseudarius” - a kind of catalog of sophisms in geometric proofs. The work “Sophisms” (in two books) was written by Aristotle’s student Theophrastus (D.L.V. 45). In the Middle Ages in Western Europe, entire collections of sophisms were compiled. For example, the collection attributed to the 13th-century English philosopher and logician Richard Sophist contains over three hundred sophisms. Some of them resemble the statements of representatives of the ancient Chinese school of names (ming jia).

Error classification

brain teaser

Since the conclusion can usually be expressed in syllogistic form, any sophism can be reduced to a violation of the rules of syllogism. The most typical sources of logical sophisms are the following violations of the rules of syllogism:

1. Conclusion with a negative minor premise in the first figure: “All people are rational beings, the inhabitants of the planets are not people, therefore, they are not rational beings”;
2. Conclusion with affirmative premises in the second figure: “All who find this woman innocent should be against punishing her; you are against punishing her, which means you find her innocent”;
3. Conclusion with a negative minor premise in the third figure: “The Law of Moses prohibited theft, the Law of Moses has lost its force, therefore, theft is not prohibited”;
4. A particularly common mistake is quaternio terminorum, that is, the use of the middle term in the major and in the minor premise does not have the same meaning: “All metals are simple substances, bronze is a metal: bronze is a simple substance” (here in the minor premise the word “metal” is not used in the exact chemical meaning of the word, denoting an alloy of metals): from here four terms are obtained in the syllogism.

Terminological

Grammatical, terminological and rhetorical sources of sophisms are expressed

Mathematicians introduced words such as “sum”, “product”, “difference” into oral speech. So - the sum of the product of two by two and five, and - double the sum of two and five.

• More complex sophisms stem from the incorrect construction of a whole complex course of evidence, where logical errors are disguised inaccuracies of external expression. These include:
  1. Petitio principii: introducing the conclusion to be proved hidden into the proof as one of the premises. If, for example, we, wanting to prove the immorality of materialism, eloquently insist on its demoralizing influence, without bothering to explain why materialism is an immoral theory, then our reasoning will contain a petitio principii.
  2. Ignoratio elenchi consists in the fact that having begun to prove a certain thesis, gradually in the course of the proof they move on to proving another position similar to the thesis.
  3. A dicto secundum ad dictum simpliciter replaces a statement made with a reservation with a statement not accompanied by such a reservation.
  4. Non sequitur represents the lack of internal logical connection in the course of reasoning: any disordered sequence of thoughts represents a special case of this error.

Psychological

Psychological causes of S. are of three types: intellectual, affective and volitional. In any exchange of thoughts, interaction is assumed between 2 persons, a reader and an author, or a lecturer and a listener, or two disputants. S.'s persuasiveness therefore presupposes two factors: α - the mental properties of one and β - the other of the parties exchanging thoughts. S.'s credibility depends on the dexterity of the one who defends him and the compliance of the opponent, and these properties depend on various characteristics of both individuals.

Intellectual reasons

The intellectual causes of sophism are the predominance in the mind of a person susceptible to S., associations by contiguity over associations by similarity, the lack of development of the ability to control attention, actively think, weak memory, unaccustomed to precise word use, poverty of factual knowledge on a given subject, laziness in thinking (ignava ratio), etc. Reverse qualities, of course, are the most beneficial for the person defending S.: let us denote the first negative qualities by , the second corresponding positive qualities by .

Affective reasons

This includes cowardice in thinking - fear of dangerous practical consequences arising from the acceptance of a certain position; the hope of finding facts that confirm views that are valuable to us, encouraging us to see these facts where they do not exist, love and hatred, strongly associated with known ideas, etc. A sophist who wants to seduce the mind of his opponent must be not only a skilled dialectician, but and a connoisseur of the human heart, who knows how to masterfully manage other people’s passions for his own purposes. Let us denote the affective element in the soul of a skilled dialectician, who wields it like an actor in order to touch his opponent, by , and those passions that awaken in the soul of his victim and darken his clarity of thinking by . Argumentum ad hominem, which introduces personal scores into a dispute, and argumentum ad populum, which influences the emotions of the crowd, represent typical arguments with a predominance of the affective element.

Volitional reasons

When exchanging opinions, we influence not only the mind and feelings of the interlocutor, but also his will. In any argumentation (especially oral) there is a volitional element - an imperative element - an element of suggestion. The categorical tone that does not allow for objection, certain facial expressions, etc. () have an irresistible effect on persons who are easily suggestible, especially on the masses. On the other hand, the passivity () of the listener is especially favorable for the success of the opponent’s argumentation. Thus, every S. assumes a relationship between six mental factors: . S.'s success is determined by the size of this amount, which constitutes an indicator of the strength of the dialectician, and is an indicator of the weakness of his victim. An excellent psychological analysis of sophistry is given by Schopenhauer in his “Eristics” (translated by D. N. Tsertelev). It goes without saying that logical, grammatical and psychological factors are closely interconnected; therefore S., representing, for example, from a logical point of view, quaternio ter.

A method for finding errors in sophistry

• Carefully read the conditions of the task proposed to you. It is better to start searching for an error with the conditions of the proposed sophistry. In some sophisms, an absurd result is obtained due to contradictory or incomplete data in the condition, an incorrect drawing, a false initial assumption, and then all reasoning is carried out correctly. This makes it difficult to find the error. Everyone is accustomed to the fact that tasks suggested in various literature do not contain errors in the condition and, therefore, if an incorrect result is obtained, then they certainly look for the error during the solution.
• Establish areas of knowledge (topics) that are reflected in sophistry and proposed transformations. Sophistry can be divided into several topics, which will require a detailed analysis of each of them.
• Find out whether all conditions for the applicability of theorems, rules, formulas are met, and whether logic is observed. Some sophisms are based on the incorrect use of definitions, laws, and on “forgetting” the conditions of applicability. Very often, in the formulations and rules, the main, main phrases and sentences are remembered, everything else is missed. And then the second sign of equality of triangles turns into the sign “by a side and two angles.”
• Check the conversion results in reverse.
• Often you should break the work into small blocks and check the correctness of each such block.

Examples of sophistry

Half empty and half full

Half-empty is the same as half-full. If the halves are equal, then the wholes are equal. Therefore, empty is the same as full.

Even and odd

5 is (“two and three”). Two is an even number, three is an odd number, it turns out that five is both an even and odd number. Five is not divisible by two, just like , which means both numbers are odd.

You don't know what you know

Do you know what I want to ask you?
- No.
- Do you know that virtue is good?
- I know.
- This is what I wanted to ask you about. And it turns out you don’t know what you know.

Medicines

The medicine taken by the patient is good. The more good you do, the better. This means you need to take as many medications as possible.

Thief

The thief does not want to acquire anything bad. Acquiring something good is a good thing. Therefore, the thief means well.

Horned

Do you have something that you haven't lost? Of course have. You didn't lose your horns, so you still have them.

2=3

The mistake is that you cannot divide by zero (5-5).

Literature

• Akhmanov A. S., Aristotle’s logical doctrine, M., 1960;
• Brutyan G. Paralogism, sophistry and paradox // Questions of Philosophy. 1959. No. 1. P. 56-66.
• Bradis V.M., Minkovsky V.L., Elenev L.K., Errors in mathematical reasoning, 3rd ed., M., 1967.
• Bilyk A.M., Bilyk Ya.M. On the question of the problematic technique of sophism (its connection with the modern understanding of a scientific problem) // Philosophical Sciences. No. 2. 1989. - P.114-117.
• Morozov N.A. On the scientific significance of mathematical sophisms // Proceedings of the Scientific Institute named after. P. F. Lesgaft. Pg., 1919.T.1.S.193-207.
• Pavlyukevich V.V. Logical and methodological status of sophisms // Modern logic: problems of theory, history and application in science. St. Petersburg, 2002. pp. 97-98.
• Read, Stephen (ed.): Sophisms in Medieval Logic and Grammar, Acts of the 8th European Symposium for Medieval Logic and Semantics, Kluwer, 1993
• Cassagnac, Joachim.: Merde à Celui qui le lira, Flammarion, 1974
• Tulchinsky M. E. Entertaining problems-paradoxes and sophisms in physics. M. 1971.
• Demin R. N. Collection of “problems” of Richard Sophist as a context for the “paradoxes” of the ancient Chinese school of names // Bulletin of the Russian Chemical Academy No. 6, St. Petersburg, 2005. pp. 217-221. http://www.rchgi.spb.ru/Pr/vest_6.htm
• Nerkararyan K.V., Sophisms and paradoxes, 1st edition, 2001

see also

Wikimedia Foundation. 2010.

Synonyms:

Sophistry is a word of Greek origin, and it is translated as “fiction” or “trick.” This term is used to denote a statement that is false, but at the same time carries a particle of logic. Therefore, at first glance it seems true. But still, not everyone understands what sophism is and what is the difference between it and paralogism? The difference is that in sophisms conscious deliberate deception is used and there is a violation of logic.

History of the term

Sophistry began to interest people many centuries ago. Aristotle also spoke about this: sophisms are imaginary evidence, appearing as a result of a lack of logical analysis, due to which the judgment becomes subjective. Convincing arguments are used for camouflage purposes and are designed to hide the logical error that is always present in any sophistic statement.

Understanding what sophistry is is not so difficult. It is enough to turn to the example of an ancient violation of logic: “You have what you did not lose. Lost antlers? So you have horns." In this case there is an omission. If you add a new word to the phrase, you can get the following: “You have everything that you did not lose.” With this interpretation, the conclusion becomes correct, but it no longer seems interesting. The first followers of sophistry said that a statement must satisfy the main requirement - the worst argument must turn into the best, and an argument is needed in order to win it, and not to find the truth.

According to the sophists, any opinion can be considered true, but then it happens denial of the law of contradiction, which was later formulated by Aristotle. All this subsequently led to the emergence of many varieties of sophisms in different sciences.

Many sophisms originate from the terminology that is used during an argument. There are many words that have different interpretations. This is precisely what leads to a violation of logic. For example, in mathematics, sophisms are constructed by changing numbers, which are multiplied, and then the original and obtained data are compared.

Sophists can also use as a technique incorrect accent, because there are many words that lose their original meaning when the emphasis changes. Sometimes there are such confusing phrases that can cause ambiguous interpretations. A striking example of this can be the following arithmetic operation: two multiplied by two plus five. It is difficult to say what is most important in this phrase - the sum of two and five multiplied by two, or the sum of the product of two and five.

Complex sophisms

There are also more complex logical sophisms that require detailed consideration. For example, a phrase may contain a premise that requires proof. In other words, an argument can only be considered as such when it is proven. The violation may also be criticism of an opponent's opinion, designed to destroy the judgments erroneously attributed to him. Each of us very often encounters this phenomenon in everyday life, when people attribute to each other certain motives that do not belong to them.

Also, instead of a phrase said with a certain reservation, an expression in which such a reservation is absent can be used. Since attention is not focused on a specially omitted fact, the statement takes on a rather logically correct and justified appearance.

A striking example of a violation of the normal course of reasoning is women's logic. In fact, this is the construction of a chain of thoughts between which there is no logical connection, but upon superficial examination it may be present.

Reasons for sophistry

It is customary to highlight the psychological causes of sophisms, among which the most common are:

• degree of suggestibility;
• emotionality;
• human intelligence.

In other words, if a more savvy person is participating in the conversation, then he only has to lead his opponent into a dead end, and then the latter will easily accept the point of view proposed to him. A person who is unstable to affective reactions easily succumbs to his feelings and takes sophistry for a true statement. Situations like this are very common, and emotional people often find themselves in them.

When speaking to others with sophistry, a person must be convincing. Then he will have there is a greater chance that people will believe him. This is exactly what the bet is on when people use such techniques in an argument. But in order to better understand why people resort to this technique, it is necessary to become more familiar with it, because often sophistry in logic very often goes unnoticed by an unprepared person.

Intellectual and affective reasons

A well-versed person, familiar with the basics of sophistry, always pays attention to how and what he says, and also notices all the arguments the interlocutor makes in his speech. Such people are very attentive and will not miss a single detail. They are accustomed to looking for answers to unknown questions, rather than acting according to templates. In addition to this, they have a large vocabulary, which allows maximum express your thoughts accurately.

The amount of knowledge also plays an important role here. With the correct use of sophisms in mathematics, it is easier for an intellectually developed person to achieve victory in an argument than for an illiterate and undeveloped person.

One of the reasons for losing an argument may be fear of consequences, so a person may very quickly abandon his original point of view, being unable to provide convincing arguments.

Strong-willed

When two people discuss their points of view, they affect each other's mind and feelings, as well as the will. If a person is confident in himself and has such a valuable quality as assertiveness, then he has more chances to defend your opinion, even if it was formulated with a violation of logic. It is most effective to use this technique against large crowds of people who are susceptible to the crowd effect and are not able to see sophistry in a person’s speeches.

When faced with such people, a person will have no difficulty in presenting convincing evidence, regardless of what is the subject of discussion. But during an argument in which a person uses sophistry, he must be very active. The audience he addresses must remain passive, since such people are most easily influenced by others.

From this we can conclude: in order to achieve the desired result with the help of sophistic statements, each party that participates in the conversation must behave in a special way. Moreover, the qualities of each individual individually influence the outcome of the subject under discussion.

Sophisms: examples

Many centuries ago, the first adherents of sophistry formulated a statement where they showed simple violations of logic. They are designed to practice arguing skills, since it is very easy to see the inconsistency in these phrases.

Logical paradoxes

You should be able to distinguish between paradoxes and sophisms, because these are not identical concepts to each other. A paradox is usually understood as a judgment that can prove that a judgment can be both false and true. This phenomenon comes in two types:

• aporia;
• antinomy.

In the first case, a conclusion arises that contradicts experience. This clearly demonstrates the paradox that was formulated by Zeno: the fleet-footed Achilles always lagged behind the tortoise, since with each new step it moved away from him at a certain distance, not allowing him to catch up with himself, since the process of dividing a segment of the path is endless.

Antinomy should be seen as a paradox, which implies the presence of two mutually exclusive judgments, which are simultaneously considered true. An example of this is the phrase “I’m lying.” It can be considered both true and false. But if a person speaks the truth while pronouncing it, then he cannot be considered a liar, although the phrase indicates the opposite. There are other interesting logical paradoxes and sophisms that will be discussed below.

Violation of logic in mathematics

Most often in mathematics, sophisms are used to prove the equality of unequal numbers or arithmetic expressions. A striking example is when five and one are compared. If you subtract three from five, the result is two. Subtracting one from three, we get two. If you square both numbers, the result will be the same in each case. Therefore, we can conclude that five is equal to one.

The appearance of sophistic problems in mathematics mainly occurs by converting the original numbers. For example, when they are squared. After performing these simple steps, you can obtain that the results of these transformations will be the same, which allows us to talk about the equality of the original data.

Reason, obstacle

Frédéric Bastiat is the author of some of the most widespread sophisms. Among them, the violation of the logic “reason, obstacle” is quite well known. Primitive man was very limited in his capabilities. Therefore, in order to obtain any thing and result, he had to solve many problems.

If we consider a simple example of overcoming a distance, we can see from it that it is difficult for a person to independently overcome all the barriers that may arise on the path of any single traveler. We live in one where the problem of overcoming obstacles is dealt with by people who specialize in this type of activity. And these people managed to make such obstacles one of their main sources of income.

The appearance of any new obstacle puzzles many people who are trying to overcome them. Therefore, the presence of obstacles is unthinkable for modern society, because they provide the opportunity to enrich each person individually, and, therefore, the entire society as a whole.

Conclusion

Today only intellectually literate people know about the existence of sophisms. This is one of the effective techniques that helps a person achieve victory in an argument, although he has no reason for this. A person builds a conversation with people in such a way that the phrases used in his statements help convince other people that he is right. One could even say that he simply confuses a person and does not allow him to provide effective counterarguments that would help defend his point of view.

Sophisms are sometimes so convincing that no other arguments of opponents can withstand them. However, victory in such a dispute largely depends not only on the person who uses sophisms, but also on the behavior of those people for whom they are intended.

Logical errors that impair the correctness of thinking can be divided into two types - paralogisms and sophisms. Examples of sophistry, which are not always easy to understand - below.

What are paralogisms and sophisms?

Both terms mean error in , however the first term implies unintentional error . Sophism and - a deliberate violation of the requirements of logic, intellectual fraud, an attempt to pass off the truth as a lie.

The term "sophism" translated from Greek means “cunning.” Initially, in Ancient Greece, sophists were craftsmen who had achieved mastery in their craft. Later, the nickname migrated to professional philosopher-thinkers, only later did it acquire a common meaning for those who cunningly deceive listeners. As you can see, philosophers in Ancient Greece were perceived very skeptically.

Famous sophists and their sophisms

Protagoras

The first person to call himself a sophist and publicly acted as a teacher of virtue, was, according to Plato, Protagoras. Only a few fragments of his works have survived. The most significant of the passages was his documented dispute with Euathlus. This dispute is considered one of the first sophisms, which I personally really like:

Euathlus was a student of Protagoras. According to the agreement concluded between them, Evatl had to pay for training only if he won his first trial. But, having completed his studies, he did not participate in the processes, it lasted quite a long time, the teacher’s patience ran out, and he sued his student. Protagoras justified his demand as follows:
“Whatever the court’s decision, Evatl will have to pay me.” He will either win this lawsuit or lose. If he wins, he will pay according to our agreement. If he loses, then the court decision will be in my favor, and I will have to pay according to this decision. Euathlus appears to have been a capable student, since he replied to Protagoras:
– Indeed, I will either win the trial or lose it. If I win, the court's decision will release me from the obligation to pay. If the court's decision is not in my favor, it means I lost my first case and will not pay due to our agreement.

Gorgias was one of the first orators of a new type - not only a practitioner, but also a theorist of eloquence, who taught young men from wealthy families to speak and think logically for a fee. Such teachers were called “experts in wisdom,” that is, sophists.

Gorgias claimed that he did not teach virtue and wisdom, but only oratory. Going off topic, he has some great advice for arguing:

Refute your opponent’s serious arguments with a joke, and jokes with seriousness.

Also among the sophists are Hippias, Critias, Antiphon and many other Hellenes.

Examples and types of sophisms

All sophistry can be divided into:

• brain teaser
• terminological
• psychological
• mathematical (algebraic, geometric).

Let's consider all types. The most extensive and fascinating type are logical sophistry. One of the most common logical fallacies used by sophists quaternio terminorum, that is, the use of the middle term in the major and in the minor premise does not have the same meaning: “All metals are simple substances, bronze is a metal: bronze is a simple substance” (here in the minor premise the word “metal” is not used in the exact chemical meaning of the word, denoting an alloy of metals).

Here's another a couple of examples:
Half-empty is the same as half-full. If the halves are equal, then the wholes are equal. Therefore, empty is the same as full
“Do you know what I want to ask you?” - "No". - “Do you know that virtue is good?” - "I know". - “This is what I wanted to ask you about. But it turns out you don’t know what you know.”
The medicine taken by the patient is good. The more good you do, the better. This means you need to take as many medications as possible.
The thief does not want to acquire anything bad. Acquiring something good is a good thing. Therefore, the thief means well

My favorite sophism, which broke my head 5 years ago:

The fleet-footed Achilles will never overtake the slow tortoise. By the time Achilles reaches the turtle, it will move forward a little. He will quickly cover this distance, but the turtle will go a little further. And so on ad infinitum. Every time Achilles reaches the place where the tortoise was before, it will be at least a little ahead

Mathematical sophisms
5 is 2 + 3 (“two and three”). Two is an even number, three is an odd number, it turns out that five is both an even and odd number. Five is not divisible by two, neither is 2 + 3, which means both numbers are odd.

I did not give examples of other mathematical sophisms, you can familiarize yourself with them, but each of them will require calculations.

Terminological

• Petitio principii: introduction of the conclusion to be proved, hidden in the proof as one of the premises. If, for example, we, wanting to prove the immorality of materialism, eloquently insist on its demoralizing influence, without bothering to explain why materialism is an immoral theory, then our reasoning will contain a petitio principii.
• Ignoratio elenchi consists in the fact that having begun to prove a certain thesis, gradually in the course of the proof they move on to proving another position similar to the thesis.
• A dicto secundum ad dictum simpliciter replaces a statement made with a reservation with a statement not accompanied by such a reservation.
• Non sequitur represents the lack of internal logical connection in the course of reasoning: any disordered sequence of thoughts represents a special case of this error.

Psychological sophistry

The psychological causes of sophistry are of three types: intellectual, affective and volitional. In any exchange of thoughts, interaction is assumed between 2 persons, a reader and an author, or a lecturer and a listener, or two disputants. The persuasiveness of sophism therefore presupposes two factors: α - the mental properties of one and β - the other of the parties exchanging thoughts. The credibility of sophism depends on the skill of the one who defends it, and the pliability of the opponent, and these properties depend on the various characteristics of both individuals.

How to see through sophistry?

• Carefully read the conditions of the task proposed to you. It is better to start searching for an error with the conditions of the proposed sophistry. In some sophisms, an absurd result is obtained due to contradictory or incomplete data in the condition, an incorrect drawing, a false initial assumption, and then all reasoning is carried out correctly. This makes it difficult to find the error. Everyone is accustomed to the fact that tasks offered in various literature do not contain errors in the condition and, therefore, if an incorrect result is obtained, then they will certainly look for the error as they solve it.
• Establish areas of knowledge (topics) that are reflected in sophistry and proposed transformations. Sophistry can be divided into several topics, which will require a detailed analysis of each of them.
• Find out whether all conditions for the applicability of theorems, rules, formulas are met, and whether logic is observed. Some sophisms are based on the incorrect use of definitions, laws, and on “forgetting” the conditions of applicability. Very often, in the formulations and rules, the main, main phrases and sentences are remembered, everything else is missed. And then the second sign of equality of triangles turns into the sign “by a side and two angles.”
• Check the conversion results in reverse.
• Often you should break the work into small blocks and check the correctness of each such block.