Paradoxes of formal logic and logical errors. Sophisms and paradoxes Paradoxes of imprecise concepts
In examples No. 4, 5,6, the same technique is used: different meanings, situations, themes are mixed in identical words, one of which is not equal to the other, that is, the law of identity is violated.
2. Logical paradoxes
Paradox (from the Greek unexpected, strange) is something unusual and surprising, something that diverges from usual expectations, common sense and life experience.
A logical paradox is such an unusual and surprising situation when two contradictory propositions are not only simultaneously true (which is impossible due to the logical laws of contradiction and the excluded middle), but also follow from each other and condition each other.
A paradox is an insoluble situation, a kind of mental impasse, a “stumbling block” in logic: throughout its history, many different ways to overcome and eliminate paradoxes have been proposed, but none of them is still exhaustive, final and generally accepted.
Some paradoxes (paradoxes of the “liar”, “village barber”, etc.) are also called antinomies (from the Greek: contradiction in law), that is, reasoning in which it is proven that two statements that deny each other follow from each other . It is believed that antinomies represent the most extreme form of paradoxes. However, quite often the terms “logical paradox” and “antinomy” are considered synonymous.
A separate group of paradoxes are aporia (from the Greek - difficulty, bewilderment) - reasoning that shows contradictions between what we perceive with our senses (see, hear, touch, etc.) and what can be mentally analyzed (contradictions between the visible and the imaginable).
The most famous aporia was put forward by the ancient Greek philosopher Zeno of Elea, who argued that the movement we observe everywhere cannot be made the subject of mental analysis. One of his famous aporias is called "Achilles and the Tortoise." She says that we may well see how the fleet-footed Achilles catches up and overtakes the slowly crawling turtle; However, mental analysis leads us to the unusual conclusion that Achilles can never catch up with the tortoise, although he moves 10 times faster than it. When he covers the distance to the turtle, during the same time it will cover 10 times less, namely 1/10 of the path that Achilles traveled, and this 1/10 will be ahead of him. When Achilles travels this 1/10th of the way, the turtle will cover 10 times less distance in the same time, that is, 1/100th of the way, and will be ahead of Achilles by this 1/100th. When he passes 1/100th of the path separating him and the turtle, then in the same time it will cover 1/1000th of the path, still remaining ahead of Achilles, and so on ad infinitum. We become convinced that the eyes tell us one thing, but the thought tells us something completely different (the visible is denied by the imaginable).
Logic has created many ways to resolve and overcome paradoxes. However, none of them is without objections and is not generally accepted.
2.1 Examples of logical paradoxes
The most famous logical paradox is the “liar” paradox. He is often called the “king of logical paradoxes.” It was discovered back in Ancient Greece. According to legend, the philosopher Diodorus Kronos vowed not to eat until this paradox was resolved and died of hunger, having achieved nothing. There are several different formulations of this paradox. It is most briefly and simply formulated in a situation when a person utters a simple phrase: “I am a liar.” Analysis of this statement leads to a stunning result. As you know, any statement can be true or false. Let us assume that the phrase “I am a liar” is true, that is, the person who uttered it told the truth, but in this case he is really a liar, therefore, by uttering this phrase, he lied. Let us assume that the phrase “I am a liar” is false, that is, the person who uttered it lied, but in this case he is not a liar, but a truth-teller, therefore, by uttering this phrase, he told the truth. It turns out something amazing and even impossible: if a person told the truth, then he lied; and if he lied, then he told the truth (two contradictory judgments are not only simultaneously true, but also follow from each other).
Another famous logical paradox discovered in the 20th century. English logician and philosopher Bertrand Russell, is the “village barber” paradox. Let's imagine that in a certain village there is only one barber who shaves those residents who do not shave themselves. Analysis of this simple situation leads to an extraordinary conclusion. Let's ask ourselves: can a village barber shave himself? Let us assume that the village barber shaves himself, but then he is one of those village residents who shave themselves and whom the barber does not shave, therefore, in this case he does not shave himself. Let us assume that the village barber does not shave himself, but then he is one of those village residents who do not shave themselves and whom the barber shaves, therefore, in this case, he shaves himself. It turns out incredible: if a village barber shaves himself, then he does not shave himself; and if he does not shave himself, then he shaves himself (two contradictory judgments are simultaneously true and mutually condition each other).
The Protagoras and Euathlus paradox appeared in Ancient Greece. It is based on a seemingly simple story, which is that the sophist Protagoras had a student Euathlus, who took lessons in logic and rhetoric from him. The teacher and student agreed in such a way that Euathlus would pay Protagoras a tuition fee only if he won his first trial. However, upon completion of the training, Evatl did not participate in any process and, of course, did not pay the teacher any money. Protagoras threatened him that he would sue him and then Euathlus would have to pay in any case. “You will either be sentenced to pay a fee, or you will not be sentenced,” Protagoras told him, “if you are sentenced to pay, you will have to pay according to the verdict of the court; if you are not sentenced to pay, then you, as the winner of your first trial, will have to pay according to our agreement.” To this Evatl answered him: “Everything is correct: I will either be sentenced to pay a fee, or I will not be sentenced; if I am sentenced to pay, then I, as the loser of my first lawsuit, will not pay according to our agreement; if I am not sentenced to pay, then I will not pay the court’s verdict.” Thus, the question of whether Euathlus should pay Protagoras or not is unanswerable. The contract between teacher and student, despite its completely innocent appearance, is internally, or logically, contradictory, since it requires the implementation of an impossible action: Evatl must both pay for training and not pay at the same time. Because of this, the agreement itself between Protagoras and Euathlus, as well as the question of their litigation, represents something other than a logical paradox.
Task 2
Determine the structure, type of judgment, make a symbolic relationship between terms, indicating their distribution:
"Individuals have high intellectual abilities"
- Judgment structure:
1) Subject – “high intellectual abilities”
2) Predicate – “in individual people”
3) The ligament is expressed
4) Quantifier word “Is” (expressed)
Frequently affirmative some S is P
QS is P
2. The judgment is general in quantity and affirmative in quality
3. In an explicit logical form: “Individuals have high intellectual abilities.”
4. Formula: All S are P. Judgment – A.
5. R
7. The subject is distributed, the predicate is not distributed.
10 -
“There is no such person who would not like gifts.”
- Judgment structure:
1) Subject – “Gifts”
2) Predicate – “Man”
3) The link is expressed – which would not be liked
4) Quantifier word “Everything” (not expressed)
2. The judgment is general in quantity and generally negative in quality
3. In an explicit logical form: “All people love gifts.”
4. Formula: No S is P. Judgment – E. generally negative
5. R
6. The terms are in a relationship - subordination.
7. The subject is distributed, the predicate is not distributed
11 -
Task 3
Determine the type of inference, draw a conclusion, construct an inference diagram, establish the logical consistency of the reasoning:
“A person who has committed a minor crime for the first time may be released from criminal liability if he has repented or reconciled with the victim. Ivanov is determined to either repent or reconcile with the victim, which means...”
Ivanov is determined to either repent or reconcile with the victim, which means that if he has committed a crime of minor gravity for the first time, he can be released from criminal liability.
1. Type of judgments in premises:
1st premise: “A person who has committed a crime of minor gravity for the first time may be released from criminal liability if he has repented or reconciled with the victim. Ivanov is determined to either repent or reconcile with the victim.” – an implicative-conjunctive proposition, consisting of two implications united by a conjunction.
p – a person may be exempt from criminal liability
g – it repented of what it did or it reconciled itself with the victim
q – it did not repent and did not try
2nd premise: “The person will either repent and reconcile with the victim, or not.” – a disjunctive judgment consisting of 2 alternatives.
2.Scheme of inference:
(p→g) Λ (¬p→q)
p V ¬p________________
g V q
3. Simple design dilemma
4. Conclusion: “A person who has committed a minor crime will either be released or not.”
5.References
1) Getmanova A.D. Logic textbook. M.: Vlados, 1994.
2) Gusev D.A. Textbook on logic for universities. Moscow: Unity-Dana, 2004
3) Ivin A.A. The art of thinking correctly. M.: Education, 1990.
4) Koval S. From entertainment to knowledge / Transl. O. Unguryan. Warsaw: Scientific and Technical Publishing House, 1972.
This episode with the clever missionary is one of the paraphrases of the paradox of the ancient Greek philosophers Protagoras and Euathlus.
But every researcher who tried to strictly define all the concepts in his theory encountered a similar paradox of formal logic. No one has ever succeeded in this, since everything ultimately came down to a tautology like: “Motion is the movement of bodies in space, and movement is the movement of bodies in space.”
Another version of this paradox. Someone has committed a crime punishable by death. At the trial he has the last word. He must say one statement. If it turns out to be true, the criminal will be drowned. If it is false, the criminal will be hanged. What statement must he make to completely confuse the judge? Think for yourself.
Puzzled by this paradox, Protagoras devoted a special essay to this dispute with Euathlus, “The Litigation of Payment.” Unfortunately, it, like most of what Protagoras wrote, has not reached us. The philosopher Protagoras immediately felt that behind this paradox there was hidden something essential that deserved special study.
Formal logic is based on the concept of discreteness of the world, the beginning of which should be sought in the teachings of Democritus about atoms and emptiness, and perhaps in the earlier philosophical teachings of ancient Greece. We do not think about the paradoxical nature of formal logic when we say that speed is the number of meters or kilometers traveled by a body, which it travels per second or per minute (physics teaches us that distance divided by time is speed). We measure distance in discrete units (meters, kilometers, versts, arshins, etc.), time - also in discrete units (minutes, seconds, hours, etc.). We have a standard distance - a meter, or another segment with which we compare the path. We measure time with the standard of time (essentially, also a segment). But distance and time are continuous. And if they are discontinuous (discrete), then what is at the junctions of their discrete parts? Other world? A parallel world? Hypotheses about parallel worlds are incorrect, because... are based on reasoning according to the laws of formal logic, which assumes that the world is discrete. But if it were discrete, then movement would be impossible in it. This means that everything in such a world would be dead.
The liar paradox.“What I am saying now is false,” or “This statement is a lie.” This paradox was formulated by the philosopher of the Megarian school Eubulides. He said: “The Cretan Epimenides said that all Cretans are liars.” . If Epimenides is right that all Cretans are liars, then he is also a liar. If Epimenides is a liar, then he lies that all Cretans are liars. So are the Cretans liars or not? It is clear that this chain of reasoning is flawed, but in what way? |
In science, this means that it is impossible to understand and explain a system based on the elements of only this system, the properties of these elements and the processes occurring within this system. To do this, we should consider the system as part of something larger - the external environment, a system of a larger order, of which the system we are studying is a part. In other words: in order to understand the particular, one must rise to the more universal.
This paradox suggests that in order to characterize the elements of a system by the elements of this system, it is required that the number of elements in this system be more than two. Thesis and antithesis are not enough to characterize an element. If a statement is not true, then it does not follow that it is false. Conversely, if a statement is not false, this does not mean that it is true. It is not easy for our minds to agree with this statement, because we use formal alternative logic. And the case with the statements of Plato and Socrates suggests that this is possible. Judge for yourself: they tell us: “The ball in the box is not black.” If we think that it is white, then we may be mistaken, since the ball may turn out to be blue, red, or yellow.
In the last two examples we see that paradoxes are born from the defectiveness of formal (binary) logic. Let's think about how the phrase should be constructed correctly: “History teaches a person, but he learns nothing from history.” In such a formulation, with such clarification, there is no longer any paradox. The last two paradoxes are not antinomies; they can be eliminated within the framework of the laws of formal logic by constructing the phrase correctly.
A paradox from the category of antinomies is generated by an error in reasoning, in the construction of a phrase. The following paradox also applies to antinomies.
In this case, we must remember that a person must learn to think, and not just remember. Learning as mechanical memorization has no great value. Approximately 85-90% of what a person remembers while studying at school and university, he forgets during the first 3-5 years. But if he was taught to think, then he has mastered this skill almost all his life. But what will happen to people if, during training, they are given to remember only those 10% of information that they remember for a long time? Unfortunately, no one has ever conducted such an experiment. Although...
There was one man in our village who completed only the 4th grade of school in the early 30s. But in the 60s, he worked as the chief accountant of a collective farm and did a better job than the accountant with a secondary technical education who later replaced him.
But if a ship is defined as a system, the essence of which is determined by its properties as a whole: weight, displacement, speed, efficiency and other characteristics, then even when all parts are replaced with similar parts, the ship remains the same. The properties of the whole differ from the properties of its parts and cannot be reduced to the properties of these parts. The whole is greater than the sum of its parts! Therefore, even at 50 years old, a person remains himself, although 95% of the atoms of his body have already been replaced many times during this time by others, and there are more atoms in his body than there were at the age of 10 years.
So the ancient philosopher was not entirely right when he said that you cannot enter the same river twice, since the water flows in it and all the time its molecules in the stream are replaced. In this case, it is implicitly postulated that the river is the sum of precisely these water molecules and no other water molecules. But this is not so, because we perceive a river not as a set of water molecules, but as a flow of a certain depth and width, with a certain flow speed, in a word, a river is a dynamic system, and not the sum of its parts.
Often the answer to the question about baldness lies in a different plane than the one in which it was formulated. To answer such a question, one must move from one plane of reasoning and perception to a completely different one. For example, the publications of one scientist are cited 100 times a year, and another 1 time a year. Question: which of them is a brilliant scientist? There can be four different answers to this question: 1 - no one, 2 - both, 3 - the first, 4 - the second. And all four answers in this case are equally probable, since the number of citations, in principle, cannot be a sign of genius. The correct answer to this question can only be obtained in 100 years or a little less.
The paradox of democracy(voting): “It is impossible to combine all the requirements for an electoral system in one system.” If you achieve equal representation in parliament from states or regions, then it is impossible to achieve equal representation in parliament from voters. But there are still religious denominations, etc. |
But in politics, even formal logic is not held in high esteem, and often it is violated deliberately in order to fool the electorate. In the USA, “brain powdering” technologies are simply excellently developed. Their elections are not democratic, but majoritarian, but Americans firmly believe that they have a democratic state and are ready to tear apart anyone who thinks differently about their social system. They manage to pass off the aristocratic form of government as democratic. Are democratic elections possible in principle?
But in practice, the Monte Carlo conclusion may be false for another reason. After all, the condition about the independence of elementary events when playing roulette may not be satisfied. And if elementary events are not independent, but “linked” to each other, both in ways known to us and still unknown... then in this case it is better to bet on black rather than red.
It may turn out that there are other carriers of energy and information in the Universe, and not just oscillations of the electromagnetic field and flows of elementary particles. If at its core the Universe is not discrete (vacuum), but continuous, then this paradox is inappropriate. Then every part of the Universe is influenced by the rest of it, then every atom of the universe is connected and interacts with all other atoms, no matter how far they are from it. But in the infinite Universe there must be an infinite number of atoms... Stop! The brains are starting to boil again.
This paradox stems from our misunderstanding of what time is. If time is the flow of the world with many channels (as is often the case with a river), and the speed of flow in the channels is different, then a sliver that falls into a fast channel will then again fall into a slow channel, when the fast channel merges with the slow one in which another sliver is floating , with which they once sailed next. But now one sliver will be ahead of its “friend” and will no longer meet with her. To meet them, the lagging “friend” must get into another fast channel, and the one ahead must swim in a slow channel at the same time. It turns out that the twin brother, who flew away on a sublight ship, in principle cannot return to the past and meet his brother. The slow flow of time (sublight ship) delayed him in the time flow. During this time, his brother not only grew older, but he went into the future, and with him everything that surrounded him went into the future. So, in principle, a brother who has fallen behind in time will no longer be able to get into the future.
And if the river of time does not have channels at different speeds, then there can be no paradox. Maybe the theory of relativity is incorrect, and time is not relative, but absolute?
And thank God! Therefore, the grandfather is not in danger of his grandson coming from the future and killing him. And today there are many such grandchildren who have smoked marijuana.
China's Central Bureau of Film, Radio and Television recently banned time travel films because they "show disrespect for history." Film critic Raymond Zhou Liming explained the reasons for the ban by saying that now time travel is a popular topic in TV series and movies, but the meaning of such works, as well as their presentation, is very questionable. “Most of them are completely fictitious, do not follow logic and do not correspond to historical realities. Producers and writers are taking the story too lightly, distorting it and pushing this image on the audience, and this should not be encouraged,” he added. Such works are not based on science, but use it as an excuse to comment on current events.
I believe that the Chinese hit the nail on the head when they realized the harm of such films. Fooling people with nonsense, passing it off as science fiction, is dangerous. The fact is that such films undermine people’s sense of reality, the boundaries of reality. And this is the right path to schizophrenia.
Salvador Dali showed the absurdity of our ideas about time through painting. The current clock is not time yet. What is time? If there were no time, there would be no movement. Or maybe it would be more correct to say this: if there were no movement, then there would be no time? Or maybe time and movement are one and the same thing? No, rather, with the help of the categories time and space, we are trying to characterize and measure movement. In this case, time is something like an arshin malalan. To travel in time, you must stop being living (living) people and you must learn to move within the movement itself.
There is no time, there is movement, and movement is time. All paradoxes associated with time arise from the fact that the properties of space are attributed to time. But space is a scalar and time is a vector.
|
This is how we change over time. Traveling into the past is only possible by viewing old photographs and old movies. Also with the help of our memory. Maybe memory is precisely what makes us fifth-dimensional entities? Probably, memory is the only possible time machine that can rush us into the past. You just need to learn to remember everything. Photo from the site: http://loveopium.ru/page/94 |
Achilles and the tortoise: Swift-footed Achilles will never catch up with a leisurely tortoise if at the beginning of the movement the tortoise is in front of Achilles, since by the time he moves to the point where the tortoise was at the beginning of the competition, it will have time to move at least a little forward. By the time Achilles reaches the point where the turtle was, it will have time to move a certain distance forward. Now Achilles will have to run again some distance to the place where the turtle was, and during this time it will again move forward, and so on - the number of points of approach of Achilles to the turtle tends to infinity. It turns out that Achilles will never catch up with the turtle, but we understand that in reality he will easily catch up and overtake it. Why does this happen, what caused this paradox? But the fact is that distance is not a collection of points. After all, a point has no size and on any geometric segment the number of points can be infinite. To visit an infinite number of points, Achilles will need an infinite amount of time. Therefore, it turns out that discrete mathematics and formal logic are not applicable to reality, and if they are applicable, then with great reservations. |
This paradox is due to the fact that formal logic operates in a discrete world with discrete bodies consisting of points, and phenomena that also represent collections of points in four-dimensional space-time. This paradox is not so harmless. For 2.5 thousand years now, he has been showing scientists the absurdity of formal logic and the limitations of mathematics. But scientists stubbornly believe in formal logic and mathematics and do not want to change anything. Although... Timid attempts to change logic were made both in philosophy and mathematics. |
Achilles runs after the turtle. In reality, he easily catches up with her, but in the logical design of this process, he cannot catch up with her. The turtle has a head start of 100 meters. Both runners start moving at the same time. While Achilles reaches point A, the tortoise will move to point B, Achilles will again reduce the distance between himself and the tortoise and move to point C. But at this time, the tortoise will move forward and will be in front of Achilles at point D. Achilles will again reduce the distance between himself and the tortoise and will end up at point E. But during this time the turtle will crawl forward again and end up at point J. And so on ad infinitum. The distance between Achilles and the turtle will decrease, but he will not be able to catch up with it. This conclusion follows from formal logic. Picture from the site: http://nebesa87.livejournal.com/ |
In mathematics, an attempt to break out of the captivity of formal logic was the creation of differential and integral calculus. Both presuppose a continuous change of some quantity depending on the continuous change of another quantity. Column diagrams depict the dependence of discrete phenomena and processes, and graphs (lines) depict continuous processes and phenomena. However, the transition from a diagram to a graph is a kind of sacrament - something like sacrilege. After all, all experimental data (results of specific measurements) are discrete. And the researcher takes and draws a graph instead of a diagram. What is this? If we approach strictly, then the situation here is like this: a graph is a transformation of a diagram into a graph that approximates this diagram. By constructing a graph in the form of a continuous line, we make a transition from the world of discrete phenomena and objects to the continuous world. This is an attempt to break out of the boundaries of formal logic and thereby avoid its paradoxes.
In philosophy, already in the 19th century, scientists realized the inferiority of formal logic, and some began to try to solve this problem. They started talking together about dialectics, about the triad (Hegel), about a different theory of knowledge. Philosophers understood earlier than scientists that formal logic leads knowledge to a dead end. The result of the introduction of dialectics into science was, for example, the doctrine of evolution (development). After all, if you strictly adhere to the positions of formal logic, then development is impossible in principle. Preformationism is a pathetic attempt by formal logic to explain the evolution occurring everywhere. Preformationists argue that everything is predetermined in some program in embryo, and the observed development is only the implementation (deployment) of this program. Formal genetics was born from preformationism, but it could only explain the development of the organism in ontogenesis. But formal genetics could not explain the change in species and macroevolution. It was necessary to add a new building to that original formal genetics, which turned out to be several orders of magnitude larger than the building of classical genetics, even to the point of denying discrete genes. But even in this modified form, genetics could only explain microevolution, and macroevolution was too tough for it. And the attempts that geneticists make to explain macroevolution give paradoxes similar to those discussed above.
But even today the positions of formal logic are very strong in the minds of scientists: biologists, biophysicists, geneticists, biochemists. Dialectics has difficulty making its way into this science.
A pile of sand consists of 1,000,000 grains of sand. If you take one grain of sand out of it, it will still be a heap of sand. If you continue this action many times, it turns out that 2 grains of sand, and even one grain of sand is also a heap of sand. One can object to this that one grain of sand is just one grain of sand, but in this case the principle of interconnectedness of statements is violated, and we again come to a paradox. The only way to save this situation is to introduce an exception for one grain of sand that is not a heap. But two grains of sand can hardly be called a heap either. So how many grains of sand does a heap start with? |
In reality, this does not happen, since in the world there are no identical things, phenomena, bundles of hay, or equivalent types of execution. Even if the bundles of hay are the same in taste and size, then one of them may be a little further than the other, or one of the donkey’s eyes may be more keen than the other, etc. Unfortunately, formal logic does not take this into account, so it should be used carefully and not in all judgments, and it should not always be trusted.
People in life and in their activities (including economic activity) do not behave at all like “ideal” balls in theory. In addition to profit, people strive for sustainability and comfort in the broad sense of the word. An unknown risk can be either less than or greater than the known one. You can, of course, win more and become richer. But you can lose more and become bankrupt. But non-poor people give money on loan; they have something to value, and they don’t want to end up homeless.
Let's try to reason. The logical error in this case is that the debt is counted along with what we have, what we did not lose - a bottle of beer. Indeed, I borrowed 100+50=150 rubles. But I reduced my debt by returning 30 rubles to my friend, after which I owed her 70 rubles and I owed my friend 50 rubles (70+50=120). In total, my debt now amounted to 120 rubles. But if I give a bottle of beer worth 20 rubles to a friend, then I will only owe him 30 rubles. Together with the debt to my friend (70 rubles), my debt will be 100 rubles. But this is exactly the amount I lost. |
The theory of black holes has become very fashionable in cosmophysics today. According to this theory, huge stars in which thermonuclear fuel “burns” are compressed - collapse. At the same time, their density increases monstrously - so that electrons fall onto the nuclei and intra-atomic voids collapse. Such a collapsed super-dense extinct star has strong gravity and absorbs matter from outer space (like a vacuum cleaner). At the same time, such a neutron star becomes denser and heavier. Finally, her gravity becomes so powerful that not even light quanta can escape her. This is how a black hole is formed.
This paradox casts doubt on the physical theory of black holes. It may turn out that they are not so black after all. They most likely have structure and therefore energy and information. Moreover, black holes cannot absorb matter and energy indefinitely. In the end, having eaten too much, they “burst” and throw out clumps of super-dense matter, which become the cores of stars and planets. It is no coincidence that black holes are found in the centers of galaxies, and in these centers there is the highest concentration of stars escaping from these centers.
Any contradiction in the theoretical dogmas of science should encourage scientists to change (improve) the theory. Such a large number of paradoxes in logic, mathematics, and physics shows that not everything is going well in these sciences with theoretical constructs.
But everything goes fine until a production crisis occurs. And with a production crisis in the United States, the balance of payments deficit disappears. A lot of capital has accumulated in banks, but there is nowhere to invest it. Capital lives only through circulation through production. As they say: “Airplanes only live in flight.” And capital lives only in the processes of production and consumption. And without production and consumption, capital disappears - it turns into nothing (yesterday it was, but today it is not), this causes the balance of payments deficit to grow in the USA - the airbags of other countries in US banks have disappeared without a trace. The United States, having made the dollar an international currency, has put itself on the dollar needle. The global economic crisis is sharply aggravating the situation and the health of the dollar “addict”. In an effort to acquire the next “dose,” the addict goes to great lengths and becomes aggressive.
China is developing well under socialism. Not at all because there is little private property there, but more state property. It’s just that the Chinese began to determine the price of goods by the demand for them. And this is only possible in a market economy.
But inflation will inevitably lead to the loss of capital - savings that the population keeps in banks. They say that under the euro, the Greeks lived beyond their means; the Greek budget had a large deficit. But after receiving this money in the form of salaries and benefits, the Greeks bought goods produced in Germany and France and thereby stimulated production in these countries. Production began to collapse and the number of unemployed increased. The crisis also worsened in countries that considered themselves donors to the European economy. But the economy is not only about production and its lending. It's also about consumption. Ignoring the laws of the system is the cause of this paradox.
Conclusion
Concluding this article, I would like to draw your attention to the fact that formal logic and mathematics are not perfect sciences and, boasting of their proofs and the rigor of their theorems, are based on axioms taken on faith as completely obvious things. But are these axioms of mathematics so obvious?
What is a point that has no length, width or thickness? And how does it happen that the totality of these “incorporeal” points, if they are lined up in a row, is a line, and if in one layer, then a plane? We take an infinite number of points that have no volume, line them up in a row, and get a line of infinite length. In my opinion, this is some kind of nonsense.
I asked my math teacher this question back in school. She was angry with me and said: “How stupid you are! It’s obvious.” Then I asked her: “How many points can be squeezed into a line between two adjacent points, and is it possible to do this?” After all, if an infinite number of points are brought close to each other without distances between them, then the result is not a line, but a point. To get a line or plane, you need to place the points in a row at some distance from each other. Such a line cannot even be called dotted, because dots have no area or volume. It’s as if they exist, but it’s as if they don’t exist at all, they are immaterial.
At school, I often wondered: do we do arithmetic operations, such as addition, correctly? In arithmetic, when adding, 1+1 = 2. But this may not always be the case. If you add another apple to one apple, you get 2 apples. But if we look at this differently and count not apples, but abstract sets, then by adding 2 sets, we get a third one, consisting of two sets. That is, in this case 1 + 1 = 3, or maybe 1 + 1 = 1 (two sets merged into one).
What is 1+1+1? In ordinary arithmetic it turns out to be 3. But what if we take into account all combinations of 3 elements, first by 2, and then by 3? Correct, in this case 1+1+1=6 (three combinations of 1 element, two combinations of 2 elements and 1 combination of 3 elements). Combinatorial arithmetic at first glance seems stupid, but this is only true out of habit. In chemistry, you have to count how many water molecules you get if you take 200 hydrogen atoms and 100 oxygen atoms. You will get 100 water molecules. What if we take 300 hydrogen atoms and 100 oxygen atoms? You will still get 100 water molecules and 100 hydrogen atoms remaining. So, we see that a different arithmetic finds application in chemistry. Similar problems occur in ecology. For example, Liebig's rule is known that plants are influenced by a chemical element in the soil that is at its minimum. Even if all other elements are in large quantities, the plant will be able to absorb as much of them as the minimum element allows.
Mathematicians boast of their supposed independence from the real world; their world is an abstract world. But if this is so, then why do we use the decimal counting system? And some tribes had a 20 system. Very simply, those southern tribes that did not wear shoes used the decimal system - according to the number of fingers and toes, but those who lived in the north and wore shoes used only their fingers when counting. If we had three fingers on our hands, we would use the six-digit system. But if we descended from dinosaurs, we would have three fingers on each hand. So much for the independence of mathematics from the outside world.
Sometimes it seems to me that if mathematics were closer to nature (reality, experience), if it were less abstract, if it did not consider itself the queen of the sciences, but if it were their servant, it would develop much faster. And it turns out that the non-mathematician Pearson came up with the mathematical chi-square test, which is successfully used when comparing series of numbers (experimental data) in genetics, geology, and economics. If you take a closer look at mathematics, it turns out that everything fundamentally new was introduced into it by physicists, chemists, biologists, geologists, and mathematicians, at best, developed it - they proved it from the standpoint of formal logic.
Non-mathematical researchers constantly pulled mathematics out of the orthodoxy into which “pure” mathematicians tried to plunge it. For example, the theory of similarity and difference was created not by mathematicians, but by biologists, the theory of information by telegraph operators, and the theory of thermodynamics by thermal physicists. Mathematicians have always tried to prove theorems using formal logic. But some theorems are probably impossible to prove in principle using formal logic.
Sources of information used
Mathematical paradox. Access address: http://gadaika.ru/logic/matematicheskii-paradoks
Paradox. Access address: http://ru.wikipedia.org/wiki/%CF%E0%F0%E0%E4%EE%EA%F1
The paradox is logical. Access address: http://dic.academic.ru/dic.nsf/enc_philosophy/
Paradoxes of logic. Access address: http://free-math.ru/publ/zanimatelnaja_matematika/paradoksy_logiki/paradoksy_logiki/11-1-0-19
Khrapko R.I. Logical paradoxes in physics and mathematics. Access address:
Logical dead ends (Paradoxes)
It is necessary to distinguish from sophistry logical paradoxes(from Greek paradoxes –"unexpected, strange") A paradox in the broad sense of the word is something unusual and surprising, something that diverges from usual expectations, common sense and life experience. A logical paradox is such an unusual and surprising situation when two contradictory propositions are not only simultaneously true (which is impossible due to the logical laws of contradiction and the excluded middle), but also follow from each other and condition each other. If sophistry is always some kind of trick, a deliberate logical error that can be detected, exposed and eliminated, then a paradox is an insoluble situation, a kind of mental impasse, a “stumbling block” in logic: throughout its history, many different methods have been proposed overcoming and eliminating paradoxes, however, none of them is still exhaustive, final and generally accepted.
The most famous logical paradox is the “liar” paradox. He is often called the “king of logical paradoxes.” It was discovered back in Ancient Greece. According to legend, the philosopher Diodorus Kronos vowed not to eat until he resolved this paradox and died of hunger, having achieved nothing; and another thinker, Philetus of Kos, fell into despair from the inability to find a solution to the “liar” paradox and committed suicide by throwing himself from a cliff into the sea. There are several different formulations of this paradox. It is formulated most briefly and simply in a situation where a person utters a simple phrase: I am a liar. Analysis of this elementary and ingenuous at first glance statement leads to a stunning result. As you know, any statement (including the above) can be true or false. Let us consider successively both cases, in the first of which this statement is true, and in the second it is false.
Let's assume that the phrase I am a liar true, i.e. the person who uttered it told the truth, but in this case he is really a liar, therefore, by uttering this phrase, he lied. Now suppose that the phrase I am a liar is false, that is, the person who uttered it lied, but in this case he is not a liar, but a truth-teller, therefore, by uttering this phrase, he told the truth. It turns out something amazing and even impossible: if a person told the truth, then he lied; and if he lied, then he told the truth (two contradictory propositions are not only simultaneously true, but also follow from each other).
Another famous logical paradox discovered at the beginning of the 20th century by the English logician and philosopher
Bertrand Russell, is the paradox of the “village barber”. Let's imagine that in a certain village there is only one barber who shaves those residents who do not shave themselves. Analysis of this simple situation leads to an extraordinary conclusion. Let's ask ourselves: can a village barber shave himself? Let's consider both options, in the first of which he shaves himself, and in the second he does not.
Let us assume that the village barber shaves himself, but then he is one of those village residents who shave themselves and whom the barber does not shave, therefore, in this case, he does not shave himself. Now suppose that the village barber does not shave himself, but then he belongs to those villagers who do not shave themselves and whom the barber shaves, therefore, in this case, he shaves himself. As we see, the incredible thing turns out: if a village barber shaves himself, then he does not shave himself; and if he does not shave himself, then he shaves himself (two contradictory propositions are simultaneously true and mutually condition each other).
The “liar” and “village barber” paradoxes, along with other similar paradoxes, are also called antinomies(from Greek antinomia“contradiction in the law”), i.e., reasoning in which it is proven that two statements that deny each other follow from one another. Antinomies are considered to be the most extreme form of paradoxes. However, quite often the terms “logical paradox” and “antinomy” are considered synonymous.
A less surprising formulation, but no less famous than the paradoxes of the “liar” and the “village barber,” is the paradox of “Protagoras and Euathlus,” which, like the “liar,” appeared in Ancient Greece. It is based on a seemingly simple story, which is that the sophist Protagoras had a student Euathlus, who took lessons in logic and rhetoric from him
(in this case – political and judicial eloquence). Teacher and student agreed that Euathlus would pay Protagoras his tuition fees only if he won his first trial. However, upon completion of the training, Evatl did not participate in any process and, of course, did not pay the teacher any money. Protagoras threatened him that he would sue him and then Euathlus would have to pay in any case. “You will either be sentenced to pay a fee, or you will not be sentenced,” Protagoras told him, “if you are sentenced to pay, you will have to pay according to the verdict of the court; if you are not sentenced to pay, then you, as the winner of your first trial, will have to pay according to our agreement.” To this Evatl answered him: “Everything is correct: I will either be sentenced to pay a fee, or I will not be sentenced; if I am sentenced to pay, then I, as the loser of my first lawsuit, will not pay according to our agreement; if I am not sentenced to pay, then I will not pay the court’s verdict.” Thus, the question of whether Euathlus should pay Protagoras a fee or not is indecisive. The contract between teacher and student, despite its completely innocent appearance, is internally, or logically, contradictory, since it requires the implementation of an impossible action: Evatl must both pay for training and not pay at the same time. Because of this, the agreement itself between Protagoras and Euathlus, as well as the question of their litigation, represents nothing more than a logical paradox.
A separate group of paradoxes are aporia(from Greek aporia“difficulty, bewilderment”) - reasoning that shows the contradictions between what we perceive with our senses (see, hear, touch, etc.) and what can be mentally analyzed (in other words, the contradictions between the visible and the imaginable) . The most famous aporia was put forward by the ancient Greek philosopher Zeno of Elea, who argued that the movement we observe everywhere cannot be made the subject of mental analysis, that is, movement can be seen, but cannot be thought. One of his aporias is called “Dichotomy” (Greek. dihotomia"bisection"). Suppose a certain body needs to go from point A to point IN. There is no doubt that we can see how a body, leaving one point, after some time reaches another. However, let's not trust our eyes, which tell us that the body is moving, and let's try to perceive the movement not with our eyes, but with our thoughts; let's try not to see it, but to think about it. In this case, we will get the following. Before you go all the way from the point A to point IN, the body needs to go half of this way, because if it doesn’t go half the way, then, of course, it won’t go the whole way. But before the body goes halfway, it needs to go 1/4 of the way. However, before it goes this 1/4 part of the way, it needs to go 1/8 part of the way; and even before that he needs to go 1/16th of the way, and before that - 1/32nd, and before that - 1/64th, and before that - 1/128th, and so on ad infinitum. So, to go from point A to point IN, the body must travel an infinite number of segments of this path. Is it possible to go through infinity? Impossible! Therefore, the body will never be able to complete its journey. Thus, the eyes testify that the path will be passed, but thought, on the contrary, denies this (the visible contradicts the conceivable).
Another famous aporia of Zeno of Elea - “Achilles and the Tortoise” - says that we may well see how the fleet-footed Achilles catches up and overtakes the tortoise slowly crawling in front of him; However, mental analysis leads us to the unusual conclusion that Achilles can never catch up with the tortoise, although he moves 10 times faster than it. When he covers the distance to the turtle, then during the same time (after all, it also moves) it will travel 10 times less (since it moves 10 times slower), namely 1/10 of the path that Achilles traveled, and this 1/10th will be in front of it.
When Achilles travels this 1/10th of the way, the turtle will cover 10 times less distance in the same time, i.e. 1/100th of the way and will be ahead of Achilles by this 1/100th. When he passes 1/100th of the path separating him and the turtle, then in the same time it will cover 1/1000th of the path, still remaining ahead of Achilles, and so on ad infinitum. So, we are again convinced that the eyes tell us about one thing, and the thought - about something completely different (the visible is denied by the thinkable).
Another aporia of Zeno - “Arrow” - invites us to mentally consider the flight of an arrow from one point in space to another. Our eyes, of course, indicate that the arrow is flying or moving. However, what will happen if we try, abstracting from the visual impression, to imagine its flight? To do this, let’s ask ourselves a simple question: where is the flying arrow now? If, in answer to this question, we say, for example, She's here now or She's here now or She's there now then all these answers will mean not the flight of the arrow, but precisely its immobility, because being Here, or here, or there - means to be at rest and not to move. How can we answer the question - where is the flying arrow now - in such a way that the answer reflects its flight, and not its immobility? The only possible answer in this case should be this: She is everywhere and nowhere now. But is it possible to be everywhere and nowhere at the same time? So, when trying to imagine the flight of an arrow, we came across a logical contradiction, an absurdity - the arrow is everywhere and nowhere. It turns out that the movement of the arrow can be seen, but it cannot be conceived, as a result of which it is impossible, like any movement in general. In other words, moving, from the point of view of thought, and not from sensory perceptions, means being in a certain place and not being in it at the same time, which, of course, is impossible.
In his aporia, Zeno brought together in a “confrontation” the data of the senses (talking about the multiplicity, divisibility and movement of everything that exists, assuring us that the fleet-footed Achilles will catch up with the slow tortoise, and the arrow will reach the target) and speculation (which cannot conceive of movement or multiplicity objects of the world, without falling into contradiction).
Once, when Zeno was demonstrating to a crowd of people the inconceivability and impossibility of movement, among his listeners was the equally famous philosopher Diogenes of Sinope in Ancient Greece. Without saying anything, he stood up and began to walk around, believing that by doing this he was proving better than any words the reality of movement. However, Zeno was not at a loss and answered: “Don’t walk and don’t wave your hands, but try to solve this complex problem with your mind.” Regarding this situation, there is even the following poem by A. S. Pushkin:
There is no movement, said the bearded sage,
The other fell silent and began to walk in front of him.
He could not have objected more strongly;
Everyone praised the intricate answer.
But, gentlemen, this is a funny case
Another example comes to mind:
After all, every day the Sun walks before us,
However, stubborn Galileo is right.
And indeed, we see quite clearly that the Sun moves across the sky every day from east to west, but in fact it is motionless (in relation to the Earth). So why don't we assume that other objects that we see moving may actually be motionless, and not rush to say that the Eleatic thinker was wrong?
As already noted, many ways to resolve and overcome paradoxes have been created in logic. However, none of them is without objections and is not generally accepted. Consideration of these methods is a long and tedious theoretical procedure, which remains beyond our attention in this case. An inquisitive reader will be able to get acquainted with various approaches to solving the problem of logical paradoxes in additional literature. Logical paradoxes provide evidence that logic, like any other science, is not complete, but constantly evolving. Apparently, paradoxes point to some deep problems of logical theory, lift the veil over something not yet entirely known and understood, and outline new horizons in the development of logic.
Considering this sophism, you should pay attention to the fact that the point from which the train left and the point at which it should arrive move together with the Earth in the same direction and at the same speed, i.e. their relative position, and This means that the distance between them does not change. Thus, both these points can be considered as stationary relative to each other. Consequently, no matter how fast a certain body moves, it will always leave one of the points and will certainly reach another. Why, in our sophistical reasoning, did it turn out that a train coming from the east needs to develop a very high speed in order to reach its western destination? Because in sophistry this western point is considered as motionless, not taking part in the rotation of the Earth. Indeed, if we assume a certain point somewhere above the earth’s surface, which is stationary, then a body moving towards it against the rotation of the Earth, of course, needs to develop a speed greater than the speed of the planet. However, this point (or point) moves with the Earth, and is not at all stationary. In the reasoning, the fact of its movement is cunningly and imperceptibly replaced by an implicit statement about its immobility, as a result of which the effect required in sophistry is achieved (the law of identity is violated by identifying non-identical phenomena: movement and immobility). Exactly the same in the argument about an escalator moving down and a person running up it. In order to reach the top, stationary part of the escalator, a person actually needs to run faster than the escalator is moving. If he needs to get not to the upper, stationary part of the escalator, but to a passenger who, standing on the escalator, is moving towards him, then in this case, no matter how fast the person running upward moves, he will in any case reach the one who moves towards him. In sophistry, the western point to which the train is heading is deliberately and incorrectly compared with the stationary part of the escalator, while it should be compared with some object that moves with the escalator (the fact of movement is imperceptibly replaced by a statement of immobility).
So, any sophism is fully revealed, or exposed, only if we have been able to clearly and definitely establish what non-identical things are deliberately and imperceptibly identified in this or that reasoning. Sophistry occurs quite often in various areas of life. Russian writer V.V. Veresaev in his “Memoirs” says:
“...Pechernikov easily reinterpreted my words, slightly shifted my objections to a different plane and victoriously refuted them, but I did not know how to keep track of where he moved my thoughts. It was pure sophistry, and I was powerless against it...” In order not to be powerless against sophistry, we must know well what sophisms are, how they are constructed, what logical errors they usually hide, and always look for some non-identity, less or more disguised, in sophistic reasoning.
Let's give a few more sophisms. Please note that in all examples the conclusions are false, and in some places their falsity is obvious, and in others not at all.
1. Why do people need ears? To see. It's strange - eyes are for seeing, and ears are for hearing. Actually this is not true. The ears hold the hat, and if they weren’t there, the hat would slide over the eyes and nothing would be visible. Therefore, ears are needed in order to see.
2. One elderly man proves that his strength, despite his advanced years, has not diminished at all:
– In my youth and youth, I could not lift a barbell weighing 200 kg and now I cannot, therefore, my strength has remained the same.
3. A girl was born into a Chinese family. When she was one year old, a neighbor came to her parents and began to marry the girl to his two-year-old son. Father said:
“My girl is only a year old, and your boy is two, that is, he is twice her age, which means that when my daughter is 20 years old, your son will already be 40. Why should I marry my daughter to an old groom?!”
The wife heard these words and objected:
– Now our daughter is one year old, and the boy is two, but in a year she will also be two and they will become the same age, so it is quite possible in the future to marry our girl to a neighbor’s boy.
4. Several people argued about which part of the human body is the most honorable. One said that these were the eyes, another - that the heart, the third - that the brain. One of the disputants said that the most honorable part of the body is the one on which we sit.
- How will you prove this? - they asked him.
He replied:
– People say: whoever sits down first gets the most honor; and the part of the body I have named always sits first, therefore it is the most honorable.
– Of course, Africa, because the Moon is visible from here, but Africa is not!
6. Five diggers dig 5 meters of a ditch in 5 hours. Therefore, in order to dig 100 meters of a ditch in 100 hours, one hundred diggers will be required.
Logical dead ends (Paradoxes)
It is necessary to distinguish from sophistry logical paradoxes(from Greek paradoxes –"unexpected, strange") A paradox in the broad sense of the word is something unusual and surprising, something that diverges from usual expectations, common sense and life experience. A logical paradox is such an unusual and surprising situation when two contradictory propositions are not only simultaneously true (which is impossible due to the logical laws of contradiction and the excluded middle), but also follow from each other and condition each other. If sophistry is always some kind of trick, a deliberate logical error that can be detected, exposed and eliminated, then a paradox is an insoluble situation, a kind of mental impasse, a “stumbling block” in logic: throughout its history, many different methods have been proposed overcoming and eliminating paradoxes, however, none of them is still exhaustive, final and generally accepted.
The most famous logical paradox is the “liar” paradox. He is often called the “king of logical paradoxes.” It was discovered back in Ancient Greece. According to legend, the philosopher Diodorus Kronos vowed not to eat until he resolved this paradox and died of hunger, having achieved nothing; and another thinker, Philetus of Kos, fell into despair from the inability to find a solution to the “liar” paradox and committed suicide by throwing himself from a cliff into the sea. There are several different formulations of this paradox. It is formulated most briefly and simply in a situation where a person utters a simple phrase: I am a liar. Analysis of this elementary and ingenuous at first glance statement leads to a stunning result. As you know, any statement (including the above) can be true or false. Let us consider successively both cases, in the first of which this statement is true, and in the second it is false.
Let's assume that the phrase I am a liar true, i.e. the person who uttered it told the truth, but in this case he is really a liar, therefore, by uttering this phrase, he lied. Now suppose that the phrase I am a liar is false, that is, the person who uttered it lied, but in this case he is not a liar, but a truth-teller, therefore, by uttering this phrase, he told the truth. It turns out something amazing and even impossible: if a person told the truth, then he lied; and if he lied, then he told the truth (two contradictory propositions are not only simultaneously true, but also follow from each other).
Another famous logical paradox discovered at the beginning of the 20th century by the English logician and philosopher
Logics is a science about forms of thinking, laws of thinking and reasoning, a science about operations with mental forms, about correct thinking.
Communicative models of official communication and types of argumentation:
Monologue can be defined as an extended statement by one person. There are two main types of monologue. Firstly, monologue speech is a process of purposeful communication, conscious appeal to the listener and is characteristic of the oral form of book speech: oral scientific speech, judicial speech, oral public speech. The monologue received its most complete development in artistic speech.
Secondly, a monologue is speech alone with oneself. The monologue is not directed to the direct listener and, accordingly, is not designed for the interlocutor’s response.
According to the purpose of the utterance, monologue speech is divided into three main types:
1. Information speech serves to transfer knowledge. In this case, the speaker must take into account the intellectual abilities of perceiving information and the cognitive capabilities of listeners. Types of informational speech - lectures, reports, messages, reports.
2. Persuasive I speech addressed to the emotions of the listeners, in this case the speaker must take into account his receptivity. Types of persuasive speech: congratulatory, solemn, parting.
3. Encouraging speech is aimed at inducing listeners to various kinds of actions. Here there are political speech, speech-call to action, speech-protest.
Monologue speech is distinguished by the degree of preparedness and formality. An oratorical speech is always a pre-prepared monologue delivered in an official setting. However, to a certain extent, a monologue is an artificial form of speech, always striving for dialogue. In this regard, any monologue can have means of dialogizing it.
Dialogue is a logical-communicative process where subjects (of different levels) interact through semantic positions to solve certain problems.
The emergence of dialogue as a form of joint search for truth was due to the development of ancient dialectics and rhetoric. Socrates is considered a recognized master of dialogue and even the founder of this form of argumentation, who did not leave written texts, but we can judge the essence of his method from the writings of his great student Plato.
Types of dialogues include conversations, discussions, interviews, etc.
Dispute- a verbal competition, a discussion of something between two or more persons, in which each side defends its opinion, its rightness.
Controversy is a type of dispute.
Controversy is a dispute aimed at winning over the opposite side and using only correct methods of arguing. The main goal of polemics is to win.
Discussion is also a type of dispute.
Discussion is a dispute aimed at achieving the truth and using only correct methods of arguing.
Discussion is one of the most important forms of communication, a method of solving controversial problems and a unique way of cognition.
The benefit of discussion is that it reduces subjectivity.
The purpose of the discussion is to achieve a certain degree of agreement among its participants regarding the thesis under discussion.
Types of disputes :
discussion
controversy
Eclecticism is a dispute aimed at achieving the truth, but using all possible methods, including incorrect ones
Sophistry is a dispute aimed at defeating the opposing side using all possible techniques.
Dispute strategy and tactics
Dispute strategy characterized by the goals of its participants. Depending on the goal that one or another participant in the dispute sets for himself, the following types of polemical strategies are distinguished: the strategy of truth, persuasion, victory, process. Directly in a dispute, both identical and different strategies can be encountered.
Truth Strategy directs the disputant to the discussion behavior of searching for the truth, to test any thought or idea, to justify it. To find the right solution, disputants compare a variety of points of view on a particular problem. The strategy of truth is characterized by the following form of polemical behavior. Participants in a dispute defend a thought from attack in order to find out what objections there may be to this thought, or, on the contrary, attack a position expressed by an opponent in order to find out what arguments there are in its favor. In such a dispute, arguments are carefully selected and analyzed, the positions and views of the opposite side are weighed, that is, in essence, a joint investigation of the truth is conducted.
Persuasion Strategy aims the disputant to convince the opponent of what he himself is deeply convinced of. But this is not always his true belief. Sometimes he assures his opponent only because it is necessary due to duty, due to some circumstances. He himself does not at all believe in the truth of what he defends, or in the falsity of what he attacks.
Winning strategy aims the disputants at the end result, the goal of which is victory at any cost.
Process strategy directs the participants in the dispute to conduct it for the sake of the dispute itself. This is a kind of “art for art’s sake,” sports passion. This strategy is most typical for young people.
Argument tactics includes polemical techniques and tricks in argument. Polemical techniques include:
1. Criticism of the arguments, which is based on refuting the opponent’s false thesis with reliable facts.
2. The principle of “beating the enemy with his weapon”» based on the use of the words, principles and arguments of the opponent against him.
3. Reduction to absurdity technique» in combination with the use of irony and sarcasm, leads the opponent’s statement to an absurd result.
4."Argument to Man"- this is a type of substitution of the thesis, when, instead of discussing the essence of this or that consideration, they begin to evaluate the merits or shortcomings of the person who put forward this consideration.
5. "Return Strike"(boomerang technique) - this is when in a dispute a remark or argument is turned against the one who expressed it.
6. Picking up a cue- this is a sharpening of the polemical dispute on the newly discovered argument of the opponent.
7. Refutation of the demonstration based on identifying that the opponent’s thesis does not logically follow from his arguments.
8. Attack with questions- this is a technique that is based on seizing the initiative in posing a question in order to make the opponent’s position difficult, force him to defend himself, justify himself, thereby creating the most favorable conditions for the attacker for an argument.
Tricks in an argument include:
1. Bet on false shame takes advantage of the opponent’s fear of discrediting himself in the eyes of others. As a rule, one of the participants in the dispute introduces a statement that is supposedly generally known, but not known to the opponent, and asserts its significance. At the same time, the opponent, feeling his uncertainty, is forced to agree with the dubious statement.
2. “Greasing the argument.” The technique is based on the use of openly flattering compliments to the opponent.
3. References to age, education, position characterized by the following statements: “Live to my age, then judge”; “First get your diploma, then we’ll talk”; “If you take my place, then you’ll start arguing,” which disavows the opponent’s incompetence.
4. Taking the conversation in another direction is used when one of the discussion participants finds it difficult to find the necessary argument, tries to avoid defeat or make it less noticeable.
5. Self-confident tone characterized by the peremptory and decisive nature of the disputant, speaking with aplomb and an impressive voice.
6. Obstruction- deliberate disruption of a dispute, which refers to crude “mechanical” tricks in which they interrupt the opponent, do not allow him to speak, clearly show their reluctance to listen to the opponent - they cover their ears.
Sophism(from Greek - skill, skill, cunning invention, trick, wisdom) - a false conclusion, which, nevertheless, upon superficial examination seems correct. Sophistry is based on a deliberate, conscious violation of the rules of logic.
Sophism- (from the Greek sophisma, “skill, skill, cunning invention, trick”) - a conclusion or reasoning that substantiates some deliberate absurdity, absurdity or paradoxical statement that contradicts generally accepted ideas. Sophistry is based on a deliberate, conscious violation of the rules of logic. Whatever the sophistry, it always contains one or more disguised errors.
Paradox is a reasoning that proves both the truth and
the falsity of a certain judgment, in other words, proving both this judgment and its negation.
Logical paradox- this is such an unusual and surprising situation when two contradictory propositions are not only simultaneously true (which is impossible due to the logical laws of contradiction and the excluded middle), but also follow from each other, condition each other.
A paradox is an insoluble situation, a kind of mental impasse, a “stumbling block” in logic: throughout its history, many different ways to overcome and eliminate paradoxes have been proposed, but none of them is still exhaustive, final and generally accepted.
Eristic– the art of remaining right in an argument at any cost.
There are quite a lot of eristic techniques, but their principles are the same - do not allow a thought to be developed naturally and consistently so that the matter is completely clarified and to assert one’s interest. There are quite a lot of eristic techniques, but their principles are the same - do not allow a thought to be developed naturally and consistently so that the matter is completely clarified and to assert one’s interest.
Eristics is divided into dialectics and sophistry.
Dialectics- the art of arguing in order to find out the truth.
Sophistry- the desire to achieve victory in a dispute through the deliberate use of false arguments.
You should not argue unless absolutely necessary. If there is an opportunity to reach agreement without dispute, it should be used.
Every dispute must have its own topic, its own subject; the topic should not change or be replaced by another throughout the entire dispute.
A dispute occurs only when there are incompatible ideas about the same object or phenomenon.
Successful argumentation requires knowledge of logic.
The dispute requires direct knowledge of the objects or phenomena in question.
In any dispute, one must strive to clarify the truth.
In a dispute you need to be flexible.
Major blunders in the strategy and tactics of the dispute should not be made.
You should not be afraid to admit your mistakes during an argument.
