LECTURE No. 23. Sophisms. Logic paradoxes

1. Sophisms. Concept, examples

Revealing this issue, it must be said that any sophism is a mistake. In logic, there is also paralogisms. The difference between these two types of errors is that the first (sophism) was made intentionally, while the second (paralogism) was made by accident. The speech of many people abounds in paralogisms. Conclusions, even seemingly correctly constructed ones, are distorted in the end, forming a consequence that does not correspond to reality. Paralogisms, despite the fact that they are allowed unintentionally, are still often used for their own purposes. You can call this tailoring to the result. Without realizing that he is making a mistake, a person in this case derives a consequence that corresponds to his opinion and discards all other versions without considering them. The accepted consequence is considered true and is not verified in any way. Subsequent arguments are also distorted in order to better suit the thesis put forward. At the same time, as mentioned above, the person himself does not realize that he is making a logical mistake, he considers himself to be right (moreover, he is more savvy in logic).

Unlike a logical error that occurs involuntarily and is the result of a low logical culture, sophism is a deliberate violation of logical rules. It is usually carefully disguised as a true judgment.

Deliberately allowed, sophisms aim to win the argument at any cost. Sophism is designed to knock the opponent off his line of thinking, to confuse, to draw into the analysis of errors that do not relate to the subject under consideration. From this point of view, sophism acts as an unethical way (and at the same time obviously wrong) of conducting a discussion.

There are many sophisms created in antiquity and preserved to this day. The conclusion of most of them is curious. For example, the sophism "thief" looks like this: "The thief does not want to acquire anything bad; the acquisition of good is a good thing; therefore, the thief wants good." The following statement also sounds strange: "The medicine taken by the sick is good; the more good you do, the better; therefore, the medicine must be taken in large doses." There are other well-known sophisms, for example: "He who is sitting has risen; whoever has risen, he is standing; therefore, the one who is sitting is standing", "Socrates is a man; a man is not the same as Socrates; therefore, Socrates is something other than Socrates" , "These kittens are yours, the dog, their father is also yours, and their mother, the dog, is also yours. So, these kittens are your brothers and sisters, the dog and the bitch are your father and mother, and you yourself are a dog."

Such sophisms were often used to mislead the opponent. Without such a weapon in their hands as logic, the rivals of the sophists in the dispute had nothing to oppose, although they often understood the falsity of sophistical conclusions. Disputes in the ancient world often ended in fights.

With all the negative meaning of sophisms, they had a reverse and much more interesting side. So, it was sophisms that caused the emergence of the first rudiments of logic. Very often they pose the problem of proof in an implicit form. It was with sophisms that the comprehension and study of evidence and refutation began. Therefore, we can talk about the positive effect of sophisms, that is, that they directly contributed to the emergence of a special science of correct, demonstrative thinking.

A number of mathematical sophisms are also known. To obtain them, numerical values ​​are shuffled in such a way as to obtain one from two different numbers. For example, the statement that 2 x 2 = 5 is proven as follows: in turn, 4 is divided by 4, and 5 by 5. The result is (1:1) = (1:1). Therefore, four equals five. Thus, 2 x 2 = 5. This error is resolved quite easily - you just need to subtract one from the other, which will reveal the inequality of these two numerical values. A refutation is also possible by writing through a fraction.

As before, so now sophisms are used to deceive. The above examples are quite simple, it is easy to notice their falsity and do not have a high logical culture. However, there are veiled sophisms, disguised in such a way that it can be very problematic to distinguish them from true judgments. This makes them a convenient means of deception in the hands of logically savvy scammers.

Here are a few more examples of sophisms: “In order to see, there is no need to have eyes, since without the right eye we see, without the left we also see; apart from the right and left, we have no other eyes, therefore it is clear that the eyes are not necessary for sight" and "What you did not lose, you have; you did not lose your horns, so you have horns." The last sophism is one of the most famous and is often cited as an example.

We can say that sophisms are caused by insufficient self-criticism of the mind, when a person wants to understand knowledge that is still inaccessible, not amenable at a given level of development.

It also happens that sophism arises as a defensive reaction in the presence of a superior opponent, due to ignorance, ignorance, when the arguing does not show perseverance, not wanting to give up positions. It can be said that sophism interferes with the conduct of the dispute, but such a hindrance should not be classified as significant. With proper skill, sophism is easily refuted, although this leads to a departure from the topic of reasoning: one has to talk about the rules and principles of logic.

2. Paradox. Concept, examples

Turning to the question of paradoxes, one cannot fail to say about their relationship with sophisms. The fact is that sometimes there is no clear line by which you can understand what you have to deal with.

However, paradoxes are considered with a much more serious approach, while sophisms often play the role of a joke, nothing more. This is due to the nature of theory and science: if it contains paradoxes, then there is an imperfection in the underlying ideas.

What has been said may mean that the modern approach to sophistry does not cover the entire scope of the problem. Many paradoxes are interpreted as sophisms, although they do not lose their original properties.

paradox one can name an argument that proves not only the truth, but also the falsity of a certain judgment, i.e., proving both the judgment itself and its negation. In other words, paradox - these are two opposite, incompatible statements, for each of which there are seemingly convincing arguments.

One of the first and certainly exemplary paradoxes was recorded Eubulides - Greek poet and philosopher, Cretan. The paradox is called "The Liar". This paradox has come down to us in this form: "Epimenides claims that all Cretans are liars. If he tells the truth, then he lies. Is he lying or is he telling the truth?" This paradox is called "the king of logical paradoxes". To date, no one has been able to solve it. The essence of this paradox is that when a person says: "I am lying", he does not lie and does not tell the truth, but, more precisely, he does both at the same time. In other words, if we assume that a person is telling the truth, it turns out that he is actually lying, and if he is lying, then he told the truth about it before. Both contradictory facts are asserted here. Of course, according to the law of the excluded middle, this is impossible, but that is why this paradox has received such a high "title".

The inhabitants of the city of Elea, the Eleatics, made a great contribution to the development of the theory of space and time. They relied on the idea of ​​the impossibility of non-existence, which belongs Parmenides. Every thought according to this idea is a thought about what exists. At the same time, any movement was denied: the world space was considered integral, the world was one, without parts.

Ancient Greek philosopher Zeno of Elea known for compiling a series of paradoxes about infinity - the so-called paradoxes of Zeno.

Zeno, a student of Parmenides, developed these ideas, for which he was named Aristotle "ancestor of dialectics". Dialectics was understood as the art of reaching the truth in a dispute, revealing contradictions in the opponent's judgment and destroying them.

The following are the direct aporias of Zeno.

"Achilles and the tortoise" represents an aporia about movement. As you know, Achilles is an ancient Greek hero. He had remarkable abilities in sports. The turtle is a very slow animal. However, in an aporia, Achilles loses the race to the tortoise. Suppose Achilles needs to run a distance of 1, and he runs twice as fast as a turtle, the last one needs to run ¹/₂. Their movement starts at the same time. It turns out that after running the distance ¹/₂, Achilles will find that the tortoise has managed to overcome the segment in the same time ¹/₄. No matter how much Achilles tries to overtake the tortoise, it will be ahead exactly by ¹/₂. Therefore, Achilles is not destined to catch up with the tortoise, this movement is eternal, it cannot be completed.

The inability to complete this sequence is that it is missing the last element. Each time, having indicated the next member of the sequence, we can continue by indicating the next one.

The paradox here lies in the fact that the endless sequence of successive events must actually come to an end, even if we could not imagine this end.

Another aporia is called "dichotomy". The reasoning is based on the same principles as the previous one. In order to go all the way, you need to go halfway. In this case, half the path becomes a path, and in order to pass it, it is necessary to measure half (that is, already half of the half). This continues ad infinitum.

Here the order of succession is reversed compared to the previous aporia, i.e. (¹/₂)n..., (¹/₂)3, (¹/₂)2, (¹/₂)one. The series here does not have the first point, while the aporia "Achilles and the tortoise" did not have the last.

From this aporia, it is concluded that the movement cannot begin. Proceeding from the considered aporias, the movement cannot end and cannot begin. So it doesn't exist.

Refutation of the aporia "Achilles and the Tortoise".

As in the aporia, Achilles appears in its refutation, but not one, but two turtles. One of them is closer than the other. The movement also starts at the same time. Achilles runs last. During the time that Achilles runs the distance separating them at the beginning, the nearest tortoise will have time to crawl a little ahead, which will continue indefinitely. Achilles will get closer and closer to the tortoise, but he will never be able to overtake it. Despite the obvious falsity, there is no logical refutation of such an assertion. However, if Achilles begins to catch up with a distant tortoise, not paying attention to the near one, he, according to the same aporia, will be able to come close to it. And if so, then he will overtake the nearest turtle.

This leads to a logical contradiction.

In order to refute the refutation, i.e., to defend the aporia, which is strange in itself, it is proposed to throw away the burden of figurative representations. And to reveal the formal essence of the matter. Here it should be said that the aporia itself is based on figurative representations and to reject them means to refute it as well. And the rebuttal is quite formal. The fact that two turtles are taken instead of one in the refutation does not make it more figurative than an aporia. In general, it is difficult to talk about concepts that are not based on figurative representations. Even such philosophical concepts of the highest abstraction as being, consciousness, and others are understood only thanks to the images that correspond to them. Without the image behind the word, the latter would remain only a set of symbols and sounds.

Stages implies the existence of indivisible segments in space and the movement of objects in it. This aporia builds on the previous ones. Take one immovable row of objects and two moving towards each other. Moreover, each moving row in relation to the immovable one passes only one segment per unit of time. However, in relation to the moving - two. which is considered contradictory. It is also said that in an intermediate position (when one row has already moved, as it were, the other has not) there is no room for a fixed row. The intermediate position comes from the fact that the segments are indivisible and the movement, even though it started simultaneously, must go through an intermediate stage when the first value of one moving series coincides with the second value of the second (movement, provided that the segments are indivisible, is devoid of smoothness). The state of rest is when the second values ​​of all rows coincide. The fixed row, if we assume the simultaneity of the movement of the rows, must be in an intermediate position between the moving rows, and this is impossible, since the segments are indivisible.

Notes

1. Makovelsky A. O. History of Logic. M., 1967.

2. V. S. Meskov, Essays on the Logic of Quantum Mechanics. M., 1986.

3. Demidov I. V. Logic: Textbook / Ed. B. I. Kaverina. 2nd ed. M.: Exam, 2006.

4. V. I. Kirillov and A. A. Starchenko, Logic. M., 2001.

5. Ibid.

6. Soviet Encyclopedic Dictionary / Ed. A. M. Prokhorova. 4th ed., rev. and additional M.: Sov. encycl., 1990.

7. Soviet Encyclopedic Dictionary / Ed. A. M. Prokhorova. 4th ed., rev. and additional M.: Sov. encycl., 1990.

8. Savchenko N. A. Course of lectures. Logics. M., 2002.

9. Savchenko N. A. Course of lectures. Logics. M., 2002.

10. Ibid.

11. Savchenko N. A. Course of lectures. Logics. Topic 4. M., 2002.

12. Savchenko N. A. Course of lectures. Logics. M., 2002.

13. Eryshev A. A. Logic. M., 2004.

14. Ibid.

15. Eryshev A. A. et al. Logic. M., 2004.

16. Savchenko N. A. Course of lectures. Logics. M., 2002.

17. Savchenko N. A. Course of lectures. Logics. M., 2002.

18. Povarnin S. I. Art of dispute: on the theory and practice of dispute. General information about the dispute. About proofs, questions of philosophy. N. 1990.

19. Ibid.

20. Ivin A. A. Logic: Textbook. M.: Gardariki, 2000.

21. Povarnin S. I. Art of dispute: on the theory and practice of dispute. General information about the dispute. About proofs, questions of philosophy. N. 1990.

Author: Shadrin D.A.

<< Back: Rebuttal (The concept of refutation. Refutation through arguments and form)

We recommend interesting articles Section Lecture notes, cheat sheets:

▪ Logics. Lecture notes

▪ Fundamentals of life safety. Crib

▪ Ecology. Crib

See other articles Section Lecture notes, cheat sheets.

Read and write useful comments on this article.

<< Back

Latest news of science and technology, new electronics:

The existence of an entropy rule for quantum entanglement has been proven 09.05.2024

Quantum mechanics continues to amaze us with its mysterious phenomena and unexpected discoveries. Recently, Bartosz Regula from the RIKEN Center for Quantum Computing and Ludovico Lamy from the University of Amsterdam presented a new discovery that concerns quantum entanglement and its relation to entropy. Quantum entanglement plays an important role in modern quantum information science and technology. However, the complexity of its structure makes understanding and managing it challenging. Regulus and Lamy's discovery shows that quantum entanglement follows an entropy rule similar to that for classical systems. This discovery opens new perspectives in the field of quantum information science and technology, deepening our understanding of quantum entanglement and its connection to thermodynamics. The results of the study indicate the possibility of reversibility of entanglement transformations, which could greatly simplify their use in various quantum technologies. Opening a new rule ... >>

Mini air conditioner Sony Reon Pocket 5 09.05.2024

Summer is a time for relaxation and travel, but often the heat can turn this time into an unbearable torment. Meet a new product from Sony - the Reon Pocket 5 mini-air conditioner, which promises to make summer more comfortable for its users. Sony has introduced a unique device - the Reon Pocket 5 mini-conditioner, which provides body cooling on hot days. With it, users can enjoy coolness anytime, anywhere by simply wearing it around their neck. This mini air conditioner is equipped with automatic adjustment of operating modes, as well as temperature and humidity sensors. Thanks to innovative technologies, Reon Pocket 5 adjusts its operation depending on the user's activity and environmental conditions. Users can easily adjust the temperature using a dedicated mobile app connected via Bluetooth. Additionally, specially designed T-shirts and shorts are available for convenience, to which a mini air conditioner can be attached. The device can oh ... >>

Energy from space for Starship 08.05.2024

Producing solar energy in space is becoming more feasible with the advent of new technologies and the development of space programs. The head of the startup Virtus Solis shared his vision of using SpaceX's Starship to create orbital power plants capable of powering the Earth. Startup Virtus Solis has unveiled an ambitious project to create orbital power plants using SpaceX's Starship. This idea could significantly change the field of solar energy production, making it more accessible and cheaper. The core of the startup's plan is to reduce the cost of launching satellites into space using Starship. This technological breakthrough is expected to make solar energy production in space more competitive with traditional energy sources. Virtual Solis plans to build large photovoltaic panels in orbit, using Starship to deliver the necessary equipment. However, one of the key challenges ... >>

Random news from the Archive Graphene Coated Aircraft 14.08.2018 Engineers from the University of Central Lancashire (UCLan) have unveiled an unmanned aerial vehicle that they say is the world's first graphene-coated aircraft. The device, which is 3,5 meters wide, was called Juno. Its fuselage is coated with graphene; in addition, the aircraft is equipped with graphene batteries and contains parts printed on a 3D printer. Graphene, being a very strong material, allows you to add strength to other fuselage materials - the latter, thus, can be used less, which naturally helps to reduce the mass of the device. In addition, as the portal notes, due to the thermal conductivity of graphene, the fuselage will be less susceptible to icing, and the electrical conductivity of the material will allow - in the event of a lightning strike - to dissipate the impact energy over the entire surface of the fuselage.

Other interesting news:

▪ Processor based on superconductors

▪ Smart watch Timex Ironman R300 GPS

▪ Single charging connector - microUSB

▪ Cell phone jammer

▪ Most Integrated Serial-to-Parallel Converters

News feed of science and technology, new electronics

Interesting materials of the Free Technical Library:

▪ section of the site Grounding and grounding. Selection of articles

▪ article Using plans for video filming. video art

▪ article What was the first highway? Detailed answer

▪ article Water jet bike. Personal transport

▪ article Computer mouse for quartz clocks. Encyclopedia of radio electronics and electrical engineering

▪ article A vase on... a lathe. Encyclopedia of radio electronics and electrical engineering

Leave your comment on this article:

All languages ​​of this page

Arabic	Hebrew	Polish
Bengali	Hindi	Portuguese
Chinese	Italian	Spanish
English	Japanese	Turkish
French	Korean	Ukrainian
German	Malay	Vietnamese

Home page | Library | Articles | Website map | Site Reviews

www.diagram.com.ua
2000-2024