Philosophical sophisms. What is Sophism? Paradox "mayor of the city"

Kuznetsova Lyudmila

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Introduction

Surely, every person at least once in his life heard a similar phrase: "Twice two are five" or at least: "Two are equal to three." In fact, such examples can be given a lot, but what are they all designate? Who invented them? Do they have any logical explanation or is it only fiction?

In contrast to an involuntary logical error - a paralogism, which is a consequence of a low logical culture, Sophism is a deliberate, but carefully disguised violation of the requirements of logic.

Here are examples of fairly simple ancient sophisons. "The thief does not want to acquire anything wrong; The acquisition of good is a good thing; Consequently, the thief wishes good. " "The medicine taken by the patient is welcome; the more do good, the better; So the medicine must be taken in large doses. "

The sophisms of the ancients were often used with the intention of misleading. But they also had another, much more interesting side. Very often, sophisms put in an implicit form of the problem of evidence. Formulated at that time when the science of logic was not yet, the ancient sophisms directly set the question of the need for its construction. It is from Sophisons to be understood and the study of evidence and refutation. And in this regard, the sophisms directly contributed to the emergence of special science on the right, evidenceful thinking.

Sophisms were used and now continue to be used for a subtle, veiled deception. In this case, they act as a special admission of intellectual fraud, attempts to give false for the truth and thereby mislead.

Chapter 1. "The concept of sofism. Historical Information

The concept of sofism:

Sophism - (from Greek Sophisma - trick, tricks, fiction, puzzle), conclusion or reasoning, justifying some kind of obelity, absurd or paradoxical statement contrary to generally accepted ideas. Whatever the soffis, it always contains one or more disguised errors.

What is mathematical sophism? Mathematical Sophism is an amazing statement, in the proof of which invisible, and sometimes quite thin errors. The history of mathematics is full of unexpected and interesting sophisons, the resolution of which sometimes served as the impetus for new discoveries. Mathematical sophisms teach carefully and wary to move forward, carefully monitor the accuracy of the formulation, the correctness of the records of the drawings, for the legality of mathematical operations. Very often, the understanding of errors in sofism leads to an understanding of mathematics in general, helps to develop the logic and skills of the right thinking. If I found a mistake in Sophism, it means that you realized it, and the awareness of the error warns from its repetition in further mathematical reasoning. Sophisms do not benefit, if they are not understood.

Concerning typical mistakes In sofesums, they are as follows: forbidden actions, neglect the conditions of theorems, formulas and rules, an erroneous drawing, support for erroneous conclusions. Often, mistakes made in sofism are so skillfully hidden that even an experienced mathematician will not immediately reveal them. It is in this that the connection of mathematics and philosophy is manifested in sofiism. In fact, the Sophistician hybrid is not only mathematics and philosophy, but also logic with rhetoric. The main creators of soffisms are ancient Greek philosophers, but nevertheless, they created mathematical sophisms based on elementary axioms, which once again confirms the connection of mathematics and philosophy in sofiism. In addition, it is very important to properly present sophism, so that the speaker believes, which means that it is necessary to own the gift of eloquence and beliefs. A group of ancient Greek scientists, which began to engage in sophies as a separate mathematical phenomenon, called themselves with the spurs. About this in more detail in the next section.

Historical reference.

Sofists were called a group of ancient Greek philosophers of the 4-5th century BC, who have achieved large art in logic. During the fall of the morals of an ancient Greek society (5th century), the so-called eloquence teachers appear, which was considered the purpose of their activities and called the acquisition and distribution of wisdom, as a result of which they called themselves with the phistas. The most famous activity of older sophists, to which the protagora from Abdra, Gorgia from Leontip, Hippius from Elida and Ditz from Keos are known. But the essence of the activities of the sophists is much more than simple eloquence learning. They trained and enlightened the ancient Greek people, tried to contribute to the achievement of morality, the presence of the Spirit, the ability of the mind to focus in any case. But the sophists were not scientists. The ability to be achieved with their help was that a person learned to keep in mind the diverse points of view. The main activity of the Sofists became a socio-anthropological problem. They considered the self-knowledge of the person, they were taught to doubt, but still, these are very deep philosophical problems that have become the basis for thinkers of European culture. As for the sophisms themselves, they have become a supplement to sophistry as a whole, if we consider it as a truly philosophical concept.

Historically, it has been found that with the concept of sofism associate the idea of \u200b\u200bintentional falsification, guided by the recognition of the protagon that the task of Sophista is to present the worst argument as the best way of ingenious tricks in speech, in reasoning, taking care of the truth, but about the success in dispute or practical benefit. There are no less, in Greece, they called simple speakers.

The most famous scientist and philosopher Socrates at the beginning was a sophist, actively participated in disputes and discussions of the sophists, but soon began to criticize the doctrine of sophists and sophistry as a whole. The same example followed his students (xenophon and plato). Socrates philosophy was based on the fact that wisdom is acquired with communication, in the process of conversation. The doctrine of Socrates was oral. In addition, Socrates to this day is considered the wiser philosopher.

As for the sophisians themselves, then, the most popular at that time in ancient Greece was the Sophism of the Ebbulid: "What you did not lose, you have. Horn You did not lose. So you have a horns. " The only inaccuracy that could be allowed is, then the ambiguity of the statement. This formulation of the phrase is illogical, but the logic arose much later, thanks to Aristotle, so if the phrase was built like this: "All you did not lose. . . ", The conclusion would be logically flawless.

Aristotle called sophistry not real, but seemingly imaginary wisdom. Sophisticatics grows on a distorted understanding of the mobility of things using the flexibility of the concept reflecting the world.

Here is one of the ancient samples.
- Do you know what I want to ask you?
- Not.
- Do you know that the virtue is good?
- I know.
- That's what I wanted to ask you.

Sophism is discouraged: regulations are possible when a person does not know what he knows well. On the other hand, it was good in antiquity! Everyone knew that virtue was good, and did not doubt it.

Some Evatle took the lessons of sofics at the philosopher of Protagor on the condition that he will contribute to the training fee, when, after graduation, he will win his first process. But after graduating, Evatle and did not think to take the proceedings. At the same time, he considered himself free and from paying money for study. Then Protagor threatened by the court, saying that in any case Evatle would pay. If the judges quit to pay, then according to their sentence, if they do not quit, then by force of the contract. After all, then Evatle will win his first process. But Evatle was a good student. He objected that with any outcome of the case he would not pay. If they quit to pay, the process will be lost and according to the contract between them it will not pay. If they do not quit, it is not necessary to pay for the court sentence. What the dispute ended, the story is silent.

But Sophism is a song of English students.

The more you study, the more you know.
The more you know, the more you forget.
The more you forget, the less you know.
The less you know, the less you forget.
But the less you forget, the more you know.
So what to learn?

Not philosophy, but the dream is lazy!

The well-known Russian joke is a direct transfer of this song to national specifics.

The more I drink, the stronger my hands tremble.
The stronger my hands tremble, the more I shed.
The more I shed, the less I drink.
Thus, the more I drink, the less I drink.

This is no longer just Sophism, but a direct paradox.

Scientists have such a property: all humanity will be put in a dead end, and then a whole generation or even several generations with difficulty are chosen from it. Showing the wonders of ingenuity and quirkness.

"When the experience ends in failure, the opening begins" - so said the famous German inventor of the XIX century R. Diesel, to whom humanity is obliged to highly economically internal combustion engines. And he was, without a doubt, an expert on his business. And necessarily - Pedant. Because only the pedant could have been improving his engine for a year and a half, the first copy of which was only seven revolutions. Not seven revolutions per second, but seven revolutions for all the time of their operation.

But now, it seems to me that the total number of revolutions of all diesel engines on Earth is approaching atoms in the universe. And the number of sophishes and paradoxes remains almost the same as in ancient times. Probably, because hardworking diesel engines in the history of mankind were still much more than ingenious protagors, mean eutlists and slandering epimeons. And it is encouraging.

Here are some interesting logical sophisons:

Let's start the analysis of the sophism of the cuckold: 1) what you did not lose, you have; 2) You did not lose horns; 3) Consequently, you have a horns. Paradoxically! And it is impressive, isn't it? However, after some mental voltage it becomes clear that the paradoxicality of the output in this sofism occurs due to its 1st parcel, which is an unsuccessful attempt to determine the relationship "to have": if not lost it, then it has B. Non-obvious erroneousness of this The definitions follows from its irreversibility, that is, the obvious error in its appeal: it is wrong that if it has b, then not losing it, because to lose something, you must first have it. Consequently, the correct wording looks like this: if I had b and not to have b, then I lost B. on the correctness of this wording indicates its reversibility. If now from the negation of the appeal of this parcel (if not lost it, then I had b and a having b) to exclude the 1st part of the right part (and had b), then the incorrect 1st parcel of sofism of the cuckold will be. It would be more correctly like it would look like this: in some cases, if not lost it, it also has b (namely, in those cases, when she also had b). "In some cases," and "in any case" is, as it is easy to see, Quantizern. Thus, quantifiers are also important in the statements about the relationship, they are omnipresent. But the urgelessness also the desire to lower them, which in some additional circumstances gives rise to whether deliberately, whether the sophisms are inadvertently diverse, or paralogism.

Let's see now that it will add to our knowledge about the nature of Sophisms of sofism about the sitting. This Sophism: 1) Sitting got up; 2) who got up, he stands; 3) Therefore, sitting stands. At first glance, the comments to this syllogism (from the point of view of its inner structure) is not foreseen. Obviously, only a remark to the conclusion of Sillgism: "Sitting worth" equivalent to the statement "one who sits, standing" or "and sitting and standing". Similarly, the 1st parcel "Sitting got up" is converted to "The one who sits, got up" or "and sits and stood." So, it turns out that the error is contained in the 1st parcel of syllogism, since "and sits" and "but stood" cannot be simultaneously true. Correctly it would be "Sitting got up." It is in this case that the result obtained as a result does not cause comments: "Sitting standing". Consequently, in this sophysism-paralogism, the inconspicuous occurrence of the erroneous parcel occurs due to loss of control over the category of time, the communion: as soon as the sitting got up, it can no longer be called sitting, as it immediately turns into the sitting. But since such a loss of control, apparently, is natural for a natural language (as well as loss of control over the use of quantifiers), then it passes, as a rule, unnoticed not only for receivers, but also for sources of statement.

Disassembled Sophism for Sitting Site prompted by the author of the idea of \u200b\u200bSophism about Malom: 1) Small grown; 2) who grew up, that big; 3) Consequently, small is large. It is impossible to disagree with the fact that this sophism, although it has humorous properties, still gives new knowledge of sofiism. The paradoxical conclusion is obtained here not only due to the loss of control over the form of the relationship "grow", but also due to the loss of control over the interconnection of the contents of the concepts "small" and "grow", which is that the ratio of "grow" is defined as the transformation of small Large. A similar connection between the contents of the concepts ("sit", "get up" and "stand") is also traced in the previous Sophism - about the sitting.

1. Chapter 2. "Mathematical Sophies"

Mathematical Sophism is an amazing statement, in the proof of which invisible, and sometimes quite thin errors.

It is difficult to study mathematics, not interested in mathematical sophimons. In 2003, the book of A.G. was published in the publishing house "Enlightenment" Maders and D.A.Maders "Mathematical Sophies", in which more than eighty mathematical sophisons, assembled from various sources assembled from various sources. Quote from the book: "Mathematical Sophism is, in essence, the plausible reasoning, leading to an implausible result. Moreover, the result can contradict all our ideas, but it is often not so easy to find a mistake in reasoning; Sometimes it can be rather thin and deep. The search for prisoners in the sophysism of errors, a clear understanding of their reasons lead to a meaningful comprehension of mathematics. Detection and analysis of the error concluded in sofiism often turn out to be more instructive than simply the analysis of the solutions of "error-free" tasks. The spectacular demonstration of "evidence" is clearly incorrect result, which is the meaning of Sophism, the demonstration of how nonsense gives the neglect of one or another mathematical rule, and the subsequent search and analysis of the error leading to the nonsense, allow the emotional level to understand and "consolidate" This or that mathematical rule or approval. Such an approach in teaching mathematics contributes to a deeper understanding and understanding. "

For the development of cognitive activity, mathematical software can be applied when studying mathematics at school:

1. in the lessons to make them more interesting to create problem situations;
2. in homework, for a more meaningful understanding of the material passed on the lessons (find a mistake in MS, come up with their MS);
3. when conducting various mathematical competitions, for a variety;
4. in the classes of optional, for a deeper study of themes of mathematics;
5. when writing abstract and research work.

Mathematical sophisms depending on the content and "hiding" in them the error can be used with various purposes in mathematics lessons when studying various topics.

When analyzing the MS, the main mistakes, "hiding" in MS:

1. division at 0;
2. incorrect conclusions from the equality of fractions;
3. improper extraction of square root from the square of the expression;
4. violations of the rules of action with named values;
5. confusion with the concepts of "equality" and "equivalence" against sets;
6. conducting transformations over mathematical objects that do not mean;
7. a non-uniform transition from one inequality to another;
8. conclusions and calculations on incorrectly built drawings;
9. errors arising from operations with endless rows and limit transition.

The purpose of the use of MS in mathematics lessons can be the most diverse:

1. study of the historical aspect of the topic;
2. creating a problem situation when explaining a new material;
3. checking the level of learned material;
4. for entertaining repetition and consolidation of the studied material.

Disassembly and solving any kind of mathematical tasks, and especially non-standard, helps to develop a mixture and logic. Mathematical sophisms belong to such tasks. In this section of the work, I will consider three types of mathematical sophisons: algebraic, geometric and arithmetic.

Algebraic sophisms.

1. "Two unequal natural numbers are equal to each other"

resolving the system of two equations: x + 2ow \u003d 6, (1)

Y \u003d 4- x / 2 (2)

substitution from the 2nd UR-I in 1

ray x + 8-x \u003d 6, from where8=6

where is the mistake??

Equation (2) can be written as X + 2U \u003d 8, so the source system is recorded as:

X + 2y \u003d 6,

X + 2y \u003d 8

In this system of equations, the coefficients with variable variables are the same, and the right parts are not equal to each other, it follows that the system is incomplete, i.e. Does not have a single solution. Graphically, this means that direct y \u003d 3-x / 2 and y \u003d 4-x / 2 are parallel and do not coincide.

Before you solve a system of linear equations, it is useful to analyze whether the system has a single solution, infinitely many solutions or has no solutions at all.

2. "Two two equals five."

Denote 4 \u003d a, 5 \u003d b, (a + b) / 2 \u003d d. We have: a + b \u003d 2d, a \u003d 2D-b, 2D-a \u003d b. Move the last two equality in parts. We obtain: 2DA-A * A \u003d 2DB-B * b. Multiply both parts of the received equality on -1 and add to the results D * D. We will have: a2 -2da + d 2 \u003d b 2 -2bd + d 2 , or (A - D) (A - D) \u003d (B - D) (B - D), from where A - D \u003d B - D and A \u003d B, i.e. 2 * 2 \u003d 5

Where is the mistake??

From the equality of the squares of the two numbers, it does not follow that these numbers themselves are equal.

3. " Negative number is more positive. "

Take two positive numbers a and c. Compare two relationships:

A -A.

With S.

They are equal, as each of them is equal to - (A / C). You can make a proportion:

A -A.

With S.

But if in the proportion of the previous member of the first relationship more than the subsequent, then the previous member of the second relationship is also more than its subsequent. In our case, A\u003e -C, therefore, should be -Ac, i.e. Negative number is more positive.

Where is the mistake??

This property of proportion may be incorrect if some members of the proportion are negative.

Geometric sophisms.

1. "Through the point, you can lower two perpendicular"

We will try to "prove" that through a point lying outside the straight, you can spend two perpendicular to this straight. For this purpose, take the triangle ABC. On the sides of the AV and the sun of this triangle, as in diameters, we construct a semicircle. Let these semi-rays intersect with a side of the speakers at the points E and D. connect the point E and D direct with the point B. The angle of AEV is direct, as inscribed, based on the diameter; The Angle of VVS is also straight. Consequently, it is perpendicular to the AP and VD perpendicular to the AU. Through the point in two perpendicular to the straight ax.

Where is the mistake??

The reasoning, that two perpendicular can be lowered from the point on the straight line, relied on the error drawing. In reality, the semicircle intersects with a side of the speakers at one point, i.e. Ve is coincided with cd. So, from one point in the straight can not be omitted two perpendicular.

2. "Match twice is longer than a telegraph pillar"

Let a DM - Length of match and bdm - length of the post. The difference between B and a is denoted by c.

We have b - a \u003d c, b \u003d a + c. Moving two of these equalities in parts, we find: b2 - AB \u003d CA + C 2 . Subscribe from both parts BC. Receive: B.2 - AB - BC \u003d CA + C 2 - BC, or B (B - A - C) \u003d - C (B - A - C), from where

b \u003d - C, but C \u003d B - A, therefore b \u003d a - b, or a \u003d 2b.

Where is the mistake??

In the expression B (B-A-C) \u003d -C (B-A-C), it is divided into (B-A-C), and this can not be done, since B-A-C \u003d 0. Suitable, the match cannot be twice as long as the telegraph pole.

3. "Katat is equal to hypotenuse"

Corner C is 90 o , VD - bisectaris of the angle of SPE, SC \u003d ka, OK perpendicular to sa, o - point of intersection of direct OK and VD, OM perpendicular to AV, OL perpendicular to Sun. We have: Triangle LVO is equal to the triangle MVO, Bl \u003d VM, OM \u003d OL \u003d SC \u003d KA, the Koa triangle is equal to the Ohm triangle (OA - the common side, ka \u003d ohms, the angle of the eye and the angle of Oma - direct), the angle of OAK \u003d Angle of Moa, OK \u003d Ma \u003d CL, VA \u003d VM + MA, Sun \u003d BL + LC, but VM \u003d BL, Ma \u003d CL, and because Va \u003d Sun.

Where is the mistake??

Reasoning, that catat is equal to hypotenuse relied on an erroneous drawing. The intersection point of the direct, defined bisector of the CD and the middle perpendicular to the speakers of the speakers, is outside the ABC triangle.

Here are some of the most interesting and entertaining sophisons:

1. “ In any circumference, chord, not passing through its center, is equal to its diameter "

IN arbitrary circle conduct diameterAB and chord speakers. Through the middle of D. this chord and pointIn conducting chord bes. Connecting points C andE, we get two trianglesABD and CDE. Corners of you and north are equal as inscribed in the same circle, resting on the same arc; CornersADB and CDE equal as vertical; PartiesAD and CD equal to building.

From here we conclude that trianglesABD and CDE equal (on the side and two corners). But the sides of equal triangles lying against equal angles themselves are equal, and therefore

AB \u003d CE

i.e. the circle diameter turns out to be equal to some (not passing through the center of the circumference) of the chord, which contradicts the statement that the diameter is more than any of the chord circumference.

Collapse of sofism.

In Sophism, it is proved that two trianglesABD and CDE equal, referring to the sign of the equality of triangles on the side and two corners. However, there is no such sign. Properly formulated sign of equality of triangles read:

If the side and the angles of one triangle adjacent to it are equal to the side and the angles of the other triangle adjacent to it, then such triangles are equal.

2. “ The circle has two centers "

Build an arbitrary cornerABC and, taking two arbitrary points on his partiesD. and e, we will restore the perpendicular to the sides of the angle. PERPENDICULARS These must cross (if they were parallel, were parallel to the partiesAB and SV). Denote their point of crossing the letterF.

Through three points D, E, F we carry out a circle, which is always possible, since these three points do not lie on one straight line. Connecting PointsN and G. (Points of intersection of the side of the cornerABC with a circle) with a pointF, we get two inserted into the circle of direct cornersGDF and HEF.

So we got two chordsGF and HF, on which direct corners are discouraged into circleGDF and HEF. But in the circle inscribed straight angle always relies on its diameter, therefore, chordsGF and HF. represent two diameters having a common pointF, lying on the circle.

Since these two chords, as we installed, diameters do not coincide, then, therefore, points O andAbout 19 dividing segments GF and HF in half, are nothing more than two centers of one circle.

Collapse of sofism.

The error here lies in the wrong drawing. In fact, a circle conducted through pointsE, F. and, it will definitely be through the topIn ABC angle, i.e. points in, e, f and d be sure to lie on the same circle. Then, of course, no sophism arises.

Indeed, restoring perpendicular at pointsE and d to direct sun and wa accordingly, and continuing them to mutual intersection at the point.F, we get a quadrangleBefd. . This quadrangle has the sum of the two opposite cornersBEF and BDF. equal to 180 °. But according to a well-known statement in geometry, it is possible to describe the circle then and only if the sum of the two opposite angles is 180 °.

From here it follows that all the vertices of the quadrangleBefd. must belong to one circumference. Therefore, the pointsG and N. they will coincide with the point in and the circumference will turn out to be, as it should be one center.

Arithmetic sophisms.

1. "If more than in, then and always more than 2V"

Take two arbitrary positive numbers A and B, such as the\u003e c.

Multiplying this inequality to B, we obtain a new inequality AV\u003e B * B, and using both parts A * A, we get the inequality of AV-A * A\u003e B * B - A * A, which is tantamount to the following:

A (B - A)\u003e (B + A) (in A). (one)

After dividing both parts of inequality (1) on in-and we get that

A\u003e B + A (2),

And adding to this inequality revengence initial inequality a\u003e in, we have 2a\u003e 2B + and where

2B.

So, if a\u003e in, then a\u003e 2B. This means, for example, from inequality 6\u003e 5 it follows that 6\u003e 10.

Where is the mistake??

Here was an unequal transition from inequality (1) to inequality (2).

Indeed, according to condition A\u003e B, so in

1. "One ruble is not equal to one hundred kokes"

It is known that any two inequalities can multiply by rear, not disturbing equality, i.e.

If a \u003d b, c \u003d d, then AC \u003d BD.

Apply this position to two obvious equalities

1 r. \u003d 100 kopecks, (1)

10P. \u003d 10 * 100Kop. (2)

multiplying these equalities by rear, we get

10 r. \u003d 100000 kopecks. (3)

and finally, dividing the last equality to 10 we get that

1 r. \u003d 10 000 kopecks.

thus, one ruble is not equal to one hundred kokes.

Where is the mistake??

The error made in this software is in violating the rules of action with named values: all actions performed above the values \u200b\u200bmust also be performed over their dimensions.

Indeed, multiplying equality (1) and (2), we will not get (3), and the following equality

10 r. \u003d 100 000 to.,

which after division by 10 gives

1 r. \u003d 10 000 kopecks, (*)

and not equality 1p \u003d 10,000 K, as it is recorded in the condition of sofism. Removing the square root from equality (*), we obtain the faithful equality 1p. \u003d 100 kopecks.

1. « The number equal to another number is simultaneously more, and less than it. "

Take two arbitrary positive equal numbers A and in and write and write the following obvious inequalities for them:

A -B and in\u003e -B. (one)

Alternating both of these inequalities, we get inequality

A * B\u003e B * B, and after his division on B, which is completely legal, because in\u003e 0, we will come to the conclusion that

A\u003e c. (2)

Referring the same two others as indisputable inequalities

In\u003e -A and a\u003e -a, (3)

Similarly, we obtain the previous one that B * A\u003e A * A, and dividing on a\u003e 0, we will come to inequality

A\u003e c. (four)

So, the number A, equal to the number in, at the same time, and more, and less it.

Where is the mistake??

Here was an unequal transition from one inequality to another with unacceptable multiplication of inequalities.

We will do the correct transformations of inequalities.

We write inequality (1) in the form of a + in\u003e 0, B + V\u003e 0.

Left parts of these inequalities are positive, therefore, multiplying both of these inequalities

(A + c) (B + c)\u003e 0, or a\u003e -B,

what is simply faithful inequality.

Similar to the previous, recording inequalities (3) in the form of

(B + a)\u003e 0, a + a\u003e 0, we will simply get faithful inequality in\u003e -A.

1. "Achilles will never catch up to the turtle"

The ancient Greek philosopher Zenon argued that Achilles, one of the strongest and brave heroes, precipitated the ancient three, will never catch up with a turtle, which is known to be extremely slow vehicle speed ..

Here is an exemplary scheme of Zenon's reasoning. Suppose that Achilles and Turtle begin their movement at the same time, and Achilles seeks to catch up with a turtle. We will take for certainty that Achilles moves 10 times faster than the turtle, and that they are separated from each other 100 steps.

When Achilles runs the distance of 100 steps, separating it from the place where the turtle began to move, then in this place he will not find it, as it will go ahead of the distance in 10 steps. When Achilles passes and these 10 steps, then there will no longer be there, because it will have time to go to 1 step forward. Having achieved this place, Achilles again will not find a turtle there, because she will have time to go through a distance equal to 1/10 step, and again will be somewhat ahead of him. This reasoning can be continued to infinity, and will have to admit that a quick-legged Achilles will never catch up a slowly crawling turtle.

Where is the mistake??

The considered Sophism of Zenon even today far from its final permission, so here I will indicate only some of his aspects.

First, we define the time T, for which the Achilles will catch up with a turtle. It is easily located from the equation A + VT \u003d WT, where A is -Acurity between the Achilles and the turtle before the start of the movement, V and W - the velocities of the turtle and the Achilles, respectively. This time as conditions taken in sofism (V \u003d 1 step / s and w \u003d 10 steps / s) is 11, 111111 ... sec.

In other words, approximately 11, 1 s. Achilles will catch up the turtle. Now suit now to the statements of Sophism from the point of view of mathematics, follow the logic of Zenon. Suppose that Achilles must pass as many segments as their turtle passes. If the turtle, until the meeting with Achilles, will pass M seglings, then the Achilles must pass the same m segments plus another segment that separated them before the start of the movement. Consequently, we come to the equality m \u003d m + 1, which is impossible. Hence it follows that Achilles will never catch up to the turtle !!!

So, the path passed by the Achilles, on the one hand, consists of an infinite sequence of sections that take an endless series of values, and on the other hand, this endless sequence, obviously does not have the end, still ended, and it ended with its limit equal to the amount of geometric Progression.

The difficulties that arise when operating with the concepts of continuous and infinite and so masterfully opened by paradoxes and sophisticates of Zenon, have not yet been overcome, and the resolution of the contradictions contained in them served to a deeper understanding of the foundations of mathematics.

Conclusion.

We can talk about mathematical sophysums infinitely a lot, as well as about mathematics in general. From day to day, new paradoxes are born, some of them will remain in history, and some existence one day. Sophisms have a mixture of philosophy and mathematics, which not only helps to develop logic and look for a mistake in reasoning. Literally remembering who these were sophists, it can be understood that the main task was to comprehend philosophy. But nevertheless, in our modern world, if there are people who are interested in sophisms, especially mathematical, then they study them as a phenomenon only on the part of mathematics to improve the skills of the correctness and logic of reasoning.

Understand the Sophism as such (to solve it and find a mistake) is not immediately. Requires a certain skill and incistent. The developed logic of thinking will help not only in solving any mathematical tasks, but can also come in handy in life.

Historical information about sophistry and sophistants helped me figure out where the history of Sophisoms began from all the same. At first, I thought that sophysms were exclusively mathematical. Moreover, in the form of specific tasks, but, starting a study in this area, I realized that Sophisticatics is a whole science, namely, mathematical sophisms are only part of one large current.

Explore the sophisms are really very interesting and unusual. Sometimes you fell on the tricks of the Sofista, at such an impeccability of his reasoning. Before you opens some special world of reasoning, which truly seem true. Thanks to sophimons (and paradoxes), you can learn how to seek errors in the arguments of others, will learn how to competently build your reasoning and logical explanations. If there is a desire, then you can become a skillful sophist, to achieve exceptional skill in the art of eloquence or simply at leisure to test your smell.

http://www. lebed.com/2002/art2896.htm.

http://fio.novgorod.ru/projects/project1454/logich_sof.htm

Sophism is the word of Greek origin, and it is translated as "fiction" or "trick". This term is used to designate the assertion, which is false, but at the same time carrier particle of logic. Therefore, at first glance, it seems true. But still not everyone is clear what is sophism and what is the difference between it and paralogenesis? The difference is that in sophies used conscious deliberate deception, there is a violation of logic.

The history of the emergence of the term

Sophies began to be interested in a person many centuries ago. An Aristotle spoke about this: Sophism is imaginary proofappearing due to lack of logical analysis, because of which the judgment acquires a subjective nature. Convincing arguments are used for disguise purposes and are designed to hide a logical error that is always present in any sophist statement.

Understand what software is, not so difficult. It is enough to turn to the example of an ancient violation of logic: "You have something that did not lose. Lucky horns? So you have a horns. " In this case, there is a omission. If you add a new word to the phrase, you can get the following: "You have everything that did not lose." With a similar interpretation, the conclusion becomes true, but it does not seem interesting. The first followers of sofics said that the statement must meet the main requirement - the worst argument should turn into the best, and the dispute is needed to win it, and not find the truth.

According to the sophists, any opinion can be recognized correct, but then happens denial of the law contradictionwhich later formulated Aristotle. All this subsequently led to the emergence of many species of soffisms in different sciences.

Many sophisms originate from terminology, which is used during the dispute. There are quite a few words with different interpretations. It just leads to violation of logic. For example, in mathematics, the sophisms are built by changing numbers that change, and then compare the initial and obtained data.

Still sophists can use as a reception incorrect strokeAfter all, there are quite a few words that lose their original meaning when changing the emphasis. Sometimes there are so confusing phrases that can cause ambiguous interpretations. A vivid example of this may be such an arithmetic operation: two multiply by two plus five. It is difficult to say what is most important in this phrase - the amount of twos and fives multiplied by two or the amount of the works of twos and fives.

Sophisticated sophisms

There are also more complex logical sophisms that require a detailed consideration. For example, the phrase may contain a parcel that requires proof. In other words, the argument can be considered as only when it is proved. Also violation can be criticism Opponent's opinions, designed to destroy mistakenly attributed judgments. This phenomenon is very often faced by each of us in everyday life, when people attribute to each other certain motives that do not belong to them.

Also, instead of the phrase, a certain reservation, an expression in which there is no such reservation can be used. Since attention does not sharpen on a specially missed fact, the approval acquires a rather logically correct and reasonable appearance.

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

Causes of Sophisoms

It is customary to allocate psychological causes of sophisons, among which the most common are:

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

In other words, if a more accredited person is involved in the conversation, he should only start his opponent in a dead end, and then the latter will easily take the point of view suggested him. A person who unstable to affective reactions is easily amenable to its feelings and accepts sophisms for true statement. Such situations are very common, and emotional people often fall into them.

Speaking in front of those surrounding with Sophism, a person must be convincing. Then he will have more chances that people will believe him. It is on this that the rate is made when people use such techniques in the dispute. But in order to better understand why people resort to this reception, it is necessary to get acquainted with it more in more detail, because Sophism is often in logic very often be ignored by an unprepared person.

Intelligent and affective causes

A well-pitched man familiar with the basics of sofics, always pays attention to how and what he says, and also gets all the arguments of the interlocutor who leads in his speech. Such people are very attentive and not melted by any little thing. They are accustomed to looking for answers to unknown questions, and not act in templates. In addition to this, they possess a large vocabulary that allows maximum make one's thoughts.

Not the last role is also played by the volume of knowledge. With the right use of soffisms in mathematics, an intellectually developed person is easier to achieve victory in a dispute than a small and undeveloped.

One of the reasons for the defeat in the dispute may be afraid of the consequences, so a person can very quickly abandon his initial point of view, being not capable of bringing convincing arguments.

Volitional

When two people discuss their points of view, they affect the mind and feelings of each other, as well as to the will. If a person is confident and has such a valuable quality as an assertion, then he has there is more chances to defend your opinionEven if it was formulated with a violation of logic. Most effectively apply this technique against large clusters of people who are susceptible to the effect of the crowd and cannot be seen in human speeches.

Being in front of such people, a person will not be difficult to bring convincing evidence regardless of what is the subject of discussion. But during the dispute in which a person uses the reception of sofism, it should be very active. The audience, to which he drawn, should remain passive, since such people are easiest to be exposed to someone else's influence.

From this we can conclude: to achieve the necessary result with the help of sophist statements, each party, which participates in the conversation, should behave in a special way. At the same time, the quality of each personality separately affect the outcome of the subject discussed.

Sophism: examples

Many centuries ago, the first supporters of sofics formulated the statement where they were shown simple violations of logic. They are designed to work up the ability to argue, since it is very simple to see the inconsistency in these phrases.

Logic paradoxes

It should be able to distinguish paradoxes and sophysms, because it is universal concepts. Under the paradox it is customary to understand the judgment that can prove that judgment can be both false and true. This phenomenon is two types:

• apriya;
• antinomy.

In the first case, there is a conclusion that contradicts the experience. This clearly demonstrates the paradox, which was formulated by Zeno: Fresh-legged Achilles lagged behind the turtle all the time, because at each new step she moved to him for a certain distance, without giving him to catch up with himself, as the process of dividing the segment of the path is endless.

Antinomy should be considered as a paradox that implies the presence of two mutually exclusive judgmentswhich are simultaneously considered true. An example of this can serve as the phrase "I LDU". It can be viewed simultaneously as truth and lies. But if a person speaks the truth during her pronunciation, it cannot be considered a liar, although the phrase points to the opposite. There are other entertaining 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 bright example - when the five and one compares. If there are three out of five, then the result will be twice. Utrievable from the top three, we will get a twice. If you build both numbers per square, then in each case the result will be the same. Therefore, we can conclude that five is equal to one.

The appearance in mathematics of tasks-soffisms is mainly happening due to the transformation of source numbers. For example, when they are elevated in a square. After performing these simple actions, it is possible to obtain that the results of these transformations will be the same, which makes it possible to talk about the equality of the source data.

Cause obstacle

Frederick Bastia is the author of one of the most common sophisons. Among them are quite aware of the violation of the logic "Cause, obstacle". Primitive man was very limited in his capabilities. Therefore, to obtain any item and result, he had to solve many tasks.

If you consider a simple example with overcoming the distance, then it can be seen from it that it is difficult for a person to independently overcome all barriers that may arise on any single traveler. We live in such where the solution to the problem of overcoming obstacles is engaged in people who specialize in this kind of activity. And these obstacles these people managed to do for themselves one of the main sources of earnings.

The emergence of any new obstacle puzzles many peoplewho are trying to overcome them. Therefore, the presence of obstacles is unthinkable for modern society, because they make it possible to enrich each person individually, and, it means, the whole society as a whole.

Conclusion

Only intellectually competent people know about the existence of sophisons today. This is one of the effective techniques that helps a person to see victory in the dispute, although it has no reason for this. A person thus lines a conversation with people that the phrases used in his statements help convince other people in his rightness. You can even say that he is simply confused by man And it does not allow him to bring effective counterprocements that would help to defend his point of view.

Sometimes sometimes are so convincing that no other arguments of opponents cannot resist. However, the victory in such a dispute largely depends not only on the person himself, which uses sophisms, but also the behavior of those people for whom they are intended.

SOPHISM

SOPHISM

(Greek Sophisma is a tricky trick, fabrication) - reasoning, apparent correct, but containing a hidden logical error and serving to give the visibility of the truth of a false statement. S. is a special technique of intellectual fraud, an attempt to issue for the truth and thereby introduce in. From here "" in odious meaning is ready with any, incl. Unauthorized, techniques to defend their beliefs, not believing with the fact that they really are true or not.
Usually C. justifies K.N. Snacking absurdity, or paradoxical, contrary to generally accepted ideas. An example is the famous St. S. "Horned" famous in antiquity: "What you did not lose, then you have; Horn you did not lose; So you have a horns. "
Dr. Examples of C. Formulated again in antiquity:
"Sitting stood; who got up, he stands; Consequently, sitting stands ";
"But when they say" stones, logs, iron ", then it is silent, but they say!";
"You know what I want to ask you about now? - Not. - Do you really know what to lie is not good? - Of course I know. - But it was about this that I was going to ask you, and you answered that you do not know; It turns out, you know what you do not know. "
All these and those of S. are logically incorrect arguments issued for the correct. C. Use words of the usual language, homonymy, abbreviations, etc.; Often C. Based on such logical errors as the substitution of thesis of evidence, non-compliance with the rules of logical conclusion, accepting false parcels for true, etc. Speaking about the imaginary persuasiveness of S. Seneca compared them with the art of magicians: we cannot say how they are performed by the manipulation, although we know that everything is done at all as it seems to us. F. Bacon compared the one who resorts to S. with a fox, which loops well, and the one who reveals S. - with a hound that can unrule tracks.
It is easy to see that in S. "Horned" the ambiguity of the expression "What did not lose" begins. Sometimes it means "what I had and did not lose", and sometimes simply "what was not lost, regardless of whether or not." In the premise "What you did not lose, then you have" turnover "What I didn't lose" should mean "what you had and not lost", otherwise this will be false. But in the second premise it no longer passes: the saying "Horn is what you had and not lost" is false.
C. It was often used and used with the intention to mislead. But they also have a function, being a kind of form of awareness and verbal expression of the problem situation. The first on this feature of S. Fedal G.V.F. Hegel.
A series of S. Ancients begins the topic of the jump-like nature of all changes and development. Some S. raise the turning problem, the variability of the world and indicate the difficulties associated with the identification of objects in the stream of continuous change. Often C. put in an implicit form of proof: what is it, if you can make sure the statements explicitly incompatible with the facts and common sense? Formulated at that time, when science has not yet existed, the ancient C. Although indirectly, the question of the need to build it. In this regard, they directly contributed to the emergence of science on the right, evidenceful thinking.
The use of S. In order to deceive is an incorrect admission of argument and is quite reasonable to criticize. But this should not blame the fact that S. is also inevitable at a certain stage of the development of thinking implicit formulation of problems.

Philosophy: Encyclopedic Dictionary. - M.: Gardariki. Edited by A.A. Ivin. 2004 .

SOPHISM

(from greek. - Sandy trick, fabrication), logically incorrect (imaginary) reasoning (conclusion, proof), issued for the right one. Hence the "" in odious meaning - a person who builds false conclusions and is looking for a caustic from such imaginary argumentation. A variety of examples of S. leads in their dialogs to Plato ("Evtidad" and dr.) . Logic. S. and their classification gave Aristotle in cit. "On Sophistic. refutations " (cm. Cit. t. 2, M., 1978). An example of the ancient S. is C. "Horned": "What you have not lost, you have; You did not lose horns; Consequently, you have them. " The error here is in unlawful conclusion from general rules To a private case, which does not essentially envisage. Common S. are eg, reasoning, built on arbitrarily selected, favorable alternatives for Sofist, with the help of which, generally speaking, you can prove anything. C. Sometimes calling reasoning, which are essentially paradoxes (eg, "Liar", "Pile"). However, these concepts should be distinguished: in contrast to paradoxes in S., valid logic is not manifested. Difficulties. C. Arrive as a result of knowingly incorrect application logic. and semantich. rules and operations.

Jevons V.S., elementary textbook of the logic of deductive and inductive, per. from english, St. Petersburg, 1881; Minto V., deductive and, per. from english, M., 18983.

Philosophical encyclopedic dictionary. - M.: Soviet Encyclopedia. GL Editorial: L. F. Ilyichev, P. N. Fedoseev, S. M. Kovalev, V. G. Panov. 1983 .

SOPHISM

(from Greek. Sophisma - Sunbreaking)

visibility of proof. see also Wrong conclusion.

Philosophical Encyclopedic Dictionary. 2010 .

SOPHISM

(from Greek. σόφισμα - Sunnaya trick, fiction, false) - logically incorrect (insolvent) reasoning (conclusion, proof) issued for the right one. Hence the "Sofist" in odious meaning - persons ready with the help of any techniques to defend K.L. Abstracts, not believing with their objective truth or falsity, which was characteristic of some late ancient Greek. Sofists, in the first reasoning and arguments were degenerated into the art of "dispute for the sake of a dispute". A variety of examples of S. leads in their dialogs to Plato ("Evtidey" and others). Logic. The analysis of S. gave Aristotle in Op. "Refuture of sophistic arguments"; He pointed out that C. may result from ambiguity of the value. words (or their combinations) or due to violation of the rules of logic. A common view of C. are reasoning built on arbitrarily selected, favorable alternatives, with the help of to-ry, generally speaking, you can prove anything. The argument of this kind is usually equal to the right to oppose the opposite reasoning. So, according to the story of Aristotle, one Athenian woman inspired her son: "Do not interfere in societies. Cases, because if you tell the truth, you will be raised by people, if you are going to tell you, you will be hated the gods" - for what, of course, You can argue: "You have to participate in societies. Affairs, because if you tell the truth, you will love the gods, and if you are going to tell you, people will love you." C. Sometimes they call reasoning, which are essentially paradoxes (eg, "liar", "pile"). But these concepts should be distinguished. In contrast to paradoxes, in S. do not manifest actual logic. Difficulties are knowingly incorrect use of semantich. and logic. rules and operations.

LIT: Jevons V.S., elementary textbook of logic deductive and inductive with questions and examples, [per. from English], spb, 1881; Minto V., deductive and inductive logic, per. from English, 6 ed., M., 1909; Akhmanov A.S., Logic. Aristotle's teachings, M., 1960.

A. Subbotin. Moscow.

Philosophical encyclopedia. In 5 tons - M.: Soviet Encyclopedia. Edited by F. V. Konstantinova. 1960-1970 .

SOPHISM

Sophism (from Greek. Sophisma is a trick, tricks, fiction, puzzle) - reasoning, conclusion or convincing (argument), justifying any obvious absurdity (absurd) or a statement contrary to generally accepted ideas (paradox). Here is a sophism based on separation of the meaning of a whole: "5 \u003d 2 + 3, but 2 even, and 3 is odd, therefore 5 at the same time even and odd." But the Sophism, built with a violation of the law of identity and the semiotic role of quotes: "If Socrates and man is not the same, then Socrates is not the same that Socrates, since Socrates is a man." Both of these sophysism leads Aristotle. He called "imaginary evidence" sophysms, in which the validity of the conclusion only apparent and is obliged to a purely subjective impression caused by the lack of logical or semantic analysis. The external persuasiveness of many sophisons, their "logicality" is usually associated with a well-disguised error - semiotic (due to metaphoricity of speech, amonymy or polisia of words, amphibolia, etc.), which violates the uniqueness and leading to the mixing values \u200b\u200bof terms, or logical (by ignoring or replacing the thesis in case of evidence or refutation, errors in the removal of the consequences, the use of "unresolved" or even "prohibited" rules or actions, for example, dividing to zero in mathematical sofesums).

Historically, with the concept of "Sophism", they invariably connect about the intentional falsification, guided by the recognition of the protagodore that the task of the Sofist is to present the worst as the best way of ingenious tricks in speech, taking care of not about the truth, but about the practical benefit, about the success in dispute or in litigation. With the same task, its famous "base criterion" is usually associated: there are truths of man. Already Plato, who called the Sophistic of the "Shamed Rhetoric", noticed that it should not be in the subjective will of a person, otherwise the contradictions will have to recognize, and therefore any judgments are considered reasonable. This thought of Plato found in the Aristotelian "principle of consistent" (see the law logical) and, already in modern logic, - in the requirement of evidence of absolute consistency of theories. But it is quite relevant in the "Truth of Mind", this requirement is not always justified in the field of "actual truths", where the bases of the protagora, understood, however, is more widely, as the relativity of the truth to the conditions and means of its knowledge, it turns out to be very significant. Therefore, many reasoning leading to paradoxes, but otherwise flawless, are not sophisms. Essentially, they only demonstrate the interval associated gnoseological situations. Such, in particular, the well-known Aquaries of Zenon Elayky or so-called. Sophism "Pile": "One grain is not a bunch. If η grains are not a bunch, then η + 1 is also not a bunch. Consequently, any grains are not a bunch. " This is not Sophism, but only one of the transitivity paradoxes arising in situations of indistinguishability (or interval equality) in which mathematical induction not applicable. The desire to see in this kind of situations "intolerable contradiction" (A. Poancare), overcome in the abstract concept of mathematical continuity (continuum), does not solve the issue in the general case. It suffices to say that the ideas of equality (identities) in the field of actual truths significantly depends on what means of identification use. For example, it is not always possible for us to replace an abstraction of indistinguishability to replace the abstraction of identification. And only in this case, it is possible to count on "overcoming" contradictions of the type of transitivity paradox.

The first to understand the importance of theoretical analysis of soffisms were, apparently, themselves (see Sophisticatics). The doctrine of the correct speech, the proper use of the names of the prerigation considered the most important. Analysis and examples of sophisons are also presented in Plato's dialogues. But their systematic analysis, based on the theory of syllogistic conclusion (see Silchistics), belongs to Aristotle. Later, the mathematician Euclid wrote a "pseudarium" - a kind of catalog of soffisms in geometric evidence, but it has not been preserved.

Lit.: Plato. Op., T. 1. M., 1968 (Dialogues: "Protagor", "Gorgay", "Menon", "Paint"), t. 2. M., 1970 (Dialogues: "Theette", "Sofist") ; Aristotle. "On sofissistic refutations." Op., Vol. 2. M., 1978; Akhmanova, S. logical Teaching Aristotle. M., I960, ch. 13.

M. M. Novoselov

New philosophical encyclopedia: 4 tt. M.: Thought. Edited by V. S. Stupina. 2001 .

Synonyms:

Watch what is "Sophism" in other dictionaries:

- (Greek, from Sophos wise). Intentionally false conclusion, incorrect judgment that came appearance Truths. A dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. Sophism of Greek. Sophismos, from Sophos, wise. False judgment, ... ... Dictionary of foreign words of the Russian language

Sophism - Sophism ♦ Sophisme This case has happened to me for fifteen years ago, in Montpellier, in the courtyard of an excellent mansion of the XVIII century, turned into an amphitheater. Within the framework of the festival conducted by the Society "Culture of France", I participated in the dispute about ... ... Philosophical Dictionary Sponville

See trick ... Synonym dictionary

Sophism

But modern Sophism, justifying that with the age of "years of life" not only seem, but in fact, in short: "Every year of your life is its part, where - the number of years lived by you. But. Hence, ".

Historically, the concept of "Sophism" invariably connect the idea of \u200b\u200bintentional falsification, guided by the recognition of the protagora that the task of the Sofist is to present the worst argument as the best way in cunning tricks in speech, in reasoning, taking care of not about truth, but about the success in dispute or practical Become. (It is known that Protigor himself was a victim of "Evatla Sophism"). With the same idea, the "base criterion" is usually associated with prothagora: the opinion of man is a measure of truth. Already Plato noticed that the foundation should not be concluded in the subjective will of a person, otherwise it will have to recognize the legality of the contradictions (which, by the way, and approved the sophists), and therefore any judgments are considered reasonable. This idea of \u200b\u200bPlato was developed in the Aristotelian "principle of non-contradiction" (see Logical Law) and, already in modern logic, - in interpretations and the requirement of evidence of "absolute" consistency. Transferred from the field of clean logic to the "actual truth" region, it spawned a special "style of thinking", ignoring the dialectic "interval situations", that is, such situations in which the criterion of the protagora, understood, however, is more widely as the relativity of truth to the conditions and The means of its knowledge, it turns out to be very significant. That is why many reasoning, leading to paradoxes and otherly impeccable, qualify as sophysms, although essentially they only demonstrate the intended nature of the gnoseological situations associated with them. Thus, Sophism "Pile" ("One grain is not a bunch. If the grain is not a bunch, then the grain is also not a bunch. Therefore, any number of grain is not a bunch") - this is just one of the "transitivity paradoxes" arising in the situation " Indistentness. " The latter serves as a typical example of an interval situation, in which the property of transitivity of equality in the transition from one "interval of indistinguishability" to another, generally speaking, is not preserved, and therefore the principle of mathematical induction in such situations is not applicable. The desire to see in this characteristic of the experience "intolerable contradiction", which the mathematical thought "overcomes" in the abstract concept of numerical continuum (A. Poancare) is not justified, however, general evidence of elimination of this kind of situations in mathematical thinking and experience. It is enough to say that the description and practice of applying such important "laws of identity" (equality) in this area, generally speaking, as in empirical sciences, depends on what sense is investing in the expression "one and the same object", which At the same time using the means or criteria of identification. In other words, whether there is a speech about mathematical objects or, for example, about the objects of quantum mechanics, the answers to the question of identity are subjectly connected with the interval situations. At the same time, it is not always that a solution to this question "inside" the interval of indistinguishability can be opposed to the decision "above this interval", that is, replace the abstraction of indistinguishability by the abstraction of identification. And only in this last case, and you can talk about "overcoming" contradictions.

Apparently, the first to understand the importance of semiotic analysis of soffisms, the Sofists themselves were. The doctrine of speech, the proper use of the names of the predica considered the most important. Analysis and examples of sophisons are often found in Plato's dialogues. Aristotle wrote a special book "On Sophistic Denials", and Mathematics Euclidean - "Pseudaria" - a peculiar catalog of sophisons in geometric evidence. The writing of "Sophism" (in two books) wrote a student of Aristotle Feofrast (D.L. V. 45). In the Middle Ages in Western Europe Completed whole collections of sophisons. For example, a meeting attributed to the English philosopher and the logic of the XIII century Richard Sofista, there are over three hundred sophishes. Some of them resemble the statements of representatives of the Ancient Chinese School of Naming (Min Jia).

Error classification

brain teaser

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

1. Conclusion with a negative smaller parcel in the first figure: "All people are reasonable creatures, residents of the planets are not the essence of people, therefore, they are not the essence of reasonable creatures";
2. Conclusion with affirmative parcels in the second figure: "All those who are in innocent women should be against punishment; You are against punishment, it means that you find her innocent ";
3. Conclusion with a negative smaller package in the third figure: "The law of Moses prohibited theft, the law of Moses lost its strength, therefore, theft is not prohibited;";
4. Especially common QUATERNIO Terminorum error, that is, the use of an average term in large and in a smaller premise is not in the same meaning: "All metals - simple substances, Bronze - Metal: Bronze is a simple substance "(here in a smaller premise The word" Metal "is used not in the exact chemical value of the word, denoting the alloy of the metals): From here, four term is obtained in Slogism.

Terminological

Grammatical, terminological and rhetorical sources of sophisons are expressed

In oral speech, mathematicians introduced such words as the "amount", "work", "difference". So - the amount of the work is two to two and five, and the double sum of two and five.

• More complex sophisms result from improperly constructing a whole complex course of evidence, where logical errors are disguised inaccuracies of external expression. These include:
  1. Petitio PrinciPII: Entering the conclusion that you want to prove, in a hidden form in proof as one of the parcels. If we, for example, wanting to prove the immorality of materialism, will be eloquently insist on its demoralizing effect, without worrying up to give a report, why it is materialism - an immoral theory, then our reasoning will enter into Petitio PrinciPii.
  2. Ignoratio Elenchi is that by starting to prove some thesis, gradually in the course of evidence, they transfers to proof of another position similar to the thesis.
  3. A DICTO SECUNDUM AD DICTUM SIMPLICITER replaces the assertion that said with the reservation is not accompanied by this reservation.
  4. Non Sequitur presents the absence of an internal logical connection during the reasoning: any disorderly following of thoughts represents a special case of this error.

Psychological

Psychological reasons for C. There are a trojaci kind: intellectual, affective and volitional. In any ways to exchange thoughts, interaction is assumed between 2 persons, a reader and author or lecturer and a listener, or two arguing. Conviction C. Therefore, there are two factors: α - the mental properties of one and β - another of the sides exchanging. The plausibility of S. depends on the agility who protects it, and the reducibility of the opponent, and these properties depend on the various features of both individualities.

Intelligent reasons

Intelligent reasons for sofism are to prevail in the mind of a person who suggested by S., associations on arrangement of associations in similarity, in the absence of the development of the ability to manage attention, actively think, in poor memory, unusual to accurately word, the poverty of actual knowledge on this subject, tension in Thinking (IGNAVA Ratio), etc. Reverse qualities, of course, are the most beneficial to the person protecting S.: Denote the first negative qualities through, the second corresponding positive through them.

Affective reasons

This includes cowardice in thinking - fear of dangerous practical consequences arising from the adoption of a well-known position; hope to find facts confirming the valuable views of us, which encourages us to see these facts where they are not, love and hatred, firmly associated with well-known ideas, etc. Wishing to seduce his opponent's mind Sofist should be not only a skillful dialectic, but and a human heart connoisseably able to masterly dispose of other people's passions for their purposes. Denote the affective element in the soul of a skillful dialectic, which managed to them as an actor to touch the enemy, through, and those passions that are awakened in the soul of his victim and drench the clear thinking through it. Argumentum Ad Hominem, introducing personal accounts, and Argumentum Ad Populum, affecting the crowd's affects, represent typical C. with the predominance of an affective element.

Volware reasons

When exchanging opinions, we are impact not only on the mind and feelings of the interlocutor, but also on his will. In any argument (especially oral), there is a volitional element - an imperative - element of suggestion. The categorization of the tone that does not allow the objection defined by the Mimica, etc. () apply irresistiblely on persons who are easy to sustain, especially for the masses. On the other hand, the passivity () of the listener is especially favored by the success of the opponent's argument. Thus, any S. involves the relationship between six mental factors :. Success C. Determined by the value of this amount in which the indicator of the dialectic force is indicator of the weakness of its victim. A wonderful psychological analysis of sofics gives Schopenhauer in his "erystics" (Transl. KN. D. N. Cerevyev). It goes without saying that logical, grammatical and psychological factors are closely related to each other; Therefore, S., representing, for example, from a logical point of view of Quatenio Ter.

Method for finding a mistake in sofism

• Carefully read the condition proposed to you. Start your error search is better from the terms of the proposed sophism. In some sophies, the absurd result is obtained due to contradictory or incomplete data in the condition, the incorrect drawing, false initial assumption, and then all the arguments are carried out correctly. This causes difficulties when searching for an error. Everyone got used to the tasks, alleged in various literature, do not contain errors in the condition and, therefore, if it turns out an incorrect result, then they are looking for an error by certainly in the course of the solution.
• Install the areas of knowledge (themes), which are reflected in the Sophism proposed by transformations. Sophism can be divided into several topics that will require a detailed analysis of each of them.
• Find out whether all the conditions of applicability are respected by theorems, rules, formulas, whether logical is observed. Some sophisms are built on incorrect use of definitions, laws, on "forgetting" conditions of applicability. Very often in the wording, the rules are remembered by the main, main phrases and suggestions, everything else is missed. And then the second sign of the equality of triangles turns into a sign "on the side and two corners."
• Check the conversion results with reverse action.
• Often, work should be divided into small blocks and monitor the correctness of each such unit.

Examples of Sofamov

Semi-empty and half-metal

The semi-empty is the same as half-footed. If half are equal, it means that are equal and integers. Consequently, there is an empty the same as complete.

Thick and odd

5 is ("two and three"). Two - the number is onely, three - odd, it turns out that five is the number and something and odd. Five is not divided into two, as well as, it means, both odd numbers.

You do not know what you know

Do you know what I want to ask you?
- Not.
- Do you know that the virtue is good?
- I know.
- I wanted to ask you about it. And you, it turns out, do not know what you know.

Medicine

The medicine taken by the patient is good. The more do good, the better. So, drugs need to be taken as much as possible.

Thief

The thief does not want to acquire anything wrong. The acquisition of good is a good thing. Consequently, the thief wishes good.

Horned

Do you have what you did not lose? Of course have. You did not lose horns, then you have.

2=3

The error is that it is impossible to divide on zero (5-5).

Literature

• Akhmanov A.S., Logical Teaching Aristotle, M., 1960;
• Brutin G. Paraloogism, Sophism and Paradox // Questions philosophy. 1959.№ 1.S.56-66.
• Brandis V. M., Minkowski V. L., Elenev L. K., Errors in mathematical reasoning, 3 ed., M., 1967.
• Bielik A.M., Bilyk Ya.M. To the question of the problematic technology of Sophism (its connection with a modern understanding of the scientific problem) // Philosophical Sciences. # 2. 1989. - p.114-117.
• Morozov N. A. On the scientific meaning of mathematical sophisons // Izvestia Scientific Institute. P. F. Lesgafta. GH., 1919.t.1.c.193-207.
• Pavlyukevich V. V. Logical and Methodological status of Sofamov // Modern Logic: Problems of Theory, History and Applications in Science. St. Petersburg., 2002. P. 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 challenges and sophisms in physics. M. 1971.
• Dyubin R. N. Collection of "Tasks" Richard Sofista as a context for "paradoxes" of the ancient Chinese school of names // Bulletin of RHGA No. 6, St. Petersburg., 2005. P. 217-221. http://www.rchgi.spb.ru/pr/vest_6.htm.
• Narcarryan KV, Sophism and Paradoxes, 1 Edition, 2001

see also

Wikimedia Foundation. 2010.

Synonyms: §47. Trick - Error - Sophism

§ 47. In conclusion of this section, it is necessary to say a few words about those cases when the speaker deliberately resorts to unauthorized techniques and is trying to influence the audience with sophisons.

Sometimes the question arises: whether it is necessary to get acquainted with dishonest techniques for the impact on the audience, do we encourage the speakers in such a way? This question needs to categorically answer negatively. Observations show that, unconsciously copying the current oratorical practice, people consume socialism in their speech, without giving themselves the report in the fact that they are resorting to the deception of the audience. The "ladies' argument", an imposed consequence, insinuation, anticipation of the foundation, are especially often used. But here, as in legal practice, ignorance does not relieve responsibility. Therefore, the consideration of unauthorized receptions and the qualifications of them as invalid will help much more reliably protect the beginners of the speakers from their use. At the same time, if the speaker still uses speculative techniques, this gives the right to strongly condemn its actions without making discounts on the uninimed nature of this act. There is another side of this phenomenon. As already mentioned, in modern social practice to socialism, they are resorted very actively. It is clear that rhetorically prepared listeners should be able to recognize dishonest techniques used against them, not to deceive themselves. As the famous aphorism reads: "warned, it means armed." About the need for a mandatory acquaintance with sophimons for all students writing a French philosopher Pierre Abelar in the twentieth century: "After all, just as a just man needs to also know the evil to make it, but in order to avoid disgraced evil , like this, the dialectic should have an understanding of sophisms in order to avoid themselves from them. And he will understand in reasonable arguments only if, disinterested as false and true, it will be able to distinguish the first from the second And just judged about both "..." Since it is necessary to know them the opposite to know any items. "

That is why in all sections of the book we tried to draw the attention of readers to the most common techniques of use in the modern speech practice of rhetorical categories in speculative purposes. And in conclusion, we give several generalizing comments.

The most fully and accessible described unacceptable techniques for the construction of the impact speech Famous Russian Logic S.I. Cook at the beginning of our century. All later work on this topic is largely the retelling or variations on the classification given to them in the book "Spore about the theory and practice of the dispute." That is why we will refer everywhere to this work. In addition, it is also interesting to the fact that it gives the distinction of the concepts of "trick", "error" and "Sophism".

Trick, according to S.I. Cook, is a tactical reception that helps win a dispute. It has a trick, but there is no direct deception. A typical example of a trick is "flattery opponent": " the person is not enough formed will not appreciate this argument, but you ...". Nothing prevents the listener, throwing the flattery, correctly appreciate this argument.

Sophisms are intentional errors in proof. In practice, it is very difficult to distinguish sophism from unsighted error (paralogism). Therefore, sophisms and errors are not divided, although in essence these are different things: sophisms are talking about dishonesty, dishonesty, and paralogism - only about the inefficiency of the speaker. Sophisticates (or errors) are, such techniques: indication of a contradiction between the words and actions of a person, the substitution of the point of disagreement, the translation of the issue to the point of view of the benefit or harm, etc. In this case, the speaker tries to hide, entail its intentions, and requires a certain Preparation to find in his words deception.

Typology Sophisoms is very complex. In most manuals on logic, they are simply brought by lists, and these lists are quite significantly different in both the quantity and composition of the elements included in them. At the same time, some classification of sophisons was taken yet by S.I. Cook. He highlighted such categories: 1) the retreat from the tasks of the dispute; 2) retreat from the thesis; 3) Diversion against arguments. The latter, in turn, are divided into 1) false arguments; 2) arbitrary arguments; 3) "imaginary evidence"; 4) Sophysome inconsistency.

Anyway, but the classifications offered by the logics do not fully satisfy the needs of oratory of practice, so we can only rely on the opinion of logic, but are forced to offer a rhetorized version of the classification of sophisons found in public speeches.

§48. Logic sophisms

§ 48. So, the speaker decided to resort to the deception of the audience. At the same time, it can remain as part of a violation of only logical requirements for the construction of the argument or resort to rhetorized techniques that are beyond the borders of logic. In the first case, it usually applies one of two tactics:

1. It is not about the essence of the case, but discusses the identity, intention of the opponent, assesses his actions and arguments, that is, it is observed here diversion against opponent . In this case, such techniques are most typical:

1) Turning labels (insinuitions). The speaker gives an opponent with all sorts of non-extent characteristics, assesses his personality and actions. It should be borne in mind that, in contrast to the AD HOMINEM argument, which indicates the addictability of the argument to a person, here we have an argument AD PERSONAM, that is, the appeal to the qualities of approving as a basis for assessing the approval, which is unacceptable.

This technique was witty M. Zhvanetsky: " What can say chrome on the art of Van Gogh? If he immediately declare that he was chrome, he recognizes himself defeated. What can a person argue, who has not changed the passport? What views on architecture can a man without registration? Caught with political, he recognizes himself defeated. And in general, will we really be interested in the opinion of a person bald and with such a nose? Let first fix his nose, growing his hair, will acquire weight, gait, and then speaks unfortunately, - we will understand it."

In business, judicial, etc., this Sophism is absolutely unacceptable. At the same time, in political rhetoric, he has some right to exist, because here the values \u200b\u200band ideals are often personified, and the image of the political leader becomes a symbol of the value orientation of the party, flow, etc. The person who leads the political movement, thereby gives consent to the use His personality as such a symbol and cannot be offended by the fact that political opponents use the AD Personam argument in assessing the activities of his party. "Analysis of the correctness of socio-political argumentation is associated not only with an impartial assessment of the argument, but also with a predensive assessment of the subject of the argument. And this, in our opinion, expresses the specifics of socio-political argument." Of course, there are certain boundaries that cannot be proceeded, and the assessment of the political enemy must be reasonable, and not turn into the dirt stream.

2) Flying an opponent. Reporting a dubious argument, speaker says: " you, as a smart man, will not deny that ...", "everyone is known to your honesty and principle, so you ..."And so on. Usually it acts trouble-free.

3) In an effort to defeat, the speaker is trying make one mad Opponent so that he appears in the unprofitable light. In addition, angry, annoyed person is not able to soberly assess the situation and reasonably argue. Wed:

It seemed that the lawyer deliberately tried to keep as possible as possible and insulting. The conversation has not yet begun, and he already, no matter how casual, rushes, that "no luck will not be afraid - the conversation should go for purity," that challenge objected very softly, although it was indignant in the soul. And in the future, every word of the chalk came out on distrust, irony or direct rudeness. The chalk saw that this man was deliberately trying to pour it out, to bring out himself and provoke to some unwritten statement in the presence of reporters. Having embraced this strategy, the chalk did not want to get on the fishing rod at all. He made over himself an effort and continued to speak offense and politely, as always. (A. Haley)

2. Direct deception, distortion of the essence of the question under discussion. In this case, two strategies are possible. The first is diversion against the thesis.

1) Treatment or expansion of the thesis. At the same time, in difficult cases, his thesis is narrowed - then it is easier to prove it, but the thesis of the opponent is expanding - then it is easier to refute it. For example, the thesis is put forward: " Children do not like and do not read Dostoevsky"If this is my thesis, then in the process of discussion, I narrow it and pretending that the thesis is proved" in our school, children do not like and do not read Dostoevsky"If it is the thesis of the opponent, I will expand it and pretending to be proved by the thought" people do not like and do not understand Dostoevsky". Wed. Also:

"I ask you to leave at the work of an old Kolychev specialist, because he is a walking card file, a very experienced specialist. Without it, my brigade will be very difficult to work.

- What do you think, if we dismiss all the old specialists, then the ship of the revolution will take place? (K \\ f "Born by Revolution")

2) Submerement Tezisa. In this case, the speaker discloses not the subject that is declared in the subject or in the question of the interlocutor, and the one that it is easier to reveal. This technique has already been mentioned when considering the specifics of the thesis of speech.

3) Transfer the question to the point of view of harm or benefit. "I must say that the thought is true or false; prove that it is useful for us or harmful. It is necessary to prove that the act is moral or immoral; prove that it is beneficial or unprofitable for us, etc. For example, you need to prove that" God exists ": Prove that he and faith in his being brings consolation and happiness." Indeed, in the form, as this technique describes S.I. Cooknine, it is a rough sophism. However, we want to recall that in itself an indication of harm or benefit cannot be considered a sophism when it comes to conviction, and not about the proof of truth. This is how psychological arguments are built. From the fact that they can be used in speculative purposes. It is important to make the right conclusion: not "psychological arguments are not allowed," but "it is necessary to use these arguments appropriate (in cases where it comes to decisions) and without breaking ethics."

The essence of the discussed can be tried to distort with the help of the appropriate construction of the argument. In this case is observed diversion against arguments.

1) Making disadvantageous facts and events. Here is a simple household example. A person sells a new medicine that helps to lose weight. He praises the wonderful qualities of the drug, demonstrates slim patients who are delighted with a new medicine that helped them. However, the seller is silent that about 30% of patients acquired, due to this drug, chronic gastric and liver diseases, and some in severe form. This, of course, dishonest towards students.

But an example from a public speech. " However, not all museums are in distress. Some of them continue to actively visit. The record Museum of toys installed here, whose attendance for the last year not only did not fall, but even grew up."(Radio, 06/10/1994)Orator, however, forgot to mention that no one attended this third-rate museum voluntarily. The cost of a ticket to the museum is automatically included in the cost of an excursion from Moscow to the Trinity-Sergiev Lavra. Consequently, once over the past year the number of people willing to visit the Lavra, it also increased the number of forced toy museum.

2) "Reading in the hearts". The meaning of this reception is to point out the intended secret motives and the intentions, which, according to the speaker, is guided by opponent. "For example, the interlocutor expresses you in dispute:" You say it's not because they themselves are convinced of this, but from perseverance "," just to argue, "" You yourself think the same, just do not want to recognize your mistake "," you Speak from the envy of it, "" From the estate interests "," How much did you give to maintain this opinion? "," You are talking to the party discipline ", etc., etc., what to answer is" Reading in the hearts "? It" pins the mouth "by many, because it is not possible to disprove such an accusation, as well as prove it."

Here it is necessary to make one reservation. This and similar tricks are called in the logic "Argument to Man", or the AD HOMINEM argument, and are strictly condemned. However, it is notened to remind once again: for rhetorics, there are almost no techniques that are invalid in principle. It all depends on the goal of the speaker and its moral landmarks. In life, the situation is frequent when this technique can be used on completely legal grounds. Moreover, this thought is found in the works on logical argument. So, A.P. Alekseyev, considering such a trick, indicates the inadmissibility of mixing the gnoseological and pragmatic estimates, but at the same time warns against the unique refusal of all AD HOMINEM arguments, since this would lead to excessive formalization and unjustified complication of argumentation. "Getting some information, we often wonder what is the source of this information. Having learned that N. Something and then, we can ask who N. by profession, where he lives, what is his personal interest in propaganda This statement, whether he has obligations on its propaganda. Perhaps we will want to find out what the floor, age, the nationality of the speaker, what is his reputation, and the knowledge of all these factors can affect our assessment of his statements. It is legitimate to argue that always and Everywhere this kind of influence is only negative and darkening the essence of the case? Eliminating such an impact completely, whether we do not eliminate one of the natural precautionary mechanisms having roots in the history of human communication? Politician calling the fellow citizens to limit his material needs, while He himself bathes in luxury, hardly deserves confidence. If someone tells you: "Don't believe it, he has a reputation of a person the ideological "or" dove left, leave you this thought, and then, God forbid, you will have from this trouble, "or" This is a honest person, you can follow his advice, "you always should always be dishearted from this kind of argument only the fact that it contains ad hominem? " Moreover, such a warning is legitimate not only in relation to rhetorical arguments, oriented on preference and the feasibility of committing certain actions, but also with respect to the argument is purely logical: "N. said that A. is known, meanwhile that N. often deceives. So, it is very likely that A. False. " In this case, the truly assessment of the assertion A. is justified by references to the personal qualities of Human Human to which this statement belongs. According to traditional canons, this demonstration is vicious. However, looking at her an uncompressed look, we can come to the conclusion that it is legitimate. In fact, if N. often lies, it is likely that he lies and in this case (of course, if this question relates to the circle of issues by which N. often lies). Since it is likely that N. Lzhet in this case probably also that A. falsely. "

3) False dilemma.Often, the arguments describe how it seems as if it seems to choose only from the two opposite characteristics of the subject, for example, smart / stupid, good / poor, kind / angry, while all intermediate stages are ignored. However, if it is impossible to prove that a person is very clever, then it does not follow from this that he is a fool. Any positive and negative assessment of a phenomenon is extreme points on the score scale, where a number of intermediate positions can be placed. This error is even more obvious in cases where estimates that are not related to each other are opposed to the extreme points of one quality. So, from the fact that this student is not an Astrakhan, it does not imply that he is Rosovchan. Ignoring all other places from where this person could come to study is a rough mistake. An even more difficult case of a false dilemma occurs when it is already known in advance that one of the alternative solutions is incorrect or undesirable. Here all other possibilities are not just ignored, but the second part of the dilemma itself is discarded. In logic, this kind of false dilemma is called the "Lady argument". "The essence of it is in which. In many questions, it is imminently not one, not one, not two, but a few, a lot of solutions, a few assumptions, etc. Some of them are opposed to each other. For common sense and according to the requirements of logic, it is necessary to take into account all of them . But Sofist comes around. Wanting, for example, to protect your opinion, he chooses the most extreme and most ridiculous opposite question from other conceivable issues of the issue and opposes its opinion. However, he invites us to choose: or recognize this absurdity, or accept his thought . The brighter the contrast between the absurdity and the opinion protected by him, the better. All other possible solutions are deliberately silent. Here is an example from life:

A. - that you did so dry with him. He, poor, felt like us very awkward.

B. - And how can I contact him to contact him? Place angle instead of images and pray?

There are thousands of ways to handle people in addition to these two. But B. chose the most ridiculous ridiculous ways for the contrast. Or another example is from "serious" disputes. So "serious" that the ladies' argument is mixed with chopstick. Men argue.

A. In my opinion, the current composition of the government is completely unsuitable for the country management.

Q. What does it mean, in your opinion, you need to return Nikolai and Rasputin again? "

4) Imposed effect. This sophism is that the opponent's arguments are concluded, which actually does not interfere with it. For example:

Buyer: Listen, you misunderstand me: it's not enough of two rubles.

Seller: Citizens! What is this! She called me a thief!

Unfortunately, this reception is found in life quite often, and not only in the reasoning of public speakers, but also in rhetoric benefits. Wed, for example, as in one such manual is given an example of imposed investigation: "In the newspaper" AIF "No. 51 for December 1991, reported:" The best material for the manufacture of prostheses is corals. So, in any case, Japanese dentists consider. The doctor Isiro Yamashita said that artificial teeth of corals are stronger and serve longer than prostheses of gold, platinum, silver or porcelain. "As you understand, that from this notes it follows a false conclusion: do not use artificial braids from gold, platinum, porcelain And, moreover, from plastics. " In fact, the false conclusion makes the author of this reasoning: because of the fact that there are five-star hotels, a diamond necklace and the services of the Chinese porcelain, which everyone recognizes the best, does not follow the idea of \u200b\u200bthe need to immediately destroy tourist campings, jewelry and glass glasses, because in life It has the right to exist not only the best, but all that we compare it with it (the best). Therefore, after the opening of Japanese scientists there will be people who want to restrict themselves with gold or porcelain teeth, and even the poor who are on the pocket only plastic. The output "Do not use" would be legitimate only if it was proved by the harm to the health of all other teeth, except coral.

This may include sophisms mentioned earlier in other sections: false argument, arbitrary argument, hidden arbitrary argument, anticipation of the foundation, etc.

5) Hurry (or false) generalization. This software is in the improper endowment of the entire number of phenomena of the qualities that are marked with one or more components. For example, from the listing of 5-6 deputies of the Duma, which advocate public non -ethic statements, does not follow the idea that all deputies are uncompatible people. "Sophisticizms of inconsistency or improper reasoning. First of all, you need to mention a" false generalization. "A person cites several examples of the fact that such persons or such objects have a well-known sign, etc., and without further reasoning concludes that all Such faces and items have this sign. It seems to how the Gogol Hero saw that all Orthodox, which he met, dangling gallushki, and from here it concluded that all Orthodox don't eat dangling, and who did not eat them, not Orthodox. " Cf. An example from a public speech, where without any instructions on objective criteria for assessment is concluded that all people and all countries hate the Americans: " But while they still dominate almost the entire planet. She already hates Americans. There is not a single country in the world where Americans would love. All they hate them. Because their sixth fleet went to the Arab countries, in the Turkish ports, in Italian - and everywhere it caused hatred. Because everywhere rudeness and violence, debauchery, violation of the rights of citizens of those countries where American troops are. "(B. Zhirinovsky)

6) False analogy.Comparable phenomena must have similar signs. "Two or more phenomena can be substantially similar and still differ in the lack of similarity required from the point of view of the provoked position. The following obvious absurdity identifies an error possible in this regard: whales and elephants - mammals; consequently, those and others are found on land. " Wed:

Mistress rupture: about Tambov! How much will the mile from Moscow before Ryazan and back?

Librental: One way I can say, without even coping with the calendar, but I do not know back.

(Everyone is turned away in one direction and snort, making mocking sound with nose).

Librental: I can assure you! After all, from Christmas to Easter so many days, and from Easter to Christmas so much, but not as much as from Christmas to Easter. Consequently ... (goat rods)

This sophis is often used in advertising. Wed, for example: " Real American jeans. From Asia? (throws) Real Japanese equipment. From Africa? (throws) real instant coffee. From Europe? (throws out) - in Europe does not grow coffee. Drink real instant coffee from Brazil! " In this example, the first two cases are combined according to the sign that these are fakes under well-known firms. However, in the third case, the fake does not have a fake, it is not necessary to process raw materials in the country where it grows, and the famous European coffee processing firms are most famous and respected all over the world, so the analogy should be recognized completely unreasonable.

§49. Rhetorized sophisms

§ 49. Although logic tricks and sophisms are used in modern speech practices and themselves, they are often subject to rhetorization. In this case, the essence of the violation remains the same as in situations described in the previous paragraph, but additional emotional accents and psychological pressure appear. In relation to rhetorized sophimons, it is always possible to say with confidence that they are constructed consciously and are designed to suppress the audience. In our public life, these sophies acquire often differently different.

Diversion against personality Opponent can take such forms:

1) Riding or foaming opponent. It is usually applied to undermine the confidence in a person who speaks against the Sofist. So, if a man feels that he is not right, he speaks with a smile: " What a woman argue! "Usually this replica can serve as a sign that he internally recognized his defeat.

This technique is often used to justify their non-residential deeds. Recall the episode from our parliamentary practice. 09/13/1995 In the State Duma there was a fight, during which the city of Zhirinovsky and his associates fought with the deputy E. Tishkovskaya. This episode caused extremely negative assessments of the actions of Zhirinovsky, who personally stole and dragged a woman for his hair. To restore his renome, he chose the tactics of foaming E. Tishkovskaya. At a press conference, he said: " A woman is lonely, wanted a strong male society, it can be understood. Here and climbed it and quietly brought to the side. One deputy told how she balded when he touched certain parts of her body"And so on. And all this, of course, with irony and mockery. If television, against the background of this speech, did not show the record of the fight itself, the reputation of the woman would really be risen. Another time he said:" How was it not to calm her, because she was lying all the time to hit men in the most vulnerable place". And again, if not to repeat the scene, where it is clearly seen that the Tishkovskaya, fighting from Zhirinovists, beats them only in the chest, it would be ruined. Wed. More:

– Anti-American moods are growing throughout the planet. Clinton, Take up! Stop running in panties, doing charging! Sit for history textbooks, beat! In the history textbooks everything is written. Otherwise, your flag will burn across the planet, everywhere will burn. And again, we will burn your dollars, with what will you stay with? With Pepsi Cola! All that American is bad, all this is involved in the blood. We cannot endure it. (V. Zhirinovsky)

2) Frank and obvious refusal to discuss the problem and the transition to the discussion of the individual and the actions of the opponent, extended insinuation:

Deputy: What elements is political and educational work in the army now?

P.S. Grachev: I'm not a schoolboy and the exam is not going to take here. And you in vain, Nikolai, with me so. Well, I did not give you another order, they will give, did not assign another title, so they will assign. What is the personal resentment in a public place to demonstrate! (TV, 11/17/1994)

3) Direct Bran Usually characterizes only the speaker itself as deprived of a completely oratorical ethos and is perceived as an unlawful reception even a poorly prepared rhetorically audience. Therefore, only the most extremist tuned speakers are resorted to this reception. Wed:

For Russia died and died with a smile. They need to put a monument, but they will deteriorate. This, like him, peacemaker, deputy, like him, Kovalev. Yes, he has nowhere to put a stamp. There is nowhere to put a stamp! This is the enemy of Russia. This is a traitor to Russia! And it is there everywhere there are there ... This Yushnikov, this hyadenash, it is impossible to say it differently. Heet that army, which gave him an education, gave him the title ... And he, this hyaden, protects those villains who want to ruin the country. (P.S. Grachev)

4) "Reading in the hearts" Combining with speculative estimates, becomes a shape of a sophisticated slander on opponent: " Mayor, apparently expectedthat, having heard the names of the signatories, offended by nature, the Volgograds immediately will be transparent ..."; "After all obviousthat for Mr. Chekhov and his "Team" absolutely anyway Who is at the head of the region - Shabunin, Ivanov, Petrov or Sidorov, they don't care whom to tractto grasp for chairs. The main thing is to take power, to take the keys to your hands from the regional treasury, regardless of anything.… "; "It is clear that he dreamedbring a decree on removal of the governor from office". (B. Princechenko) Such statements are primarily characterized by the author himself as a man's dishonest. The competent audience has the right to demand from the author of the rational substantiation of all the estimates that he awarded the opponse.

Sometimes, as "reading in the hearts" looks, the statements look, in fact correctly reflecting the case: " He decided that he was allowed", "He was going to leave, but at the last moment changed his mind". If you add such statements by quotes from the speeches of the person or his loved ones, the description of his actions, confirming the thoughts expressed, the whole fragment as a whole may not be impressed by Sophism, especially if it is not accompanied by vulgar estimates.

5) Event label. In contrast to the insinuation in the literal sense, when the characteristic is given to the opponent, in this case an arbitrary classification is subjected to a discussed event. Observations show that in modern spectacle practice the most popular label turns out to be " armed coup"So you can call any negatively estimated event of public life, Wed: 18.10.1996 Kulikov accused the swan in an attempt to make an armed coup in response to criticism of the Swan Kulikov. Or:" What is happening now in the Horsoud is an attempt of the state coup, since on the sixth year of democracy to judge a person for his convictions is the top of cynicism." (V. Novodvorskaya)

Examples of applying such a reception in our oratorical practice can be found quite a lot. So, if Russia refuses to discuss the issue of territorial claims to her or trying to protect its citizens in the near abroad - this imperial ambitions. If the presidential version of the Constitution is defeated in Belarus on the referendum - representatives of the Supreme Council claim that Coming dictatorship. If the "apple" argues that the agreement between Russia and Belarus has a hasty, unproduced and crude, the Communists accuse him in the reluctance to establish contacts with the fraternal people. If the Ministry of Finance accused Remakhirere Remiavea in the inefficient governance "Gazprom", he, in turn, accused the Ministry of Finance in desire to ruin"Gazprom" in favor of American gas and oil companies. None of the listed cases have been given any reasonable arguments to confirm such estimated judgments.

Diversion against Tezisa It may acquire a more intensive shape and turn into the chickness of the thesis. This technique is that, hitting an unprofitable position, the speaker begins to consciously talk about outsiders, tries to lead the discussion away from a dangerous place, often at the same time trying to force opponent to defend against attacks. An example of the application of this reception can be an episode from the famous transmission of A. Lyubimov "one-one" in August 1995. When V. Zhirinovsky felt that B. Nemtsov was going to betray the unwanted facts for him (about interviews the magazine "Play Fight") , He began with a machine-gun speed to rage about the miscalculation of the leadership of the Nizhny Novgorod region in common words, not giving the interlocutor to open her mouth and trying to make him justify.

Another way of sabotage against the thesis of the opponent is a distortion, putting it in a caricature form. This reception is especially common in cases where the opponent's speech is the time from the initial performance and the audience has already forgotten (or did not hear) speech of proponent.

Especially often rhetorized diversion against arguments Because the arguments are the most mobile part of the argument and their distortion can be easier. In this case, logical sophisms may acquire a particularly arbitrary and exaggerated form in public speeches.

1) Shipping facts Acquires a speculative form when well-known truths are produced in the hope that our poorly prepared listener will not notice this sabotage. Wed: " Cannot be conducted in St. Petersburg Olympics. This is a crazy idea. Our city will not lead it. Cheat those who claim that all cities where the Olympics were prosperous cities. Look, as Sarajevo is a bit. So and we will not bring the material well-being of the Olympiad." (A. Nevzorov) There is no need to explain why in 1995 the Sarajevo did not flourish and that the Olympiad was completely nothing to do with it.

2) "Lady argument" Acquires a generalized-blurred form for which the essence of opposition is hiding. So, the whole presidential pre-election campaign 1996 was built on the principle of opposing Yeltsin and Zyuganov, the remaining candidates were not taken into account. People obviously suggested the idea that you can choose only between these two candidates, the rest must be ignored. The meaning of this reception is obvious: Yeltsin could explain to the voters, in which its advantage compared to the communist Zyuganov, but it turned out to be very difficult to explain what its advantage compared to the independent candidate of the Swan, who eventually took the third place. At the same time, the analysis shows that if the campaign was conducted by more honest methods, the swan could take second place in the first round and complicate the task to the President. Or from speech:

Here our Cossacks are finally awakened. They came to me, all moaning: make a statement, make a statement. Now they say: we take the weapon. It was necessary that four years of their steal them in the face and in all other parts of the body. Now they begin to understand that you need to take for weapons and protect yourself and our own life on your own. Moscow will not help. Moscow walks, she meets Michael Jackson. More to meet some kind of in Moscow. Refugees Let, the soldiers are wounded let, the corpses are unidentified let - but to meet well Michael Jackson. Here it is, the salvation of Russia. (V. Zhirinovsky)

Here we see the intentional encountering two events, the announcement of them interrelated, although in fact they are in no way connected and not opposed.

Other sophisms are ritorized on the same principle. (See the relevant §§)

§fifty. Actually rhetorical sophisms

§ 50. To actually rhetorical sophimons include speculative use of rhetorical arguments. Examples of this kind of techniques have already been brought in the relevant sections, where it was about the unlawful expansion of the scope of the use of rhetorical arguments, speculative use of topos, etc. Here, only we note that the fact of replacing an objective estimate of the phenomenon is most often found in modern oratorical practice. In this case, a complex public event is uniquely and completely unconditionally estimated in such a way as he wants to imagine a speaker. Wed: " The swan in the election shouted that he would protect all Russians, the Russian nation, and he sold Russian interests in Chechnya." (Radio, 10/19/1996.) The fact that the swan "sold the interests of Russians should be separately proven. Or:

While the peoples of Germany and Soviet Union They carried out this terrible fight between themselves, the Americans traded, cut off scientists. The German scientist created them nuclear weapons. Americans had no weapons. Nothing! Rock, Heavy Rock! First of all, the head can not, it is empty. Everything that America has is us, the Europeans, we did, we have enormous wealth, our wealth will be enough for three years. Clean water, oil, gas, all metals. Here she is the nation of Zhulikov: come here under the UN flag with NATO armies, as they came to Yugoslavia. But it will not work! Will not work, Americans! We can not tolerate that their star-striped flag dominated over the planet. This is not suitable! (V. Zhirinovsky.)

Especially often speculative assessments are found in the framework of the election fight. As an example, almost any fragment from numerous articles G. V. Knyajchenko, an employee of the newspaper "Extra KP", we only give the beginning of one of them: " Famous candidate in governors without ceasing brag the presence of a "decent team", walks around the factories and on the streets, gives on the mountain fumeric speech, And his talking assistants from the press only make that inflate for any occasion " world fire, I. Trying to overthrow with a bells of risks that fairly look at things and see in front of them not a fire, but thirst for the Swarre and thirst for power"etc. (Extra KP) As part of the conviction, all the allocated estimates must be justified, that is, readers should be clear why the words "candidate" - boasting, why his "fiery speeches" are worthy of condemnation, why more just a look at the things "Rangers", etc. otherwise we We are dealing with only a very rough form of rhetorical sophism. Especially obvious unfairness in the case when the activity of an objectionable candidate qualifies like this: " he rushes to power, the authorities are eager". It remains completely unreasonable here, why the desire to defeat the elections of our" our "candidate is estimated as absolutely correct and regular, and exactly the same aspiration of the" naughty "candidate - as a disclosure of it. By law, candidates are equal in their desire for the desire and accusation of one Of these, in favor of the other, it should be qualified as a violation of the election law. It is natural that in the entire article under consideration, Knyazhechenko does not provide a single fact, an objective judgment confirming the fairness of at least one assessment of the author. By the degree of speculativity of this speaker, it can only be compared with G. Zhirinovsky, who also does not bother at least some elements of evidence, limited only by the most speculative forms of suggestion.

This, of course, does not mean that the speaker should completely abandon the estimates, limited only to the presentation of facts, but we note again: not any forms are allowed here, but only those that correspond to reality are not built on the direct cheating of the audience, t. e. Estimates must be justified in speech.

What to do if such speculative means are used against us? First of all, it is necessary to correctly understand which technique uses the speaker. Only in this case will be able to effectively resist him. Secondly, it is necessary to know the subject of discussion. And, of course, it is important to keep calm and not to indignant if the fact of the use of tricks is set. Turning labels, fading arguments, etc., must be named and evaluated. For such tricks, like flattery of the opponent or the bet on a false shame simply do not need to come across. If the opponent uses sophisms, it is necessary to point out errors in its arguments, but it should not be accused of being deliberately allowed: it is very difficult to prove that the speaker went on a direct deception, and it is better not to draw in this dispute.