Lecture
There is an interesting way of reasoning, requiring not only the mind, but also a rich imagination, full of poetic flight, but not giving a solid knowledge, and often simply misleading. This very popular method is inference by analogy.
The child sees a little monkey in the zoo and asks his parents to buy him this “little man in a fur coat” so that he can play and talk with him at home. A child is convinced that a monkey is a man, but only in a fur coat, that it can, like a man, play and talk. Where does this belief come from? In appearance, facial expressions, gestures, the monkey resembles a person. It seems to a child that with her, as with a person, you can play and talk.
Acquainted with a journalist, we learn that this intelligent, well-educated person speaks fluent English, German and French. Having then met another journalist who is intelligent, educated, and fluent in English and German, we can resist the temptation and ask if he speaks French.
In both cases, the reasoning follows the same pattern. Two objects are compared and it turns out that they are similar in some of their features. From this it is concluded that their similarity extends to other, not yet considered signs. With this reasoning, the knowledge obtained from the consideration of one subject is transferred to another less studied subject. This is an inference by analogy.
Such a conclusion in the course of thought, the logical structure is very simple.
The classic example of life on Mars that has already become a classic demonstrates this simplicity. Supporters of the hypothesis about the possibility of life on Mars argue so. There is much in common between Mars and Earth: these are two planets of the Solar System located side by side, both have water and an atmosphere, the temperature on their surface is not very different, etc. There is life on Earth. Since Mars is very similar to Earth in terms of the conditions necessary for the existence of life, it means that on Mars, in all likelihood, there is life. This example emphasizes the fundamental peculiarity of inference by analogy: it does not provide reliable knowledge. Is there life on Mars, is there life there - modern science is not known. Comparison of the Earth and Mars, tracing their similarities are not, of course, evidence of the existence of life on Mars. This comparison, no matter how far it goes, can only give a conjectural knowledge, a hypothesis that needs direct verification.
Another example of inference by analogy. France is a European country, a democratic republic with a market economy; France has moderate unemployment. Located next to France, Germany is also a republic, a democratic country with a market economy. So, probably, in Germany there is also moderate unemployment. Here the conclusion is again problematic.
The analogy does not always appear in such a transparent form. Often, when faced with reasoning by analogy, it is difficult to establish which particular objects are compared with each other and by what properties, which known features of one of them are transferred to the other.
In “Stories about Children” V. Veresaev gives the following case: “Boy Igor. All tormented by eternal annoying questions: "why?"
One familiar professor of psychology advised:
- When you get tired, answer him: "Because it is perpendicular!" See, very quickly lose the habit.
Soon:
- Igor, do not go to the table!
- Why?
- Because you can not climb on the table.
- Why not climb on the table?
- Because you are kicking him.
- Why do you stain your feet? Strictly and seriously:
- Because perpendicular!
Igor fell silent. He opened his eyes wide.
- Peck ... lane ... kulyar?
- П-е-р-п-е-Н-д-и-к-у-л-я-р! Got it? Go on! So several times it was.
Four days later. In the morning, Igor enters.
- Igor, why aren't you greeting me?
- Do not want.
- Why are you not want?
- Because I'm angry.
- Why is angry? Oh my god! Why are you angry?
- Because perpendicular!
With great difficulty, we managed to wean: in all difficult cases, I covered myself with a perpendicular ”.
Here it is clearly felt that the child argues but analogies. But what and with what he compares and what conclusion does? To answer this question, we need a small reconstruction.
At first, the child endlessly asks questions to an adult. When the latter bothers to answer, he refers to an incomprehensible "perpendicular", and this is where all the questions end. Then the adult insistently asks the child. As soon as the child gets bored to answer, he, like an adult, refers to the same “perpendicular” and expects that there will be no more questions after that.
Thus, two situations are compared: in the first, the child asks many questions to the adult, and in the second, the adult to the child. These situations are very similar. The child, moreover, notices the peculiarity of the first of them: after the "perpendicular" questions are not asked. He transfers this feature by analogy to the second situation, concluding that in this case the appeal to the "perpendicular" will remove further questions.
This conclusion is, of course, nothing more than a hypothesis, and a hypothesis having a small probability. The situations are really similar, but not completely. In one case, the questions are asked by the child, and in the other by an adult; The reaction of the adult to the “perpendicular” is likely to be different than the reaction of the child.
In ordinary thinking, inference by analogy is rarely found in a clear, not requiring analysis and reconstruction form. Most often, the analogy is minimized, some parts of the inference are omitted.
Often an analogy is called reasoning, which is obviously not an inference by analogy.
In the tale of L. Carroll "Alice in Wonderland" there is such a dialogue. Alice asks the Cheshire Cat:
- How do you know that you are out of your mind?
- To begin with, the dog is in his mind. Agree?
“Suppose,” Alice agreed.
“Next,” said the cat. - The dog grumbles when he is angry, and when he is satisfied, he wags his tail. Well, I grumble when I'm pleased, and wag my tail when I'm angry. Therefore, I am out of my mind.
The cat here compares its behavior with the behavior of the dog in the same circumstances, or, as they usually say, draws an analogy. However, the reasoning of a cat is not a conclusion by analogy. The latter requires that, on the basis of the similarity of known features, a conclusion is drawn about coincidence and other features. This is just not the case here. The dog is in his mind, from which the cat concludes that he himself, in contrast to the dog, is clearly not in his mind.
The analogy is weakly evidential. Continuing similarities may turn out to be superficial or even erroneous.
However, evidence and persuasion do not always coincide. Often the rigorous, step-by-step proof turns out to be inappropriate and convinces less than a fleeting, but figurative and vivid analogy. Proof is a potent remedy for correcting and deepening convictions, while the analogy is similar to a homeopathic medicine, taken in small doses, but having a noticeable healing effect.
Analogy is a favorite means of persuasion in fiction, which by its very essence is contraindicated in strong, straightforward persuasion techniques. The analogy is also widely used in ordinary life, in moral reasoning, in ideology, utopia, etc.
Metaphor, which is a vivid expression of artistic creativity, is, in fact, a kind of condensed, rolled up analogy. Almost any analogy, with the exception of those that are presented in frozen forms, like a parable or allegory, can spontaneously become a metaphor. An example of a metaphor with a transparent analogous relationship is the following juxtaposition of Aristotle: "... old age refers to life as evening to day, therefore, evening can be called" oldness of day ", and old age -" evening of life "." In the traditional understanding of the metaphor is a trope, a successful change in the meaning of a word or expression. With the help of metaphor, the eigenvalue of the name is transferred to some other value that suits this name only in view of the comparison that is kept in mind. Already this interpretation of metaphor connects it with an analogy. Metaphor results from the merging of analogy members and performs almost the same functions as the last one. From the point of view of influencing emotions and beliefs, the metaphor copes even better with these functions, because it strengthens the analogy, introducing it in a compressed form.
Analogy is a popular method of inductive reasoning in support of assessments. The general scheme of the evaluation analogy:
Item A has signs of a, b, c and is positive (negative, neutral) valuable. Subject B has signs of ay in, p.
This means that subject B is also probably positively valuable.
In this argument, the similarity of two objects in some signs is continued, and on the basis that the first object has a certain value, it is concluded that the second object has the same value.
For example: “Book A is a dystopia written in a good language, having an entertaining plot, deserves praise; Book B is also a dystopia, written in a good language and having an entertaining plot; then book B also seems to merit praise. ”
Often the analogy with the estimated premise appears in the form: “Subject A has properties a, b, c and should be c1; subject B possesses properties a, c> c; then subject B must probably be ё. ”
For example: “A good car has wheels, a motor and should be economical; a good tractor has wheels and a motor; then a good tractor also seems to be economical. ” Only in the rarest cases does the evaluative analogy appear in such a transparent form as in the examples given.
"A man is childish compared to a deity, says Heraclitus, like a child compared to a man." In this collapsed analogy, we are talking about the fact that a person in comparison with a higher level of development (which is a deity) should seem childish, since a child, much like an adult person (and having a higher level of development), should seem childish. In the "Doi Quixote" of Cervantes, there is such a clear analogy: "A wandering knight without a lady is like a tree without leaves, a building without a foundation, or a shadow without a body that casts it." Since a tree devoid of foliage, a building without a foundation, or a shadow without a body inspire suspicion and cannot be evaluated positively, a wandering knight without a lady causes the same reaction.
Analogy is an old concept; already known to Greek science and medieval thinking. And already in antiquity it was noted that not only objects, but also relations between them, can be similar to each other, correspond and be similar in their properties.
Aeronautical pioneers could not cope with the problem of buckling of the wings of their aircraft. In 1895, F. Shan made a bilan with wings connected by uprights. The design was similar to an openwork bridge, and it is not surprising: Shan was a bridge engineer and saw an analogy between his work and the problem of strengthening the wings of an airplane without weighting them.
The inventor of the steam turbine Charles Parsons began his work on the basis of the analogy between the flow of steam and the flow of water in a hydraulic turbine.
The assimilation of the wing of an airplane to a bridge and the flow of steam to a stream of water is the identification of similar properties of different objects. Having noticed this similarity, one can continue it and conclude that the objects being compared are similar in their other properties.
In a well-known planetary model of the atom, its structure is similar to the structure of the Solar System. Light electrons move around a massive nucleus at different distances from it along closed trajectories, just as planets turn around the Sun. This analogy establishes, as usual, similarity, but not of the objects themselves, but of the relations between them. The atomic nucleus is not like the Sun, and the electrons are like planets. But the relationship between the nucleus and the electrons is much like the relationship between the Sun and the planets. Having noticed this similarity, one can try to develop it and express, for example, the assumption that electrons, like planets, move not along circular, but along elliptical trajectories. This will be a conclusion by analogy, but it is no longer based on the similarity of the properties of objects, but on the similarity of relations between, in general, completely different objects.
The English book printer D. Danton had a happy but very short marriage: his young wife died early. After only six months, he, however, remarried. In the history of his life, Danton justified such a speedy consolation with the fact that the second wife was just a repetition of the first: “I only changed my face, the female virtues in my home circle remained the same. My second wife is nothing but the first, but only in a new edition, revised and expanded, and I would say: newly intertwined. ”
Here, the attitude of the new wife to the previous one is likened to the relation of the second edition of the book to the first. What does it matter if the second edition came right after the first? It is curious to note that, as a true lover of the book, Danton appreciates precisely the first edition, even though it is lost.
A good example of the analogy of relations is given by the Polish philosopher N. Lubnitsky. Imagine a caravan going into the desert at sunset. Shadows falling on the sand are elongated and deformed. But each position, each movement of the riders and animals corresponds to a certain position and the movement of the shadow on the sand. There is little similarity between humans and camels and their distorted shadows. Animals and people are three-dimensional, colored; the shadows are flat, black, caricaturely elongated. And at the same time between the world of things and the world of their shadows is an element of similarity and even identity. In both worlds, the same relationship exists. The mutual positions of the shadows are the same as the mutual positions of the members of the caravan. Each tilt of the head, each movement of the rider's or camel's legs is answered by exactly the same movement of the corresponding shadow on the sand. We can say that the behavior of shadows is strictly similar to the behavior of those objects that cast these shadows.
With the analogy of relationships, relationships are likened. The objects themselves, between which these relations take place, can be completely different.
The power of such an analogy, of objectivity freed from the burden, is unusually great. Using the ce, you can set an unlimited number of similarities between the most remote areas. The similarities revealed by this will be not massive, visible similarities of things in themselves, but more subtle similarities of their relations.
The analogy of relations, capable of comparing and bringing together the weight of anything, is a powerful weapon of human thinking, which, however, requires extreme caution and prudence in its application. In skillful hands, such an analogy can become a means of deep insights that are ahead of its time or vivid, poetic images that make you see the world in a new light and in an unusual perspective.
When applied superficially, the analogy of relations turns into a tool of unrestrained, unproductive fantasy, breaking ties with the real world and neglecting the connections and relationships existing in it.
About three hundred years ago, at the dawn of modern science, the analogy — and especially the relationship analogy — was extremely popular. However, the similarities established with its help turned out to be, as a rule, superficial and lightweight.
Thus, the relation of the luminaries to the sky in which they shimmer, was likened to the relation of grass to earth, living beings to the globe on which they live, minerals and diamonds to the rocks in which they are contained, the senses to the person they animate, pigment spots on the skin - to the body, which they secretly note, etc. There was an old analogy between a plant and an animal: a plant is an animal: its head is below, and its mouth - or root - is immersed in the ground.
It is clear, of course, that the cognitive value of all these assimilations is zero. They fix a purely external similarity of relations that exist between disparate things, replacing a concrete study of these relations with endless assimilations to some other relationship, vague and lacking clear content. Through such analogies, it is possible to bring together any objects, without having said anything about them in essence.
Scientists XVII. they liked to compare the human body with the globe: human skin is the surface of the earth, its bones are rocks, veins are large flows, and the seven main parts of the body correspond to seven metals.
Such analogies are not just useless, but, worse, harmful. Они опутывают объекты, нуждающиеся в исследовании, густой паутиной надуманных, вычурных и совершенно пустых конструкций, внушают иллюзию ясности и понятности того, что еще только предстоит изучить.
В мире бесконечное множество сходных между собой вещей. Абстрактно говоря, при желании и достаточной фантазии можно отыскать сходство между двумя любыми произвольно взятыми объектами. Соседствование в пространстве, в котором природа разместила две вещи, может казаться знаком их, по крайней мере, смутной близости и отдаленного родства. Охотник и дичь определенно сходны, поскольку они находятся в отношении соперничества и являются как бы зеркальным отображением друг друга, и т.д.
Но если все можно уподобить всему, возникает вопрос: какие вещи или их отношения разумно, допустимо, целесообразно и т.п. уподоблять, а какие нет?
Очевидно, что однозначного ответа на этот вопрос не существует. Можно сказать, что разумность уподобления определяется, в конечном счете, тем контекстом, той ситуацией, в которой сопоставляются предметы.
В известном стихотворении В. Брюсова «Мир электрона» эти элементарные частицы уподобляются планетам, населенным разумными существами, и даже галактикам:
Быть может, эти электроны -
Миры, где пять материков,
Искусства, знанья, войны, троны
И память сорока веков!
Еще, быть может, каждый атом -
Вселенная, где сто планет.
Там все, что здесь в объеме сжатом,
Но также то, чего здесь нет.
В романе «Восстание ангелов» А. Франс сравнивает пламя зажженной спички с Вселенной. В этом пламени есть частицы, подобные звездам и планетам; на некоторых частицах живут, подобно людям, мельчайшие существа, которых нам никогда не увидеть; эти существа влюбляются, строят, спорят, и все это до тех пор, пока человек, зажегший спичку, не дунет на ее пламя и не погасит его.
Такие «свободные аналогии» прекрасно звучат в художественном произведении. Однако в книге по физике они выглядели бы, скорее всего, нелепо. С изменением контекста меняется и само понятие разумности уподобления. То, что хорошо в искусстве, может оказаться никуда не годным в науке, и наоборот.
В той же физике можно было бы, наверное, найти аспект, в котором трепещущее, неоднородное пламя спички удалось бы уподобить Вселенной. Но эта физическая аналогия вряд ли имела бы художественную ценность. Понятие контекста является одновременно и широким и неопределенным. Контекст включает и то конкретное изложение или доказательство, в рамках которого встречается умозаключение по аналогии, и намерения, знания, переживания тех, кто прибегает к аналогии или оценивает ее, и более широкую среду общения, ситуацию, в которой они находятся. Иногда для суждения о разумности или оправданности аналогии приходится принимать во внимание целую эпоху.
Как бы широко ни простиралось и как бы вольно ни истолковывалось сходство, оно никогда не будет полным и абсолютным.
Два близнеца очень похожи, но все-таки во многом они различаются. Настолько различаются, что родители, как правило, не путают их. Две буквы «с» в слове «веер» чрезвычайно похожи, и тем не менее они разные. Одна из них может оказаться пропечатанной слабее, чем другая; если даже типографски они окажутся совершенно идентичными, они все-таки различаются соседствующими с ними буквами или знаками (как в нашем случае). Если бы и в этом буквы «е» совпадали, они все равно остались бы различными: одна из них встречается в этом слове раньше другой. Если бы и этого не было, не было бы вообще двух букв, т.е. двух разных букв.
Сходство всегда сопряжено с различием и без различия не существует. В этом плане аналогия есть попытка продолжить сходство несходного.
Once this is realized, the most important question regarding the analogy arises. Reasoning by analogy continues the similarity, and continues it in a new, unknown direction. Will this attempt to broaden the similarity stumble upon an unexpected distinction? How to reasonably continue and develop the established initial similarity? What are the criteria or guarantees that similar objects in some way will turn out to be similar in their other properties?
Inference by analogy does not provide reliable knowledge. If the premise of such a conclusion is true, then this does not mean that its conclusion will be true: it can be true, it can also be false.
Простой пример. Квадрат и прямоугольник сходны: это плоские геометрические фигуры, их противоположные стороны равны и параллельны. У прямоугольника, как подсказывает само его название, все углы прямые. Можно заключить по аналогии, что и у квадрата все углы также являются прямыми. Этот вывод истинный. Из сходства квадрата и прямоугольника и того, что у квадрата все стороны равны, можно сделать по аналогии вывод, что и у прямоугольника они равны. Но это уже будет неверно.
Проблематичность или вероятность, может быть большей или меньшей. Аналогию, дающую высоковероятное знание, принято называть строгой или точной. Научные аналогии обычно являются строгими. Рассуждения но аналогии в повседневной жизни, как правило, поверхностны и не особенно строги. От аналогий, встречающихся в художественной литературе, точность вообще не требуется. У них иная задача, и оцениваются они по другим критериям, прежде всего по силе художественного воздействия.
Как повысить вероятность выводов по аналогии?
В начале рассуждения по аналогии фиксируется сходство сопоставляемых объектов. Здесь следует стремиться к тому, чтобы было схвачено и выражено действительное, а не кажущееся или мнимое сходство. Желательно, чтобы сравниваемые объекты были подобны в важных, существенных признаках, а не в случайных и второстепенных деталях. Полезно также, чтобы круг совпадающих признаков этих объектов был как можно шире.
Для строгости аналогии важен, далее, характер связи сходных признаков предметов с переносимым признаком. Информация о сходстве должна быть того же типа, что и информация, распространяемая на другой предмет. Если исходное знание внутренне связано с переносимым признаком, вероятность вывода заметно возрастает.
Допустим, что мы сопоставляем двух людей: оба они родились в одном и том же году, ходили в один и тот же детский сад, окончили одну и ту же школу, причем по всем предметам получили одинаковые оценки, оба не женаты. Об одном из них известно, что он мастер спорта по футболу. Можно ли с достаточной вероятностью заключить, что и второй тоже мастер спорта? Hardly. Намеченная общность их биографий никак не связана с игрой в футбол. Вот если бы мы знали сверх того, что оба они посещали одну и ту же спортивную школу, а потом вместе играли в дублирующем составе известной футбольной команды, вероятность вывода несомненно возросла бы.
Or another example. Two girls lived in the same house, went to school together, studied at the same institute, at the same faculty, both dreamed of becoming astronauts. In short, in everything, not excluding trifles, their biographies were similar. It is known that one of them married an architect. Is it possible, continuing the detailed and extensive similarities between these girls, to conclude that the second of them also married the same architect? Of course no. The probability of such a conclusion would be zero.
Thus, when constructing an analogy, it is not so much the abundance of similar features of objects that is important as the nature of the connection of these features with a portable attribute.
Кроме того, при проведении аналогии необходимо тщательно учитывать не только сходные черты сопоставляемых предметов, но и их различия. Как бы ни были подобны два предмета, они всегда чем-то отличаются друг от друга. И если их различия внутренне связаны с признаком, который предполагается перенести с одного предмета на другой, аналогия неминуемо окажется маловероятной, а возможно, вообще разрушится.
Интересный пример неверной аналогии приводят биологи И. и Дж. Медавар в книге «Наука о живом».
Произведения человеческих рук, используемые в качестве орудий и инструментов, в определенной степени являются продолжением человеческого тела. Применение микроскопа и телескопа наделяет человека сверхзрением. Одежда выполняет некоторые из защитных функций шерстного покрова животных. Антибиотики иногда делают то, чего не могут сделать антитела, находящиеся в крови человека и препятствующие вторжению в его организм инфекции, гейгеровский счетчик снабжает человека органом чувств, аналога которого у него вообще нет, — он позволяет регистрировать, например, рентгеновское и гамма-излучении. Подобные инструменты иногда называют «внешними органами».
Obviously, these organs are undergoing slow, lasting changes for centuries. Along with the evolution of man himself, there is a parallel evolution of his “external organs”. For example, in both cases, one can find rudimentary organs, such as those that have long since failed to perform any function of the hair on the face of a person and the buttons stubbornly sewn onto the cuffs of their jackets. There are more serious parallels, for example, that evolutionary changes in both cases do not occur simultaneously in the entire population, but appear first in a limited number of its members and only then spread to the entire population. So, bicycles and cars were initially only for a few, and then gradually became widely available.
Although the parallel between human evolution and the evolution of "external organs" is quite obvious and somewhat instructive, it encounters important differences.
Ordinary organic evolution is due to the action of the genetic mechanism. The evolution of “external organs” is possible only due to the transfer of information from one generation to another through non-genetic channels. Absolutely dominant among them is language. Perhaps it is precisely because with the subtlety, flexibility and ability to transmit information, the language surpasses the genetic mechanism, the evolution of "external organs" and turns out to be much more fast-acting and powerful factor of variability than ordinary human evolution.
Further, the process of evolution of “external organs” has the character of gradual and consistent accumulation, inheritance of acquired features. To preserve civilization, it is necessary to transfer from generation to generation the accumulated knowledge and methods, as well as works of art and other creations of the spirit.
There is no such accumulation in the ordinary evolution. Say, the children of the mountaineers, constantly moving along the slopes, are not born at all with one foot a little longer, so that it is more convenient for them to walk.
And finally, the usual evolution is irreversible; it cannot be expected that, for example, human development will go one day in the opposite direction and lead with time to the creature from which it once came. The evolution of “external organs” in principle can turn out to be reversible - for this, it is necessary that a complete rupture of cultural ties between generations occurs. Let's hope that the human mind will not allow this.
Sometimes experts in logic and modeling say that if the conclusions by analogy relate to abstract objects like numbers or geometric figures, then under certain conditions the analogy may still lead to a reliable conclusion. This happens if a strict correspondence is established between the elements of the two systems being compared, as well as the operations, properties and relations characteristic of these systems.
As an example, the relations between the photograph and the original, the translation of the language text and the original, the geographical map and the corresponding terrain, the drawing of the machine and the machine itself, etc. are usually given.
It is not difficult, however, to note the following. The reasoning in which, say, a photo and an original or a drawing and a car are compared and additional information about the strict correspondence between them is involved, it is simply not a conclusion by analogy. Reconstructed in all its elements, such reasoning turns out to be a rather complicated deductive reasoning. The latter, as is well known, gives truth if its premises are true. The fact that in the general course of the movement of thought this deduction resembles an analogy does not mean at all that there are any exceptions to the general principle: the conclusion of the analogy is problematic.
Naturally, such a romantic method, like reasoning by analogy, involving rich imagination and allowing to bring together the most distant things, is widely used in fiction.
The heroes of the works, like all other people, constantly turn to analogies, convincing themselves and others with their help. Authors of works often put a conclusion by analogy into the basis of the plot. A favorite method of literary critics is to draw parallels: the characters of different works are compared, their authors, the thoughts and deeds of the characters are compared with the convictions and circumstances of the lives of their creators, etc. Sometimes, and more often unnoticed by a writer, reasoning by analogy turns out to be the implication of all the events described by him, the invisible thread that binds together the seemingly eccentric and seemingly poorly motivated actions of the hero.
In the novel by R. Stevenson “Treasure Island”, it is described how pirates, led by John Silver, suddenly heard a voice in a nearby grove. They immediately decided that it was the voice of a ghost. Silver first came to his senses:
“Do you think this is a ghost?” Maybe so, he said. - But one thing confuses me. We all clearly heard the echo. Tell me, has anyone seen a shadow in the ghost? If there is no shadow, then there is no echo. It can not be otherwise.
“Such arguments,” remarks the boy, on whose behalf the story is being told, “seemed to me weak.” But you can never tell what will work on superstitious people.
Silver seeks to convince his companions that the voice they heard belongs to the person, not to the ghost. He compares the relation of the body to the shadow and the relation of the voice to the echo. The human body casts a shadow, the voice of a man causes an echo. In ghosts, as they then believed, there is no body, but only its form, their voice has no echo.
In the poem of M. Lomonosov, the cook uses reasoning by analogy to confirm the correctness of Copernicus in his dispute with Ptolemy:
Two Astronomers at the Feast Happen Together
And they argued quite among themselves in the heat.
One kept saying: "The earth, spinning around the sun walks."
The other is that the Sun drives the planet with it.
One was Copernicus, the other was known as Ptolemy.
Here the cook dispute decided his grin.
The owner asked: “Do you know the stars?”
Tell me, how do you reason about this doubt? "
He gave the following answer: “What Copernicus is about,
I will prove the truth without having been in the Sun.
Who saw the simpleton of the cooks is
Who would turn the fire around Zharkov? ”
Lomonosov was convinced of the correctness of the Copernican heliocentric system. The irony in the poem is, of course, connected with the frivolity of the cook's argument. Similarity between the relationship between the sun and the planets and the relationship between the hotbed and the hot to the extreme is superficial. Moreover, the conclusion by analogy, even the deepest and strictest, is not able to give "undoubted confirmation", "prove the truth." Lomonosov knew this well. But he also knew that in matters of faith and unbelief the power of reasonable arguments is not always crucial. The unpretentious analogy of the cook, expressed in artistic images, played a role in popularizing the teachings of Copernicus.
One day, seeing an old haggard mine. L. Tolstoy told I. Turgenev: “Do you want to tell you what this horse feels?” And then he began to consistently, vividly and vividly describe her long and difficult life. The story was so convincing that Turgenev jokingly asked: "Did you once, Lev Nikolayevich, be a horse?"
Later, Tolstoy wrote a kind of autobiography of the horse - the story "Strider" with the subtitle "The History of the Horse." In this story, an old horse tells other horses about his tangled, happy and unhappy life. The horse is humanized, its inner life is interpreted by analogy with the spiritual life of man.
Reasoning by analogy underlies the plot of the Russian folk tale "Three son-in-law."
The old man and the old woman had three daughters. The older one was given by the old man in the month of Mesyatsovich, the middle one by Sunny, and the younger was taken by the Wind-Breeze. Visiting his daughters, the old man every time learned from his sons-in-law something useful, and then applied it at home.
Month Monthyovich, having thrust a finger in a crack, has lighted an old man a bath. When the old woman entered the bathhouse at home, the old man thrust a finger into the gap.
- Is it light to you, old woman?
- What a light - dark-dark dark!
Yes, as my grandmother stumbled, she beat the gangs, spilled the water, barely alive and jumped out. And the old man keeps his finger in the gap.
The sun was hot on his head for an old man pancakes. At home, the old man said that the stove in the hut is no longer needed, he will bake pancakes himself. The old woman dissolved the dough. The old man sat in the middle of the hut.
“Lei,” he says, “to my bald spot.”
- What are you, old man, is not sick?
- Know lei! - He speaks.
The old woman poured him a baldness test. What was there, what was done here! For three days the old man in the bath was washed, washed washed.
The wind-breeze blew a scarf thrown into the water with a bubble and instantly ferried the old man to the other side of the river. Returning to the old woman, the old man decided to ride her. We went to the sea, and the boat flows.
- Do not worry, wife. Throw a handkerchief on the sea!
- What are you, in your mind? Scarf expensive, wool sewn.
- Throw, I say, will not disappear! The old woman threw a handkerchief.
- Jump! - says the old man.
The old woman jumped, and let the old man blow. Blew, blew - and the old woman is already in the water on her knees. He blew, blew the old man - and the neighbors already pulled out of the water a little alive.
The old man tried to act as his sons-in-law acted, but every time the likeness fell miserably. “Since then, the old man has abandoned the zyatyam to walk. The grandfather lies on the stove, boots his boots, eats pies and tales. ”
A peculiar biological - better to say, pseudobiological - analogy is used by the English writer O. Huxley in the novel “After many years the swan dies”. In biology, neoteny refers to the situation when an animal fully matures at a developmental stage equivalent to that at which its evolutionary ancestors were relatively immature. A well-known axolotl is a vivid example of a neotenic animal: throughout its entire life, it retains a number of larval features. Undoubtedly, Huxley got his idea from here that man is just a neotepecic form and builds a novel on a bizarre zoological fantasy: if human life lasted for many years longer than its natural term, man would eventually develop adult apes. Only limited life prevents a person from “growing up” into a monkey.
An interesting, but as a result, breaking the analogy between the two paintings is carried out by the Spanish writer K. Rojas in the novel “The Valley of the Fallen”. Despite the obvious similarity and even coincidence of the interpretation of images and composition, the pictures turn out to be very different.
The first of these is the famous Menin's painting by Velazquez, the second is Goya’s most illustrious painting, The Portrait of Carlos IV Family. Velázquez wrote royal jesters, and with all the details and physical flaws, so that they reflect the inner world of his heroes. Goya shows King Carlos IV with the queen in a circle of loved ones. In the same way as Velázquez, he does not seek to either idealize or blacken his models. In the background “Meninin” you can see a mirror, which in fact may be not a mirror, but a picture, and maybe a window. Goya has two large canvases hanging on the wall behind the backs of the fourteen characters depicted in his picture. Both are works of Goya. On the first - a soft landscape in a diffused light, perhaps, the youthful work of the artist. In the second picture, in broad strokes, in the spirit of Velázquez, a strange orgy of giants is depicted. Velázquez, in the Meninas, wrote himself a writing clown. Goya in his picture, too, places himself with an easel slightly apart from the royal family.
Despite all these similarities, “the results of Velasquez and Goya,” writes Rojas, “turned out to be completely opposite. For all their misery, the royal jesters of Velázquez show heightened sensitivity and a tragic sense of life, and the royal monarchs of Goya, as Aldous Huxley will say about them a century later, reveal the stupidity bursting with their lust for power and hidden treachery.
"Don Quixote" by M. Cervantes - this is the most readable novel ever written - in essence, there is a description of one big argument by analogy.
Don Quixote read medieval knightly novels and went on a journey to continue the exploits of their heroes. He lives entirely in the fictional world of the novels he reads, incessantly consults with their heroes in order to know what to do and what to say. He is not an eccentric, as many people think, but a man of duty, a man of honor, as well as knights, whose successor he portrays himself. He is trying to prove that his favorite novels are true. To this end, he diligently establishes a similarity between the described events and real situations. Windmills, herds, maids, inns are for him giants, castles, noble ladies and warriors.
Comparing novels and life, Don Quixote brings into reality all that he learned from books, never doubting the validity of such a transfer. Everything that happens to him only confirms, as it seems to him that chivalrous romances are an impeccable model of the world around him, and their language is the language of the world itself.
The wanderings and adventures of Don Quixote are a conclusion by analogy, embodied not in a word, but in practical, substantive action. To Doi Quixote himself, his analogy seems flawless. And only to those who are close to him - and above all Sancho Panse - it is clear that the parallels between the world of chivalry novels and real life no longer exist.
Another example is from the history of literary criticism.
A. Chekhov, a prominent Russian humorist N. Leikin, publisher of the Oskolki magazine, called his literary “godfather”.
Young Leykin’s stories, young Chekhov, by his own admission, read “earnestly” and “choking” with pleasure. However, Leykin’s literary reputation was unlucky: in the minds of the Russian reader, his work was ousted by Chekhov’s work, and he became an example of a writer who stopped in his development and created works for the needs of undemanding taste. The first accuser of Leikin, a humorist of unprincipledness, was the famous literary critic and journalist N. K. Mikhailovsky.
He wrote: “Mr. Leikin is, without a doubt, a good, lively and witty cartoonist, but he is only a cartoonist ... It would be in vain to look for guiding ideas from Mr. Leikin ... Mr. Leikin’s laughter exists only for himself, ideological bases and tendentious goals ... That huge stock of facts that he has accumulated! thanks to his watchfulness, he is definitely not illuminated by any sensible idea. He takes photographs of various street scenes, paints them ... and puts them into circulation ... The conditions of newspaper and especially small-newspaper work obviously play here almost the most important role: what kind of “idea” is it when you have to work every day? ”
Ten years later, Mikhailovsky estimated Chekhov's work in almost the same terms: “For all his talent, Chekhov is not a writer, self-versed in his material and sorting it out from the point of view of some general idea, but some kind of mechanical apparatus. .. "
He accused Leikin of photographicity, the randomness of his themes and plots, the absence of a leading general idea and tendency, and associating all this with the special nature of newspaper work. Mikhailovsky saw only a cartoonist in Leykine.
Equally, Mikhailovsky approached the work of the early Chekhov and found the same flaws in him as in Leikin. Hence the conclusion that Chekhov, with all his undoubted talent, is still not a writer.
And finally, the last example is from the memoirs of S. Ermolinsky about M. Bulgakov. Comparing Bulgakov’s plays “Moliere” and “Pushkin” and his novel Master and Margarita, Yermolinsky writes that an alarming Bulgakov motive arose in Pushkin, the same as in Moliere and Master and Margarita. Shortcomings, whispers, traps - this is the atmosphere. Benkendorf barely perceptible hint tells Dubelth that, de, the duel must be prevented, however ... the duel's place can be changed. "See that people are not mistaken, otherwise they will go wrong." They went "not there", and the duel took place. Pontius Pilate, in essence, has the same scene with the head of the secret police. The procurator expresses alarm that Judas may be killed, one must make sure that nothing happens to him, and the head of the secret police understands what this means, and organizes the murder. The police motive now and then erupts in works that are far apart in time and genre. Moliere is surrounded by the intrigues of Kabala the holy one and betrayed by his disciple, whom he believed. And around Pushkin winds the web of scammers. Higher - Benkendorf, and further - bogomasovy, long-armed, finally, in the apartment pretended to be a watchmaker, his home spy - Bitkov. He has a strange spiritual attraction to Pushkin. It is embarrassing to compare Bitkov with the Roman procurator, who reached out for Nashua, but Bitkov also clouded his heart, enchanted the poems - “The storm darkens the sky ...”.
Here the analogy between several works of the same author makes it possible to more clearly understand the ideological plan of each of them and emphasize the unity and originality of the artistic manner of their author.
In science, reasoning by analogy is applied as widely as in all other areas of human activity. This is not at all hampered by the fact that the analogy does not provide solid knowledge, but only a more or less plausible assumption. Причем нельзя сказать, что ученые используют по преимуществу строгие аналогии, вероятность заключений которых относительно высока. Разумеется, ученые стремятся — и, в общем, небезуспешно — именно к такому роду аналогиям. Но вместе с тем в научном творчестве, наряду с самыми точными из всех встречающихся аналогий, нередки весьма приблизительные, а то и просто поверхностные уподобления.
Объяснение этого — в сложности процесса научного познания и в многообразии тех задач, которые решаются в науке с помощью аналогий.
Точная аналогия — конечно, идеал ученого. Она возможна, однако, только в достаточно развитых областях знания. На начальных стадиях исследования обычно приходится довольствоваться примерными уподоблениями.
Далее, ученый может обращаться к аналогии с разными целями. Она может привлекаться, чтобы менее понятное сделать более понятным, представить абстрактное в более доступной, образной форме, конкретизировать отвлеченные идеи и проблемы и т.д. По аналогии можно также рассуждать о том, что пока недоступно прямому наблюдению. Она может служить средством выдвижения новых гипотез, являться своеобразным методом решения задач посредством сведения их к ранее решенным задачам и т.д.
В конечном счете, именно цель рассуждения определяет характер аналогии. В одних случаях требуется предельно точная аналогия, в других полезной может оказаться свободная аналогия, не стесняющая творческое воображение и фантазию исследователя.
Французский инженер С. Карно, заложивший в начале XIX в. основы теории тепловых машин, смело уподобил работу такой машины работе водяного двигателя. Физическая аналогия между переходом тепла от нагретого тела к холодному и падением воды с высокого уровня на низкий — пример строгой аналогии, опирающейся па существенные черты уподобляемых объектов. В истории физики есть и примеры весьма свободных аналогий, сыгравших вместе с тем важную роль в развитии науки.
Так, И. Кеплер, открывший законы движения планет, уподоблял притяжение небесных тел взаимной любви. Солнце, планеты и звезды он сравнивал с разными обликами Бога. Эти сопоставления кажутся сейчас, по меньшей мере, странными. Но именно они привели Кеплера к идее ввести понятие силы в астрономию.
И. Гутенберг пришел к идее передвижного шрифта по аналогии с чеканкой монет. Так было положено начало книгопечатанию, открыта «галактика Гутенберга», преобразовавшая всю человеческую культуру.
Первая идея Э. Хау, изобретателя швейной машины, состояла в совмещении острия и ушка на одном конце иглы. Как возникла эта идея — неизвестно. Но главное его достижение было в том, что по аналогии с челноком, используемым в ткацких станках, он изготовил шпульку, которая продергивала дополнительную нить через петли, сделанные игольным ушком, и таким образом родился машинный шов.
В. Вестингауз долго бился над проблемой создания тормозов, которые одновременно действовали бы по всей длине поезда. Прочитав случайно в журнале, что на строительстве тоннеля в Швейцарии буровая установка приводится в движение сжатым воздухом, передаваемым от компрессора с помощью длинного шланга, Вестингауз увидел в этом ключ к решению своей проблемы.
Рассуждение по аналогии дало в науке многие блестящие результаты, нередко совершенно неожиданные.
В XVII в. движение крови в организме сравнивали с морскими приливами и отливами. Врач В. Гарвей ввел новую аналогию с насосом и пришел к фундаментальной идее непрерывной циркуляции крови.
Химик Д. Пристли воспользовался аналогией между горением и дыханием и благодаря этому смог провести свои изящные эксперименты, показавшие, что растения восстанавливают воздух, израсходованный в процессе дыхания животных или в процессе горения свечи.
Д. Гершель
продолжение следует...
Часть 1 11.7 Analogy. Inference scheme by analogy Minimized analogies Analogy of properties and analogy of relations
Часть 2 Аналогия в историческом исследовании - 11.7 Analogy. Inference scheme by
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Logics
Terms: Logics