Lecture
At the heart of one famous paradox is like a small incident that happened more than two thousand years ago and has not been forgotten until now.
The famous sophist Protagoras, who lived in the V century. BC, was a student named Evatl, who studied law. According to the agreement concluded between them, Evatl should have paid for his studies only if he won his first trial. Not. 111 But he will lose this process, he is not obliged to pay at all. However, having completed the training, Evatl did not become involved in the processes. It lasted for quite a long time, the teacher's patience ran out, and he sued his student. So for Evatl, this was the first process. Protagoras justified his claim as follows:
Whatever the court decision, Evatl will have to pay me. He will either win this first process or lose. If you win, then pay by virtue of our contract. If you lose, then pay according to this decision.
Apparently, Evatl was a capable student, as he replied to Protagoras:
Indeed, I will either win the process or lose it. If I win, the court decision will release me from the obligation to pay. If the court decision is not in my favor, it means that I lost my first process and will not pay because of our agreement.
Puzzled by such a turn of affairs, Protagoras devoted a special essay “The Cause of the Board” to this dispute with Evatl. Unfortunately, it, like most written by Protagoras, did not reach us. Nevertheless, we must pay tribute to Protagoras, who immediately sensed a problem behind a simple judicial incident that deserves special study.
Mr. Leibniz, a lawyer by education, also took this dispute seriously. In his doctoral thesis “A study on entangled incidents in law”, he tried to prove that all cases, even the most complicated ones, like Protagoras and Evatl's cases, must find the right resolution based on common sense. According to Leibniz, the court should deny Protagoras for the untimely suing, but leave, however, the right to demand payment of the money by Evatl later, namely after the first process won by him.
Many other solutions to this paradox have been proposed.
They referred, in particular, to the fact that the court decision should have greater force than the private agreement of two persons. To this it is possible to answer that the ns were this agreement, no matter how insignificant it seemed, there would be neither a court nor its decision. After all, the court must make its decision on its behalf and on its basis.
They also applied to the general principle that every work, and therefore the work of Protagoras, must be paid. But it is known that this principle always had exceptions, especially in a slave-owning society. In addition, he simply does not apply to the specific situation of the dispute: after all, Protagor, guaranteeing a high level of training, he himself refused to accept payment in the event of the failure of his student in the first process.
Sometimes reason like that. Both Protagoras and Yevatl are both partly right, and neither of them as a whole. Each of them takes into account only half the opportunities that are beneficial for themselves. Full or comprehensive consideration opens up four possibilities, of which only half is beneficial for each of the disputants. Which of these possibilities is realized, it is not logic that decides, but life. If the verdict of the judges is more powerful than the contract, Evatl will have to pay only if he loses the process, i.e. by virtue of a court decision. If the private agreement is set higher than the decision of the judges, then Protagoras will be paid only if the process is lost to Evatlu, i.e. by virtue of the contract.
This appeal to life finally confuses everything. How, if not by logic, can the judges be guided by in conditions when all relevant circumstances are perfectly clear? And what kind of leadership will it be if Protagoras, who claim to be paid through the courts, achieve it only by losing the process?
However, the decision of Leibniz, which seems convincing at first, is not much better than a vague opposition of logic and life. In essence, Leibniz proposes to retroactively replace the wording of the contract and stipulate that the first trial involving Evatl, the outcome of which decides the question of payment, should not be the court at the suit of Protagoras. This thought is deep, but not related to a particular court. If there were such a reservation in the original agreement, there would be no need for a trial at all.
If the solution to this difficulty is to understand the answer to the question of whether Evatl must pay Protagoras or not, then all these, like all other conceivable decisions, are, of course, untenable. They are nothing more than a departure from the essence of the dispute, are, so to speak, sophistic tricks and tricks in a hopeless and intractable situation. For neither common sense, nor any general principles relating to social relations are able to resolve the dispute.
It is impossible to execute together the contract in its original form and the decision of the court, whatever the last. To prove this, fairly simple means of logic. With the help of the same means it can also be shown that the contract, despite its completely innocent appearance, is internally contradictory. It requires the implementation of a logically impossible position: Evatl must simultaneously pay for the training and not pay at the same time.
The human mind, accustomed not only to its strength, but also to its flexibility and even resourcefulness, is difficult, of course, to put up with this absolute hopelessness and recognize itself driven into a dead end. This is especially difficult when the deadlock is created by the mind itself: it, so to speak, stumbles out of the blue and caters to its own networks. Ii. nevertheless, one has to admit that sometimes, and by the way, not so rarely, agreements and systems of rules established spontaneously or deliberately introduced lead to insoluble, hopeless situations. An example from recent chess life will once again confirm this thought.
International rules for chess competitions require chess players to record a game move by move clearly and legibly. Until recently, the rules also stated that a chess player, who missed the recording of several moves due to lack of time, should, "as soon as his time trouble ends, fill in his own form immediately, recording the missed moves." On the basis of this instruction, one judge at the 1980 Chess Olympiad (Malta) interrupted the game that took place in hard time pressure and stopped the clock, stating that the control moves were made and, therefore, it was time to put the records in order.
“But let me,” cried the participant, who was on the verge of losing and relying only on the passions at the end of the game, “for not a single flag had fallen yet and no one has ever (this is also recorded in the rules) telling you how many moves were made.
The judge was supported, however, by the chief arbiter, who stated that, indeed, since the time trouble had ended, one should, following the letter of the rules, proceed to recording the missed moves.
To argue in this situation was pointless: the rules themselves were brought to a standstill. It remained only to change their wording so that such cases could not arise in the future.
This was done at the congress of the International Chess Federation held at the same time: instead of the words “as soon as the time trouble ends”, the rules now write: “as soon as the checkbox indicates the end of time”.
This example clearly shows how to deal with dead ends. To argue about which side of the law is useless: the dispute is insoluble, and there will be no winner. It remains only to accept the present and take care of the future. For this, it is necessary to reformulate the original agreements or rules so that they do not lead anyone else into the same hopeless situation.
Of course, such a course of action is by no means a solution to an insoluble dispute and not a way out of a stalemate. It is rather a stop in front of an insurmountable obstacle and a road to bypass it.
In ancient Greece, the story of the crocodile and the mother was very popular, coinciding in its logical content with the paradox “Protagoras and Yevatl”.
The crocodile snatched from an Egyptian woman, standing on the bank of the river, her child. On her plea to return the child a crocodile, the strait, as always, to a crocodile tear, answered:
- Your misfortune touched me, and I will give you a chance to get the baby back. Guess if I give it to you or not. If you answer correctly, I will return the child. If you do not guess, I will not give it up.
Having thought, mother answered:
- You will not give me a child.
“You won't get it,” the crocodile concluded. - You said either the truth or the truth. If the fact that I do not give up the child is true, I will not give it up, since otherwise what has been said will not be true. If this is not true, then you have not guessed, and I will not give the child by persuasion.
However, this reasoning did not seem convincing to the mother.
“But if I told the truth, you will give me the child, as we agreed.” If I did not guess that you will not give the child, then you must give it to me, otherwise what I said will not be untrue.
Who is right: mother or crocodile? What does the crocodile promise them require? To give the child or, on the contrary, not to give it away? And to that and to another simultaneously. This promise is internally contradictory, and thus, it is impracticable by virtue of the laws of logic.
The missionary found himself at the cannibals and fell just in time for dinner. They allow him to choose in what form it will eat. To do this, he must utter some statement with the condition that if this statement turns out to be true, they will brew it, and if it turns out to be false, it will be fried.
What should the missionary say?
Of course, he must say: "You fry me."
If it is really fried, it turns out that he expressed the truth, and it means that it must be cooked. If he is brewed, his statement will be false, and it should be just fried. There will be no escape from cannibals: it follows from “frying” “cooking” and vice versa.
This episode with a cunning missionary is, of course, another of the paraphrasing of the controversy between Protagoras and Evatl.
One old paradox known in ancient Greece is played up in Don Quixote by M. Cervantes. Sancho Paisa became governor of the island of Barataria and administers the court. The first to him is some visitor and says:
- Senor, a certain estate is divided into two halves by a river with plenty of water ... So, a bridge is thrown across this river, and then there is a gallows on the edge and there is something like a court in which four judges usually sit, and they are judged by law published by the owner of the river, the bridge and the whole estate. The law is as follows: “Anyone passing over a bridge across a river must declare under oath: where and why he goes, and who will tell the truth, let those pass, and who will lie, send those to the gallows right there and execute them”. From the time when this law was made public in all its severity, many managed to cross the bridge, and as soon as the judges were satisfied that the passers-by were telling the truth, they let it through. But one day, a certain person sworn in, swore and said: he swears that he came to be hanged on this very gallows, and for nothing else. The oath led the judges to bewilderment, and they said: “If you allow this person to follow along unhindered, it will mean that he broke the oath and is guilty of death according to the law; if we hang him, then he swore that he had come only to be thrown up on this gallows, therefore, his oath is not false, and on the basis of the same law it is necessary to let him through. ” And now I ask you, senor governor, what should judges do with this person, for they are still puzzled and hesitate ...
Sancho suggested, perhaps, not without cunning: the half of the person who told the truth should be let through, and the one who lied should be hanged, and thus the rules for crossing the bridge will be observed throughout the form.
This passage is interesting in several ways. First of all, he is a graphic illustration of the fact that the desperate situation described in the paradox can be encountered - and not in pure theory, but in practice - if not a real person, then at least a literary hero.
The solution proposed by Sancho Panza was not, of course, a solution to the paradox. But it was just that decision, which only remained to be resorted to in his position.
Once Alexander of Macedon, instead of unleashing a cunning Gordian knot, which no one else could do, simply cut it. Sancho did the same. Trying to solve the puzzle on its own terms was useless - it is simply insoluble. It remained to discard these conditions and enter their own.
And one moment. Cervantes by this episode clearly condemns the excessively formal, permeated with the spirit of scholastic logic, the scale of medieval justice. But how common in his time - and this was about four hundred years ago - was information from the field of logic! This paradox is not only known to Cervantes himself. The writer finds it possible to ascribe to his hero, an illiterate peasant, the ability to understand that the task before him is insoluble!
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Logics
Terms: Logics