Saville's barber made a rule for himself: "He only shaves people in the village who don't shave themselves. So someone asked him: Who will shave your own beard? " The barber was speechless at once.

Because if he shaves himself, he belongs to the kind of person who shaves himself. However, the sign says that such people don't shave, so they can't shave themselves If another person shaves himself, he just doesn't shave himself. The sign clearly says that all men who don't shave themselves should shave themselves. So, whatever the inference,

This is the famous Barber paradox, which was put forward by the British philosopher Russell. This well-known story expresses a famous paradox in set theory-Russell paradox. Russell's paradox has other popular problems, one of which is described as follows: suppose a librarian wants to edit a bibliography for his library: it only includes all the bibliographies that are not listed in his library.

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The problem of robbers

The robber robbed a businessman. He tied the businessman to a tree and prepared to tease him before killing him. The bandit leader said to him, "I wanted to kill you at once, but I will give you another chance before I die." Do you think I'll kill you? If you are right, I will let you go, and I will never go back on my word! If it is wrong, I will kill you. "

The robber thinks this businessman born to die. He never imagined that the businessman escaped this robbery with his own cleverness. The clever businessman thought it over and said, "You will kill me." Now, it is the robber's turn to be in a daze. "If I kill you, you are right, so you should be released; If you are released, you are wrong, but you should be killed. " The robber never thought that he was in a dilemma. He admired the businessman and released him.

This is a story often told by ancient Greek philosophers. The merchant's sentence: "You will kill me." Immediately lifted the immediate predicament. How smart he is. If he says, "You'll let me go." In this way, the robber said that no matter what he did, he would definitely break his promise.

There are many interesting questions like this. For example, God is omnipotent. Do you think God can create a big stone that he can't lift?

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Liar paradox

In the 6th century BC, Epimenendez, an ancient Greek philosopher in Crete, asserted that "everything that Cretes say is a lie." If this sentence is true, that is to say, a Crete, Epimenendez, said the truth, but asserted that Cretes could not tell the truth. If this sentence is not true, that is to say, Epimenendez of Crete told a lie and asserted that Crete is also true.

In the 4th century BC, Greek philosophers also put forward this paradox: "What I am saying now is a lie." Because if what you say is true, content analysis should be deceptive. On the other hand, if what you say is a lie, then what you say should be true. The liar paradox still puzzles mathematicians and logicians.

The liar paradox takes many forms. For example, I predicted, "You're going to say' no' next, right? Answer with' yes' or' no'! " If you say "no", that means you don't agree with my prediction. In other words, you should say "yes", which goes against your original intention. If you answer "Yes!" This means that you agree with my prediction, so you have to "no", and then there will be contradictions.

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