5- 1 "Russell is the Pope"
From a purely logical point of view, absurd assumptions can infer any absurd conclusion, even if the reasoning process is impeccable.
Someone once asked Russell to prove that "Russell is the Pope" is derived from "2+2=5". Russell proved as follows:
Since 2+2=5, 2 is subtracted from both sides of the equation.
get 2 = 3； Subtract 1 from both sides,
1 = 2; Both sides move,
The total is 2= 1.
Pope and Russell are two people. Since 2= 1, the Pope and Russell are 1, so "Russell is the Pope".
This absurd conclusion is triggered by an absurd assumption.
5-2 "Aristotle is a class concept"
This is the result of strictly following syllogism. Please see:
Aristotle was a philosopher,
(2) the philosopher is the concept of a class,
Therefore, Aristotle is a class concept.
Aristotle (384-322 BC) was a great Greek philosopher and astronomer. He studied under Plato and inherited the Greek philosophy since Socrates, the most influential in the West. He systematically summarized the principles of syllogism and laid the foundation of logical thinking.
I'm afraid even Aristotle himself won't agree with this conclusion. Because it contains a "semantic paradox". Because the philosopher in sentence (1) and the "philosopher" in sentence (2) are not at the same level, the former is an object concept and the latter is a meta-concept. If the connotations of the two premises are inconsistent, the conclusion is absurd. Fundamentally speaking, this is not a language or grammar problem, but a logical error. Since Talsky put forward the theory of "language hierarchy" in 1930s, people have been paying attention to this issue.
5-3 contradiction
This example is on the contrary, it is a classic example, because of incompatible premises and can not draw a conclusion:
Everything is wrong introduces this prediction: there is a man who sells spears and shields at the same time. First he boasted that his shield was the strongest and could not pierce anything; Then he boasted that his spear was the sharpest and could pierce anything. When someone asked him what would happen if he stabbed his shield with his spear, he couldn't answer because the two were contradictory. This is a proposition that can neither be true nor false at the same time. If the premise is contradictory, it is impossible to draw a conclusion.
5-4 Card Paradox
The paradox of the card is that one side of the card says, "The sentence on the opposite side of the card is correct." On the other hand, it says, "The sentence on the back of the card is wrong." This was put forward by the British mathematician Jordan. We can't push out the result either.
5-5 Jordan's Paradox of Truth
The following sentences are correct.
The above sentence is wrong.
This is also a famous paradox, which can be regarded as a simplified form of the card paradox. Contradictory paradox, card paradox and Jordan's truth paradox basically belong to the same type.
5-6 "Which came first, the chicken or the egg?"
This causal circular reasoning itself cannot extricate itself, and it needs practical research, such as archaeological and biological research results, to break this cycle.
It also implies an incompatible premise: "chickens are hatched from eggs, and eggs are born from chickens." Individually, it is consistent with daily observation, but together it is a pair of inconsistent assumptions.
5-7 "God and Stone"
"If God is omnipotent, can he create a big stone that he can't lift?"
This is a universal paradox. If so, God meets a "big stone he can't lift", which shows that he is not omnipotent; If not, it also means that he is not omnipotent. This is the premise of using conclusions to blame.
Another expression of this "Almighty Paradox" is: "Can the Almighty Creator create something greater than him?"
5-8 "You will kill me"
There are several versions of this story. A group of robbers caught a businessman, and the robber leader said to the businessman, "Do you think I will kill you? If I am right, I will let you go; " If I am wrong, I will kill you. "The merchant thought for a moment and said," You will kill me. "So the robber let him go.
Reasoning: If the robber kills the businessman, his words are undoubtedly right and should be released; If you let people go, the businessman's words are wrong and should be killed. This is a paradox. The answer found by the clever businessman made the robber's premise incompatible.
5-9 "You will eat my baby"
This example is logically isomorphic to the above example.
A crocodile snatched a child and said to its mother, "Will I eat your child?" If the answer is correct, the child will return it to you; If the answer is wrong, I will eat him. We already know the mother's answer: "You will eat my child." "
5- 10 two children debate day
This is a fable in Liezi: Confucius met two children and quarreled. One said, "At sunrise, the sun is very close to us, and at noon, the sun is far away from us. Because the sun is as big as a wheel at sunrise and as small as a plate at noon. Isn't that it? " The other said, "At sunrise, the sun is far away from us, and at noon, the sun is close to us. Because we don't feel hot at sunrise, but it is very hot at noon. Isn't this near hot and far cold? " Confucius could not answer.
This is a question of scientific common sense today, which people did not know more than two thousand years ago. Logically, there are two criteria to measure "near big and far small" and "near hot and far cool". Before you answer the question, you should find out which standard is more accurate or inaccurate.
5- 1 1 Should Avatar pay tuition?
According to legend, Euler Ruth in ancient Greece learned to argue from Protegoras (another way is to study law). Their agreement is: Avatier pays half the tuition fee first and the other half when he wins the first defense after finishing his studies. If he loses, he won't have to pay the tuition.
But after graduation, Avatier didn't act as a defender, and he didn't intend to pay the other half's tuition.
Protegoras wants to sue him, saying, "If I win the lawsuit, the judge will sentence you to pay my tuition;" If I lose the lawsuit, you still have to pay my tuition according to the agreement. In short, I have to pay. Awajie said, "If I win the case, the judge will also sentence me not to pay tuition; "If I lose the lawsuit, I don't have to pay the other half of the tuition according to the agreement. In short, no money. " (See Wang Jiukui's Logic and Mathematical Thinking)
On the other hand, this problem is logically the same. If Evatier had said first, "If you sue me, I wouldn't have to pay the tuition." Protagoras can refute it in the same way. It is impossible to have a result if this argument goes on.
The problem here is that both of them acquiesce that "agreement" and "judgment" can solve their disputes simultaneously and equivalently, which is the premise for them to reach an agreement. The way to solve them logically is to choose one of them to make the final decision.
5- 12 Brahma scholar's "prophecy"
Similar to the above example, this is a story about the daughter of Brahma scholar (Indian prophet) embarrassing her father with paradox.
The daughter wrote a line on the paper and pressed it under the crystal ball. Then he told his father that what was written on the paper might or might not happen. If you predict it will happen, write "Yes", otherwise write "No".
The Brahma scholar wrote down his prophecy "Yes", and the daughter took out the paper under the crystal ball and read: "Just write a word" No "." Scholars are wrong. In fact, it is wrong for him to write "no" because the prophecy has already happened.
Daughter's "no" has two meanings, on the one hand, it is contrary to the literal "yes", on the other hand, it is contrary to the actual "no", with double standards. Because there is no definition in advance, Brahma scholars can also argue with their daughters indefinitely.
5- 13 People often say that "losing is a blessing"
Suppose there are two people, A and B. If A suffers, then B doesn't suffer, then A is obviously blessed, and B is not blessed relative to A, then B suffers, then B suffers and is blessed, then A is not blessed relative to B, and then it continues indefinitely. or vice versa, Dallas to the auditorium
6- 1 ares paradox
The following two formulas represent the income you will get, and x is an indefinite quantity. S 1 or S2, which would you choose?
( 1)s 1 = 0 9X+$ 100，000
(2) S2 = 0.89x+250,000 USD
Obviously, the best choice depends on what x is.
When X = 65438 USD+05,000,000, s 1 = S2 = 65438 USD+03,600,000.
When x >15,000,000 USD, S 1 > S2
When x < $15,000,000, s 1 < S2.
This paradox has a great influence on decision theory.
6-2 Newcomb Paradox
This is also one of the decision-making theories. There are two boxes a and b on the desk:
A is transparent, and you can see that there is $ 1 000 in it.
B is opaque, and it says either 1 0,000,000 or 0.
You can only choose one of the following two options (1) or (2):
(1) Select only B.
(2) choose both a and b.
What choice would you make?
A professor once did an experiment: he asked 1000 students to choose, of which 999 students chose (2) and only 1 student chose (1). 999 students each received only $65,438+0,000, while 65,438+0 students received $65,438+0,000,000. Why? Because the professor has made a prediction in advance and made this arrangement:
If you choose (2), you won't put any money in the box.
If you choose (1)B, put $ 1 million in the box.
And the professor's prediction is only one thousandth wrong. If you already know the result and choose again, which one would you choose? Note that this time, the professor may have made a new prediction.
6-3 Definition of Valley "Heap"
If 1 millet can't form a grain pile, two millet can't form a grain pile, three millet can't form a grain pile, and so on, no matter how many millet can't form a grain pile.
Proceed from the real premise and use acceptable reasoning, but the conclusion is obviously wrong. Explain that the definition of "heap" lacks clear boundaries. It is different from multi-premise reasoning based on syllogism, and it forms a paradox in the continuous accumulation of one premise. There is no clear boundary between no heap and heap, and the solution is to introduce a fuzzy "class".
This is an example of the chain paradox, which is attributed to Eubulides in ancient Greece, and later skeptics denied it as knowledge. Soros means "heap" in Greek. It started as a game: Can you describe 1 millet as a bunch? No; Can you describe two particles as a pile? No; Can you describe three grains as a pile? I can't. But sooner or later, you will admit the existence of a grain pile. Where do you distinguish them?
Its logical structure:
1 Xiaomi is not a heap,
If 1 millet is not a pile, then two millet are not a pile.
If two grains are not piles, then three grains are not piles.
……
If 99999 is not a heap, then 100000 is not a heap.
So 100000 millet is not a heap.
According to this structure, the ancient Greeks argued whether there were piles, whether they were rich or poor, whether they were small or big, and whether they were less or more.
Theme (see Encyclopedia Britannica).
6-4 Definition of Baldness
This is also an example of chain paradox, which is exactly the same as the above game. Originally called Falakros mystery:
Can you call a man with only/kloc-0 hair bald? Yes; Can you call a man with only two hairs bald? Yes; Can you call a man with only three hairs bald? You can. But you wouldn't call a man with ten thousand hairs bald. Where do you distinguish them?
6-5 "A whole bag of millet landed silently"
There is also a story in ancient Greece: if 1 millet landed noiselessly, two millet and three millet landed noiselessly, and so on, the whole bag 1 millet landed noiselessly.
Noise is caused by vibration. 1 The vibration caused by Xiaomi's landing is too small for human ears to hear, but the instrument can detect it. The vibration caused by a bag of millet falling to the ground is so great that people can naturally hear it.
It should be noted that this is not the original intention of the ancient Greek debaters. They don't really want to discuss facts, but try to find the difference between logical deduction and facts. If we admit that Xiaomi Landing is a series from noiseless to noisy, there will also be a fuzzy area of change.
6-6 Unexpected Hang Time
This paradox is called the paradox of accidental hanging in English; It was first spread by word of mouth in the 1940s.
A prisoner was sentenced on Saturday. The judge announced: "The hanging time will be held at noon on one of the seven days next week, but you will know the exact date of execution in the morning of that day." The prisoner analyzed, "Next Saturday is the last day. If I were alive next Friday afternoon, I would know that I would be executed at noon next Saturday. But this contradicts the judge's decision, so I can't be hanged next Saturday. " Then next Friday is the last day. Similarly, he can't be hanged next Friday, and so on. He thinks he can't be hanged next Thursday, Wednesday, Tuesday, Monday and Sunday. So the judge's decision will not be enforced.
This chain paradox reasoning is not difficult to understand. The judge's decision can be executed any day except next Saturday, and the prisoner's expectations have failed. There is also an "unexpected paradox of examination time" which is completely consistent with the structure of this paradox.
6-7 "Eggs with Hair"
Hui Shi once argued this subject with a debater. The debater said there was hair in the egg, but Hui Shi objected.
The debater said, "There is no hair in the egg. How can the hatched chicken have hair?" Hui Shi said, "There is only egg white and yolk in the egg, and there is no hair. Have you ever seen hair in an egg? The hair on the chicken is the hair on the chicken, not the hair in the egg. " But the debater can't accept it
Both sides of the debate take "seeing is believing" as the standard, thus ignoring the transformation process from hairless to hairy. I don't know how biology will explain this. In terms of methods, they don't define the boundaries of hair from scratch, and they don't seem to accept the fuzzy area that "the hair on a chicken may also be the hair in an egg".
6-8 Pagoda from existence to absence
This is an example of philosophical change from quantitative to qualitative. A pagoda, if its bricks are taken from below, one by one, is quantitative change. To a certain extent, the pagoda collapsed and changed qualitatively, indicating that the pagoda was gone. We can see an accurate "degree"
But taking its bricks from above and pumping them one by one is also a quantitative change. Until it was completed, the pagoda did not exist and changed qualitatively, but it is not easy for us to find an accurate "degree" from quantitative change to qualitative change.
6-8 Twin Paradox
This is a paradox related to relativity.
One of Einstein's achievements is to introduce a law, in which c stands for the constant speed of light in vacuum, and it is listed in the list of natural constants as the unattainable maximum critical speed. According to the constant speed of light, two famous "paradoxes" of relativity were introduced, which were once ridiculed as "absurd" conclusions of relativity.
"Twin Paradox" refers to a clock in a fast-moving frame of reference, which moves slower than a clock in a stationary frame of reference. According to this conclusion, we can draw a conclusion that a person who travels in space by spaceship at a speed close to the speed of light will be younger than his twin brother who lives on the earth when he returns to the earth. Because his biological clock is slower than that of people who stay on earth. Although the spacecraft is far from the speed of light.
Before Einstein's special theory of relativity was established in 1905, Newton's law was a law under the condition that the speed was much less than the speed of light. The mechanistic view of nature dominated people's spatial imagination, so it could not explain this phenomenon. Einstein's concept of time relativism is brand-new, which blocks Newton's concept of "absolute time" and makes the concept of "absolute motion" lose its foothold.
Therefore, only those who still maintain the concept of absolute time will call it a paradox-it is not a real paradox.
6-9 "Variable Scale"
This is another "paradox" derived from the theory of relativity: a fast-moving ruler is shorter in the direction of motion than in the static state. This problem was put forward from Michelson's experimental results, and later Lorenz's mechanical contraction hypothesis was formed. Einstein believes that this contraction can be explained by the relative speed between the two reference systems (see Nie's Cradle of Relativity: A Biography of Einstein).
6- 10 Why is the night sky dark?
This is the famous Olbers Paradox: If the space is infinitely extended and the stars are evenly distributed, we should meet at least one planet in any sight. So, shouldn't the sky always be bright? This conclusion is obviously inconsistent with the facts.
This problem was noticed by Kepler as early as 16 10, and was not widely concerned until 1823, when German astronomer Olbers proposed it again. In the past, there were many speculations, such as the limited number of stars in the universe, the uneven distribution of stars, the farther the stars, the less visible light, and the distant light has not yet reached the earth. After the emergence of the "Big Bang" theory, the age of the universe is not infinite, which is considered to be the most important reason. Since the Big Bang, the universe has a history of 1000 to 20 billion years. The young universe hasn't had time to fill the night sky with light (Sunday Telegraph 1997 10.05).
7- 1 What's the shape of water?
After reading the famous "Schrodinger's cat" paradox, a new model paradox, namely the water paradox, appeared. This paradox may have a far-reaching impact in science, philosophy and other fields.
The paradox of water shape is a process: there is a certain amount of water, and some people want to prove the shape of water through experiments. They will definitely prepare the experimental equipment first. If A studies water in a square cup, he will conclude that the shape of water is square. If B studies water in a rectangular vessel, it will be concluded that water is rectangular. According to this reasoning, there will be more than two conclusions about the shape of water.
In fact, we can learn a lot from this simple and profound' water paradox'. In other words, each of them came to the correct conclusion. Because this is the correct result from their respective experimental tracks. However, their correct conclusion is based on the relative environment. It can also be said that their research results are incorrect. Because, these researchers are confused and induced by this specious whole phenomenon. In essence, water is invisible. All kinds of conclusions are also of their own making. Sometimes, experiments don't necessarily yield anything.
It can be concluded that the correctness of the phenomenon does not represent the essence of things. Perhaps, when people are ready to observe or study, they are already on the road of deviating from the essence.