Classic paradox roaming (lower)

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[Classic paradox roaming (bottom)] This is the third part: the paradox caused by the premise not self-consistency and the paradox encountered by the right change.

(5) paradox caused by non-self-consistency of premises

Here we will see that if the premise is not self-consistent, the conclusions will not be self-explanatory, or even absurd or no conclusion.

5-1 "Russell is the pope"

Logically speaking, absurd assumptions can deduce any absurd conclusion, even if the reasoning process
Impeccable. Someone once asked Russell to prove that he was the Pope from "2 + 2 = 5 ". Russell proof
As follows:

Because 2 + 2 = 5, the two sides of the equation subtract 2 at the same time,
Get 2 = 3; subtract 1 from both sides at the same time,
1 = 2; shift on both sides,
2 = 1.

The Pope and Russell are two people. Since 2 = 1, the Pope and Russell are one person, so "Russell is
Pope ".

This absurd conclusion is triggered by a absurd assumption.

5-2 "Aristotle is a class concept"

This is a result derived strictly from the three-field theory. See:

(1) is a philosopher,
(2) philosophers are class concepts,
(3) Therefore, Aristotle is a class concept.

Aristotle (384-322 BC) is a great Greek philosophy.
Home and astronomy, who once learned Plato, inherited the Greek philosophy since Socrates and developed its own system in the West
Party has the greatest impact. He systematically summarized the principles of the Three-field theory and laid the foundation for logical thinking.

The conclusion above may not even be recognized by the person of the city. Because it contains a "semantic
Paradox ". Because the philosophers in Statement (1) and statement (2) are not at the same level
The former is the object concept, and the latter is the meta concept. The two premises have different meanings, and the conclusion is ridiculous. Slave Root
This is not a language or syntax problem, but a logic error. Since Tarski in 1930s
People have been paying attention to the introduction of "language hierarchy theory.

5-3 Self-conflict

This example is a classic example that fails to reach a conclusion due to incompatibility of the premise.

Han Feizi Shi Nan introduced this prediction: there is a man who sells spears and shield at the same time. He praised his shield first.
The strongest, no matter what is not broken, And then boast that his spear is the shortest, No matter what can be stabbed.
Someone asked him: If he stabbed his shield with his spear, he could not answer the question, because the two were mutually
Conflict. This is neither true nor false. The premise is conflicted.
The conclusion is not available.

5-4 card Paradox

The card paradox is that the card side says: "the opposite side of the card is right ." The other side is written
"The opposite side of a card is wrong ." This was proposed by Jourdain, a British mathematician.
We cannot push the results. The simplest form is:

5-5 "Paradox element"

The following sentence is correct,
The above sentence is wrong.

This is also a famous paradox called Jourdain Truth-Va
Lue) paradox. The above three examples basically belong to one type.

5-6 "first chicken or eggs ?"

This causal cyclical reasoning itself cannot be self-liberated and requires actual research, such as archaeology and generate
The results of research on things can break this cycle.

It also implies an incompatible premise assumption: "The chicken is incubated by the eggs, and the eggs are also by the chickens.
Generated ." Both of them comply with the daily observation, but they are a pair of non-self-consistent assumptions.

5-7 "If God is omnipotent, can he create a big stone that he cannot lift ?"

This is a widely spread paradox. If yes, God has met a huge rock that he cannot lift ",
It means 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 way to express this "omnipotent paradox" is: "the omnipotent creator can create more
Great things ?"

5-8 "you will kill me"

There are several versions in this story. A group of robbers grabbed a merchant and the chief of the robber targeted the merchant.
Said: "If you say that I will not kill you, if yes, I will release you; if yes, I will kill.
You ." The merchant said, "you will kill me ." Then the robbers let him go.

Reasoning: If a robber kills a businessman, he is undoubtedly right. He should be released. If yes,
The merchant's words are wrong. It is a paradox to kill and return to the reasoning above. Find a smart merchant
The answer makes the premise of the robbers incompatible.

5-9 "you will eat my child"

This example is logically the same as the preceding example.

A crocodile snatched a child and said to his mother, "Will I eat your child? Answer:
By the way, the child will give it back to you. If you get a wrong answer, I will eat him ." We already know our mother's answer: "You will
Eat my children ."

5-10 Children's Day

This is a prediction in the column: Confucius encountered two children arguing, one said: "At sunrise,
The sun is near us, and we are far away from us at noon. Because at sunrise, the sun is as big as a wheel and as small as a plate at noon.
Isn't it close, far, and small ?" The other said, "At sunrise, the sun is far away from us, and at noon, we are far away.
Near. We don't think it's hot at sunrise, but it's very hot at noon. Isn't it near hot and cold ?" Confucius cannot answer this question.

This is a question of scientific knowledge today, but it is unknown to people more than two thousand years ago. Logically, this
There are two measurement standards: "near big far small" and "near hot far cold. Make it clear before answering the question
Which of the following standards is more accurate or inaccurate.

5-11 should avatur pay the tuition fee?

It is said that the ancient Greek Eulathlus (Eulathlus) learned the debate from plotago (another
One is to learn the law ). Their agreement is: abatur pays half of the tuition fee first, and the other half is equal to the tuition fee.
And then pay again when the first Defense wins the case. If the case is lost, the tuition fee does not have to be paid.

However, after graduation, abatur did not assume a defense role and does not intend to pay the other half of the tuition fee.

Prolotigoras was about to sue him and said, "If I win, the judge will sentence you to pay my tuition; if I
As agreed, you still have to pay my tuition fee. In short, you need to pay .". "If I win
The judge will also decide that I will not pay the tuition fee. If I lose the case, I do not have to pay the other half of the tuition fee as agreed. Total
No ." (See Wang Jiuyi logical and mathematical thinking.)

This problem, in turn, is logically also true. If ivatyr says, "If you sue me,
I will not pay the tuition fee ." Plotago can also refute it in the same way. So argue
There is no result.

The problem here is that both parties can solve both the "Agreement" and "decision" by default at the same time and equivalent.
Resolving their disputes is the premise they share. Logically, the solution is to choose one of them.
To make final decisions.

5-12 The "predictions" of Vatican Scholars"

Similar to the above example, this is the daughter of a Buddhist scholar (the prophet of India) who uses the paradox
Difficult her father's story.

My daughter wrote a line of words on the paper under the crystal ball. Then he said to his father: what may happen on paper,
Or not. If you predict what will happen, write "yes", and vice versa ".

The Buddhist scholar wrote his prediction "yes". His daughter took out the paper below the crystal ball and read: "You will write
The word "no ." The scholar is wrong. In fact, he wrote the word "no", and it would also be wrong, because the prediction has already happened.

The daughter's "no" has two meanings: on the one hand, it is opposite to the literal "yes", on the other hand, it is similar to the actual
On the contrary, dual standards. Because it is not defined in advance, the Buddhist scholar can turn to his daughter.
Make unlimited arguments.

(6) paradox of power changes

6-1 ares (Allais) paradox

The following two statements indicate the income you will obtain. X is an indefinite amount. Which one will you choose? S1
Or S2?

(1) S1 = 0 · 9X ++ $100,000
(2) S2 = 0 · 89X + $250,000

Obviously, the best choice depends on what X is.

When X = $15,000,000, S1 = S2 = $13,600,000
When X> $15,000,000, S1> S2
When X <$ 15,000,000, S1 <s2

This paradox has a great impact on decision making theory.

6-2 newka (Newcombs) paradox

This is also one of the Decision-Making theories. There are two boxes A and B on the table:

A is transparent. You can see $1,000 in it,
B is not transparent. It indicates either $1,000,000 or 0.

You can select only one (1) or (2) in the following two options ):

(1) Select B only
(2) Select both A and B.

What do you choose?

A professor once performed an experiment: He asked 1000 students to select, of which 999 were selected.
After selecting (1), only one student chooses (2 ). The 999 students only get $
00, and the student got $1,000,000. Why? This is because of the teaching.
We have made predictions and made such an arrangement:

If option (2) B is selected,
If you select (1) Put $1,000,000 in Box B.

The professor made only 1‰ mistakes in his prediction. If you already know the result, try again.
Which one will be selected. Note that this time, the professor may have made new predictions.

6-3 Definition of "Heap"

If one grain of millet cannot form a grain heap, two grains of millet cannot form a grain heap, and three grains of millet can be implemented
It cannot form a grain heap, and so on. No matter how many grains of grain are put onto the ground, it cannot form a grain heap.

From the true premise, we can use acceptable reasoning, but the conclusion is obviously wrong. It indicates the definition
"Heap" lacks clear boundaries. It is different from the Multi-premise reasoning of the Three-field model and accumulates continuously on one premise.
Is a paradox. There is no clear boundary between no heap and no heap. The solution is to introduce
Fuzzy "class ".

This is an example of the Sorites paradox, thanks to the ancient Greek Eubuli
Des, later scammers did not recognize it as knowledge. "Soros" is "Heap" in Greek"
. Originally a game: Can you say one grain of grain as a heap? No; you can put 2 grains
Is it a heap? No; can you say three grains of grain are heaps? No. But sooner or later you will admit
Where do you distinguish them from?

Its logical structure:

One grain of grain is not a heap,
If one grain of millet is not a heap, then two grains of millet are not heap;
If two grains of millet are not heaps, the three grains are not heaps;
If 99999 grains are not heap, then 100000 grains are not heap;
Therefore, 100000 grains of millet are not heap.

According to this structure, there is no heap and heap, poverty and wealth, small and big, less and many were once argued by the ancient Greek.
Topic (see Encyclopedia of Britain).

6-4 bald head Definition

This is also an example of the chain paradox, just like the game above. The earliest name is Falakros.

Can you name only one hair bald? Yes. Can you name only two hairs bald?
Yes. Can you name three hairs bald? Yes. But you won't put 10 thousand people with hair
Bald head. Where do you distinguish them?

6-4 "there is no noise in the whole bag of millet landing"

In ancient Greece, there is also a story: If one grain of millet has no sound, two grains of millet,
There was no noise in the landing of three grains of grain, and so on, there would be no noise in the landing of one whole bag of grain.

The noise is caused by vibration. The vibration caused by the landing of a grain of millet is too small for ears,
It can be measured using an instrument. The vibration caused by the landing of a bag of millet is high, and the ears can naturally be heard.

It should be noted that the ancient Greek debates do not mean this. They do not really want to discuss the facts,
Try to find the difference between logical deduction and facts. It would be a series to admit that there has never been a noise
Column, there will also be a changed fuzzy area.

6-5 unexpected hanging time

This Paradox is called "Paradox of the Unexpected" in English.
Hanging "; the earliest oral spread was in the 1940s s of this century.

A prisoner was sentenced on Saturday. The judge declared: "The hanging time will be one day in the next seven days of the week.
It will be executed at noon, but you will be notified on the morning of the specific day ." The prisoner analyzed: "I
It will not be possible to go to jail next Saturday. This is the last day. Because I am still alive on Friday afternoon, so I know
At noon on Saturday, I must have been killed. However, this is in conflict with the judge's decision ." Based on the same push
He thinks the next Friday, Thursday, Wednesday, Tuesday, Sunday. Therefore
The judgment of an official account cannot be executed.

This kind of chain paradox reasoning is not hard to understand. The judge's decision can be any
One day was executed, and the expectations of prisoners failed. There is also an "unexpected test time paradox" and this paradox

6-6 "egg hair"

Hui Shi once discussed this topic with a debate. The debate said there was hair in the eggs, but Hui Shi opposed it.

The debate said: "If there is no hair in the eggs, how can the hatched chicks have hair ?" "
There is only egg and yolk in the eggs, and there is no hair. When have you seen any hair in your eggs? Chicken
The hair is the hair on the chicken, not the hair in the eggs ." However, it is unacceptable for the defender.

Both sides of the debate set standards for "seeing at the bottom", ignoring the transformation process from no hair to no hair.
I don't know what biology will explain about this. In terms of methods, they didn't define the world from scratch.
It seems that they do not accept the blurred area of "the hair on the chicken may be the hair in the eggs.

6-7 from having to having

This is an example from quantitative change to qualitative change in philosophy. If a treasure tower pulls its bricks from below
Blocks are extracted in one place. This is a quantitative change. When it reaches a certain degree, the pagoda collapsed and had a qualitative change, indicating that the pagoda
No. We can see an accurate degree ".

But now we take the bricks from the top and draw them one by one. This is also a quantitative change. It's not until it's finished.
There is a qualitative change, but it is not easy for us to find an accurate "degree" from the quantitative change to the qualitative change"

6-8 twins

This is a Paradox related to relativity (Twin Paradox ).

One of Einstein's achievements is to introduce a law that uses C to express a constant vacuum speed of light and
It is included in the column of natural constants as the maximum critical speed that cannot be reached. According to the constant speed of light, the theory of relativity is introduced.
They were once ridiculed as the "Absurd" conclusion of relativity.

The "twin brother paradox" refers to the clock in the reference system for fast motion, which is better than the clock in the reference system for static motion.
Slow. According to this conclusion, we can conclude that a ship is at a speed close to the speed of light.
When a person traveling in space returns to the earth, he will be younger than the twin brother living on the earth. Because
For his biological clock, it is slower than the person who stays on Earth. Although the current spacecraft is far from reaching close to light

Before Einstein's theory of special relativity was established in 1905, Newton's law was far slower than light.
The mechanical nature of law under the conditions of speed controls people's imagination, so this phenomenon cannot be explained. Love
Stan's concept of time relativity is brand new. It has banned Newton's concept of "absolute time ",
The concept of "absolute motion" has also lost its foothold.

6-9 "changed ruler"

This is another paradox of Relativity: a fast moving ruler, which is in a static state.
Ratio. This problem was raised from the results of the mederson experiment.
The mechanical contraction hypothesis of lorunz. Einstein believes that this contraction can exist between two reference systems.
To explain the relative speed (see the cradle of Relativity: the biography of Einstein).

6-10 why is the night sky dark?

This is the famous oracle (Olbers, Heinrich Willhelm)
Paradox: If the space is infinitely extended and the stars are evenly distributed, we should have at least one line of sight.
Planet. Shouldn't the sky always be bright? This conclusion is obviously inconsistent with the facts.

This problem was noted as early as September 1, 1610 by the German astronomy Obo in 1823.
It attracted widespread attention only after it was proposed again. There were a lot of guesses in the past, such as the universe with only limited stars and stars
The distribution of objects is not even, the farther the stars are, the less visible the light, and the farther the light has not reached the earth. "Big
After the emergence of the explosion theory, the age of the universe is not infinite, and being human is the most important reason. From"
Starting from the Big Bang, the universe has a history of one hundred to 20 billion years. The young universe has no time
Light fills the night sky (Sunday Telecom, October 5, 1997 ).


This article is a widely used paradox. With modern mathematics, logic, physics, and astronomy
With the rapid development of, there have been a lot of new paradox emerged, people are tirelessly exploring, predict their success
Our ideas will be greatly changed. The paradox described in this article is mostly a pipe view, and errors are inevitable,
I hope readers will criticize and correct me.

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