Q: Does the barber cut his own hair? If the barber cuts his own hair, it violates his agreement; If the barber doesn't cut his hair, then according to his rules, he should cut his hair again.
In this way, the barber is in a dilemma.
The liar's paradox: In the 6th century BC, epimenides, a philosopher in Crete, ancient Greece, asserted that "everything Crete said is a lie." If this sentence is true, that is to say, Immenendez, a Crete, told the truth, but this is contrary to his truth-everything that all Cretes say is a lie; If this sentence is not true, that is to say, Epimenendez, a Crete, lied, then the truth should be: everything that all Cretes say is true, and the opposite is true.
So it's hard to justify it. This is the famous liar paradox.
In the 4th century BC, the Greek philosopher put forward another paradox: "What I am saying now is false." Ditto, this is hard to justify again! The liar paradox still puzzles mathematicians and logicians.
The liar paradox takes many forms.
I predicted: "You are going to say' no' next, right? Answer with' yes' or' no'. " Another example is "My next sentence is wrong (right) and my last sentence is right (wrong)".
The paradox related to infinity and the paradox related to infinity: {1, 2, 3, 4, 5, ...} is natural number set: {1, 4, 9, 16, 25, ...} is a set of numbers squared by natural numbers.
These two sets of figures can easily form a one-to-one correspondence. So, are there as many elements in each * * *? Galileo Paradox: We all know that the whole is greater than the parts.
From the point on line BC to vertex A, each line will intersect with line DE (point D is on AB and point E is on AC), so it can be concluded that DE is as long as BC and contradicts the graph.
Why? Paradox of unexpected exam: A teacher announced that there will be an exam one day in the next five days (Monday to Friday), but he told the whole class, "You can't know what day it is today, and you won't be informed of the exam until eight in the morning." Can you tell me why I can't pass the exam? Elevator Paradox Elevator Paradox: In a skyscraper, there is a computer-controlled elevator that stops at each floor at the same time.
However, Mr. Wang, whose office is near the top floor, said, "Whenever I want to go downstairs, I have to wait for a long time.
The stopped elevator always goes upstairs and seldom goes downstairs.
How strange! "Miss Li is also very dissatisfied with the elevator. She works in an office near the ground floor and goes to the restaurant on the top floor for lunch every day.
She said: "whenever I want to go upstairs, the parked elevator always goes downstairs, and few of them go upstairs."
Really annoying! "What's going on? The elevator obviously stays on every floor for the same time, but why does it make people close to the top and bottom impatient? Coin Paradox Coin Paradox: Put two coins flat together, and the top coin rotates around the bottom coin for half a turn, resulting in the same pattern position in the coin as at the beginning; But according to common sense, the coin pattern that turns around the circle for half a circle should be downward! Can you explain why? Paradox of grain heap: Obviously, 1 grain is not a heap; If 1 millet is not a pile, then 2 millet is not a pile; If two grains of rice are not piles, then three grains of rice are not piles; ..... If 99999 millet is not a heap, then 100000 millet is not a heap; ..... If 1 millet can't pile up, two millet can't pile up, three millet can't pile up, and so on, no matter how many millet can't pile up.
This is the paradox of the valley heap that shocked the whole ancient Greece for a time.
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? Pagoda paradox Pagoda paradox: If a brick is taken out of a brick tower, it will not collapse; Draw two bricks, which will not collapse; ..... When the nth brick was pulled out, the tower collapsed.
Now start drawing bricks in another place. Different from the first time, when I drew the m-th brick, the tower collapsed
In another place, when the tower collapsed, l bricks were missing.
By analogy, the number of bricks lost when the tower collapses varies from place to place.
So how many brick towers will collapse? The question of chicken and egg: which comes first, the chicken or the egg? Of course, there were chickens first, but at first it wasn't chickens, it was other animals. Later, their reproductive mode changed and they became oviparous, so they had eggs.
○ There were no oviparous animals at the earliest, and many creatures were asexual reproduction and division. Later, they gradually evolved into oviparous animals and mammals, so there is reason to advance to biological ontology to have the origin of eggs.