Navigating the Paradoxes of Thinking — Advanced Cultivation (5)

Deiform Buddha

December 15, 2006

The highest form of game is the game of thinking. There are many paradoxes in thinking, and only the wise can navigate these mazes. I will present and discuss some advanced practices for Chanyuan celestials.

Where are the starting and ending points of a circle?

How does the Earth move?

If humans could travel through time and space, then if you traveled to your great-grandmother's time and killed her, would you still be born? If you are not born, then your great-grandmother would live, and thus you would be born. If you are born and kill your great-grandmother, then you could not be born. How is this paradox resolved?

The trajectory of a plane flying in a straight line is actually a curve, correct? If this is true, then a straight line equals a curve.

The statement "We don't use foul language" — where is the problem in this sentence?

The statement "There is no absolute truth in the world" — is this statement an absolute truth?

"Tao that can be told is not the eternal Tao." Since it is "not the eternal Tao," how can it be told? If it is the eternal Tao, then how can it not be told?

"I did not tell the truth; I am lying." Am I telling the truth or lying?

An egg has no feathers, right? Then where do the feathers on a chick come from?

"The wise do not speak, and those who speak do not know." Are Jesus, Sakyamuni, Laozi, etc., wise or ignorant?

A red flag waves. According to Huineng's logic, it is neither the flag that moves nor the wind that moves, but the mind of the observer that moves. My question is: If the observer's mind does not move, does the red flag stop waving?

A philosopher said, "I think, therefore I am." Does this mean you do not exist when you are not thinking? Where did you go?

Question: Does time exist?

Answer: Yes.

Question: Please prove it.

Answer: Yesterday, today, tomorrow.

Question: If the Sun and Moon were removed, would yesterday, today, and tomorrow still exist?

Answer: No.

Question: Since yesterday, today, and tomorrow would no longer exist, time does not exist.

Answer: ?

1 + 1 + 1 + 1 + 1 + 1 + ... = 1. Who can say this is incorrect? Who can say it is correct?

Russell's Paradox: In Saville Village, a barber hangs out a sign saying, "I only shave those who do not shave themselves." Someone asks him, "Do you shave yourself?" The barber is immediately at a loss for words.

This is a paradoxical reasoning: If the barber does not shave himself, he falls into the category described on the sign and should shave himself. Conversely, if the barber shaves himself, according to the sign, he only shaves those who do not shave themselves, so he cannot shave himself.

Therefore, regardless of how the barber answers, he cannot avoid the inherent contradiction.

Socrates' Paradox: "I know one thing, that I know nothing." When Socrates says "know," yet also says "know nothing," does he know or not know?

Achilles' Paradox: The slowest moving object will never be overtaken by the fastest moving object. Since the pursuer must first reach the point where the pursued started, the pursued will have already moved forward by some distance. Therefore, the pursued is always ahead of the pursuer. A human cannot outrun a tortoise. In a race where the tortoise's starting point is advanced by N meters (where N is finite), and both start at the same time, when the human reaches the tortoise’s starting point, the tortoise has already moved to point A. When the human reaches point A, the tortoise has moved to point B, and so on. The human can only infinitely approach the tortoise but never overtake it.

Zeno's Paradox: For an object to travel a distance d, it must first cover half of d, then a quarter, an eighth, a sixteenth, and so on, infinitely. Therefore, the object can never reach d.

It is practically possible to reach d, but theoretically impossible. Where is the problem?

The Arrow Paradox: A flying arrow is motionless. At each moment, the arrow has a fixed position and thus is stationary. Therefore, the arrow cannot be in motion. Zeno proposed that because the arrow has a temporary position at every instant of its flight, there is no difference between being in that position and being motionless. Zeno asked his students: "Is a flying arrow in motion or at rest?"

"Of course, it is in motion."

"Indeed, it appears to be in motion to everyone. But does the arrow have a position at each instant?"

"Yes, teacher."

"At this instant, does it occupy a space equal to its volume?"

"Yes, it occupies a space equal to its volume."

"Then, at this instant, is the arrow in motion or at rest?"

"At rest, teacher."

"This instant is at rest. What about other instants?"

"They are also at rest, teacher."

"So, is the arrow shot in motion or at rest?"

The Robber's Dilemma: A robber robs a merchant and ties him to a tree, preparing to kill him. To tease the merchant, the robber says, "Guess how I will deal with you. If you guess correctly, I will release you and never go back on my word. If you guess wrong, I will kill you, so don’t blame me." The merchant thinks carefully and says, "I guess you will kill me." The robber is unsure what to do, because if he kills the merchant, it proves the merchant guessed correctly, so he should release him. But if he releases the merchant, it proves the merchant guessed wrong, so he should kill him. What would you do if you were the robber?

The Paradox of God: Question: Is God omnipotent? Answer: Yes. Further question: Does omnipotence mean being able to do anything? Answer: Yes. Then: Can God create a stone so heavy that He cannot lift it?

"The White Horse is not a Horse" Paradox: It is said that Gongsun Long once rode a horse through a pass, and the gatekeeper said, "The law states that horses are not allowed through." Gongsun Long replied, "I am riding a white horse. A white horse is not a horse; these are two different things."

Is a white horse a horse?

The Two-Sentence Paradox:

The sentence below is true.

The sentence above is false.

Which of the two sentences is true?

The Prophet's Daughter Paradox: The prophet's daughter writes a line on a piece of paper and places it under a crystal ball, saying to her father, "What is written on the paper may or may not happen. If you predict it will happen, write ‘yes’; otherwise, write ‘no’." The prophet writes his prediction as "yes." When the daughter takes out the paper from under the crystal ball, it reads, "You will write 'no'." The prophet is wrong. In fact, if the prophet wrote "no," he would still be wrong because the prediction would have happened; how could it be "no"?

Socrates’ Dilemma”: Socrates took on a student to teach him logic. The student would pay half the fee upfront, and the rest would be paid after mastering the subject, with no payment required if the subject was not mastered. This could be called a “gentleman’s agreement.” However, after the student finished the course, he disappeared without paying the remaining fee. Socrates found the student and said, “The remaining fee must be paid. Otherwise, we’ll see each other in court.” The student was puzzled and asked, “Why?” Socrates explained, “If you win in court, it will mean you have mastered logic, and according to the agreement, you should pay the remaining fee. If you lose, the judge will still order you to pay. Either way, you have to pay; why avoid it?” The student laughed and said, “No, that’s not right. If you win, it means I have not mastered logic, so I won’t pay. If you lose, the judge will order me not to pay. In either case, I do not have to pay.”

The above are some thinking games I have created and searched for, for everyone’s enjoyment.