Into the Immortal Cultivation

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On Earth, natural sciences have long been separated from philosophy.

The essence of philosophy lies in the overall grasp of the "world". But people can see how big the world is, depending on how high the level of science is and how far the theory has gone. Russell once said that any science, as long as the knowledge about it can be determined, this science is no longer called philosophy, but has become an independent science.

Therefore, a philosopher who has worked hard to build a philosophical system that can accommodate all known worlds will always be shattered as science advances and theoretical breakthroughs are made. At this point, no great philosopher can be an exception.

However, mathematics known as the "Queen of Science" is an exception.

Mathematics has always been very close to philosophy. Although philosophers have never used mathematics to analyze the world, mathematicians have never entrusted their studies to the field of philosophy. However, both mathematics and philosophy operate alone in the "other world" of the mind. Mathematics and philosophy are really similar in this respect.

Although Gauss despised Hegel and believed that Leibniz's distraction from mathematics was a waste of talent, he was actually a person who liked mathematics.

Russell, the mathematician who raised the "barber paradox" and caused the third crisis of learning, is still a philosopher.

And Gödel, one of the most talented mathematicians in history, likes to expound his philosophical thinking in his mathematics thesis.

In summary……

A mathematician who does n’t want to be a philosopher is not a pretender!

Yes, in this rich and compelling field, may Wang Qi's previous life be exempt?

Feng Yiweixiang, how to understand it?

This "combined with the language environment, tell your own understanding" of the reading question is the rest of my teenage years! If you ask this question is to test this ... I have nothing to fear!

"It just counts."

Chen Jingyun said: "Please do a detailed explanation."

"It seems to me that the Dao is outside the heart, not made behind closed doors, but not mysterious. It is because the Dao is outside the heart, so I see this, like flowers in the fog, with a layer called" Xuan Zhi You Xuan "in between. Covering. Clearly calculating is to cover the Xuanxuan, and build a bridge between the world and the world. It is not a Tao, a very Tao, but a tool to hide and seek the way.

"Pappa" Deng Jiaxuan applauded: "That's right."

The few words of Wang Qi just now, especially the word "go to cover", can touch him!

Wang Qi smiled proudly-the correspondence between the brother of Heaven and Dao only included the field of natural science. Heidegger ’s philosophy must have never heard of it!

The point is, Wang Qi himself really thinks so. In his last life, he had another set of opinions on mathematics, and now it is definitely not simply bluffing!

Thinking of this, Wang Qi looked at Kehar again. The master of Yangshen Pavilion said to Wang Qi: "You don't have to look at me. I fine-tuned your state of mind so that you don't want to lie, so you are heartbroken. They all know it."

"In the early days of ancient times, how did you learn? How can you flourish for thousands of years?"

In the early days of ancient times, the human race was still ignorant. Who set up the mathematics? In these 80,000 years, how did mathematics develop?

"Study in mathematics begins with the needs of the human race and flourishes because of the prosperity of the human race."

"Please explain."

Wang Qi said eloquently: "In the beginning of mathematics, it was just counting. The human race fishing and hunting income all need to be counted, so there are additions, subtraction, multiplication and division. And humans are born with ten fingers, they are based on the general arithmetic. And abstract images from all things in the world, there is geometry. This is the beginning of mathematics.

And we just said that it was to cover the mysterious weapon. The more detailed the mathematics, the sharper the ‘approach to the Tao’ is to perfect the mathematics with countless free predecessors. Therefore, the mathematics and prosperity and development of the human race. "

But Harr looked surprised and turned to Chen Jingyun: "Chan Master, this kid doesn't need to ask, it's perfect! I and my disciples have been shocking people many times, but I have never heard of it again. The disciple can be like him. "

Sitting in the ground, Wang Qi rubbed his aspirations to the Yangshen Pavilion's unrestrained feelings.

Master, if you think this guy is as happy as ever!

Chen Jingyun nodded gently: "I have my own concerns." Then he said: "This is the most important question, you listen well."

Wang Qi saw that he was serious, and could not help swallowing.

"The so-called arithmetic is complete? Is it compatible? Can it be determined?"

what? Wang Qi was stunned for a moment.

This problem is too different from the previous two!

Is math complete? Can every proposition be proved or falsified?

Is mathematics compatible? Do you use the steps and order of the logic of attachment to never quit contradictory propositions?

Is mathematics decidable? Can we use a mechanical method to determine the authenticity of each proposition?

Each of these three questions goes directly to the root of mathematics, and each of them is the most profound question in the field of logic!

This kind of question appears in the question of the nature of college entrance examination? This is like letting high school students solve the normal field equation, it is impossible!

Wait a minute, because the history of the two worlds has diverged, Gordel ’s peers have not appeared in the land of China, so at present, the first two problems are unsolvable ... The third problem is Alan on the earth. Turing solved it, but ... I have n’t learned that right now, and I do n’t know if the old Turing of China has solved the judgment problem-wrong, the inspiration for the judgment problem on the earth is also from Gödel ...

In other words, this is purely a matter of faith?

Wang Qi thought of telegram transfer, and it took a while to organize the language: "Third question, I think it is negative ... If the calculator can solve all the calculation problems, then what should we do?"

But how do you edit the first two questions? The answer in my heart is, of course, that “for a formal logic system, completeness and compatibility cannot co-exist” ... but is this too specific? I can't do it if he gives me a "please explain"!

Chen Jingyun looked at Wang Qi ’s embarrassed look and nodded: “These three questions are the most acute calculations, and you do n’t need to delve into it—then the last question. Wang Qi, what is your relationship with the Daoist ? These three questions are not within the scope of the professor of the Xianyuan, but he told you? "

Eh?

Eh?

Wang Qi is still stunned, but his mouth has already spoken: "Being a neighbor for a while ..."

Hell, is this the flesh?

They really suspected that I had something to do with disapproval!

Fortunately, Chen Jingyun asked "Don't allow the Taoist" instead of "Heisenberg", otherwise I might blurt out that "Heisenberg is my most admired scientist" ... your sister, so you really jump into the Yellow River Can't wash it!

"Other than that? What did he teach you? You can solve the problem of the rear hall of the Chuan Gong Hall as soon as you enter the fairy yard. Is it related to not allowing Taoists?"

"In addition to teaching me to play chess, there is nothing more." Wang Qi considered the language: "I can solve the problem, it has nothing to do with not allowing the Taoist."

Fortunately ... if this one asked "why can I solve the problem" ... it was too reckless at first ...

Fortunately, this person doesn't understand words ...

After listening to Wang Qi's answer, Chen Jingyun glanced at Keer. But Harr nodded at him. Chen Jingyun just said, "Okay, we have been able to confirm that you have nothing to do with Taoist people."

Wang Qi breathed a sigh of relief. Nima ... The old man hurts ...

But before waiting for him to completely indulge, Maeko screamed in his mind: "Be careful!"

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