When it comes to Descartes, he is highly praised by the world.
Engels said: "The turning point in mathematics is the variable of Descartes. With variables, motion enters mathematics. With variables, dialectics entered mathematics. With variables, differentiation and integration immediately become necessary. ”
Russell believed that Descartes was the only philosopher after Aristotle who could match him.
Hegel believed that Descartes was the true founder of modern philosophy, calling him the "father of modern philosophy.".
René Descartes (31 March 1596 – 11 February 1650), born on 31 March 1596 in Tourine, André-Loire, France (now Descartes, named after Cartesian), died on 11 February 1650 in Stockholm, Sweden, and was a world-renowned French philosopher, mathematician and physicist. Descartes is known as the "father of modern philosophy" and "the father of analytic geometry", and he founded modern materialism and mind-object dualism, which played an immeasurable role in the philosophical thought of later generations. His philosophical ideas deeply influenced subsequent generations of Europeans, pioneering the so-called "continental rationalism" philosophy. He is one of the most influential masters of European philosophy and science in the 17th century, and is known as the "ancestor of modern science".
René Descartes
One philosopher who can never get around in understanding the study of philosophy and science in the 17th and 18th centuries is Descartes. Descartes' 54-year life, in this short and limited space of this article, it is obviously not advisable to evaluate his great achievements in mathematics, philosophy, science, and so on.
Below, we will only select 4 small pieces related to him to highlight and evaluate his great achievements.
<h1 class= "pgc-h-arrow-right" >, contemplation. </h1>
The Heart Sutra begins with the saying, "Contemplate yourself as a bodhisattva and practice deep Prajnaparamita." ”
So, what is self-contemplation? It is to see what you lack, and to do what you should want; to make up for what you should want. Knowing oneself, knowing all beings, knowing everything, this is self-contemplation.
According to the heart sutra, seeing that the five aggregates are empty, that is, "contemplation", and to overcome all suffering, that is, to attain freedom, so anyone who can observe the truth and attain liberation from suffering is called "bodhisattva who observes the truth."
Who does "bodhisattva who observes oneself" refer to? In the literal sense, contemplation means observation. To contemplate is to look with one's eyes, but here we observe all the Fa in this world not with the eyes of the eyes, but with the eyes of the heart and the eyes of the discerning eye.
"Freedom" means "freedom.". It is to live freely, just as birds fly freely in the sky, fish swim freely in the water, animals run freely on the earth, but this is not the freedom that the Heart Sutra says. The freedom mentioned in the Heart Sutra refers to a person observing the truth of the world with his heart and eyes, getting rid of the shackles of various troubles in life, having no attachment in his heart, no longer confused in his heart, and being free in body and mind.
Descartes was born on 31 March 1596 into a lower aristocratic family, the son of a member of the Brittany Parliament of Rennes and a judge of the District Court.
When he was more than 1 year old, his mother died of tuberculosis, and he was also infected, resulting in frailty and illness.
In 1606 or 1607, his father wanted Descartes to become a theologian in the future, so at the age of eight, descartes sent him to the most famous aristocratic school in Europe, the Royal Grand Henry College of the Jesuits in La Fleche. In order to take care of his sick and weak body, the school authorities allowed him not to be bound by the school rules, not to go to school in the morning, and to read in bed.
So he had a lot of time every morning, for observation, for thinking. This habit of contemplation and solitude, which he maintained throughout his life, laid a solid and reliable foundation for his future research in philosophy, mathematics, astronomy, physics, and so on.
He studied for 8 years and was educated in classical literature, history, theology, philosophy, law, medicine, mathematics and other natural sciences.
To be at ease is to be free in body and mind, to abandon external interference, and to concentrate on doing one thing. Obviously, Descartes's achievements in philosophy, mathematics, astronomy, physics and other aspects are inseparable from his childhood habit of liking quietness and being good at thinking about everything.
Estuary of the Loire River in France
<h1 class= "pgc-h-arrow-right" > second, doubt everything. </h1>
Descartes studied mathematics and physics at the Royal Grand Henry College, including Galileo's work, but he was disappointed with what he had learned. For the subtle arguments in his textbooks, which seemed to him to be only ambiguous and even contradictory theories, could only make him suspicious and unable to obtain conclusive knowledge, and the only thing that comforted him was mathematics. Because mathematics has a solid and reliable foundation.
Descartes, from doubting books, doubting knowledge, doubting theory, to discovering doubt about the body, doubting the mind, doubting the spirit, and even discovering the possibility of doubting the existence of God, he subverted traditional knowledge, traditional philosophy, and even finally declared war on the highest theological authority.
His suspicions are reflected in his world-famous phrase "I think, therefore I am". Here, "thinking", not the meaning of "thinking" and "thinking", but the meaning of "doubt", says it all.
How did Descartes use logic to prove that "I think, therefore I am"? "When I wonder if I'm thinking, I'm already thinking," he said. So, I can't doubt if I'm thinking. Thinking must have a subject, otherwise what is thinking, so the "I" as the subject of thinking must exist. So "I think, therefore I am." In addition, I am, referring to the existence of the physical self, but only to the thinking of the self.
Therefore, Descartes's spirit of doubting books, doubting knowledge, doubting theory, doubting truth, daring to doubt authority, daring to doubt everything, is worth vigorously advocating, and it is an indispensable tool for the study of philosophy and science.
Doubt is the beginning of discovery. Lying on the hospital bed, Descartes observed the spider spitting silk, and found that the spider was the center, calculating the distance between the wall, and the correspondence between points and coordinates, thus opening a new era of algebraic methods to solve geometric problems, announcing the birth of a new discipline - analytic geometry, thus laying the foundation for his great achievements in the direction of mathematics.
<h1 class= "pgc-h-arrow-right" > three, independent thinking. </h1>
Hegel said in his Lectures on the History of Philosophy: "René Descartes is in fact the true founder of modern philosophy, because modern philosophy is based on the principle of thinking. ”
Descartes had a feat in the history of philosophy by separating independent philosophical thinking from theological arguments, ending the pathetic state of philosophy as the handmaiden of theology since the Middle Ages. Although Descartes' philosophical thought is suspected of acknowledging the "existence of God", his transfer of the object of philosophical study to man and the study of "human mind" is undoubtedly a great progress in human understanding. Thus, Descartes was a heroic figure who took the lead in trying to reconstruct the philosophical foundations.
In Descartes' view, stupid people are partial to believing and superstitious authority, and do not know how to develop their brains; intelligent people are independent and self-doubting, and know how to sort out and correct all learned knowledge.
As an innovator in the history of philosophy, Descartes, in "On the Method" and "Philosophical Principles", uses himself as an example to discuss how he got rid of stereotypes, doubted everything, and then found the principle of indisputable, and how to reconstruct a new system of philosophical thought on this basis.
Descartes' independent thinking, the basic operation is mainly four steps:
Step 1: Get rid of the shackles of books.
As Descartes said: a person starts from the early childhood of the language, until adult independence, the knowledge we learn is basically learned through indoctrination education, there is no own value concept, cognitive system and judgment of right and wrong, just a machine shaped by others. Therefore, when a person becomes an adult, as his intellect matures, he should use reason to systematically sort out the knowledge he has learned, and mark his self-knowledge on these knowledge.
The troubles bound by educational stereotypes plagued Descartes. He thinks that what he learns from books is clear and reliable, and it will benefit him for life. But when he finished all the courses at the Royal Grand Henry College and became a top scholar, he realized how ignorant he was. Because all my views are the original stereotypes of education.
Therefore, descartes, after becoming an adult, decided to temporarily abandon theory, completely abandon book-style research, get out of the study, travel to all parts of Europe, experience life, collect materials, absorb knowledge, and establish a new knowledge system and philosophical system.
Descartes' abandonment of the shackles of books tells us that if we want to know the truth, we should get rid of the shackles of books, not superstitiously believe in the pen of the mouths of nerds, and think independently of problems in life with our own reason.
Step 2: Be bold and doubt.
In the winter of 1620, 30 years after Descartes had thrown his pen from Rong, he closed himself in a conservatory and used his contemplative methods to re-sort the knowledge in his mind.
Everyone's knowledge basically comes from different teachers and different books, just like many craftsmen carved a stone statue together, after passing through the hands, it has long become unrecognizable and characterless. Since we were before we became adults
When the intellect is immature, we must use the "method of contemplation" to systematically sort out the knowledge we have learned.
This kind of grooming is more similar to the renovation of buildings. Before he believes that a certain point of view should be accepted, take a cautious attitude. We have to doubt any argument for any argument, anything that has not been tested in practice. It is better to be suspicious and indecisive than to be gullible to others, and to use doubt to eliminate all stereotypes.
To be bold in doubt, in The words of Descartes, is to pursue the truth, we must doubt everything as much as possible once in our lives. Everything that can be doubted should also be considered false.
Bust of Descartes
Step 3: Discover a solid knowledge base.
"One plus one equals two."
"You can't step into the same river with one foot at the same time."
"Winter is over, it's spring."
"Everybody will die"
……
Descartes believed that these were knowledge that had been repeatedly validated and recognized by countless generations. And the views of a great man, the tenets of a certain religion, or the theories of a certain authority are not worthy of juxtaposition with these principles, and apart from these axioms, no theory is indisputable and cannot be put out for open discussion.
Truth, though blinded by errors and lies, once confirmed, will never be replaced by error.
So, Descartes differs from other philosophical schools in that he did not aim at doubt, but as a means. For through doubt, all unreliable knowledge can be uprooted. In this way, what remains indisputable becomes the solid foundation of a new system of knowledge or a new philosophical system.
In Descartes' view, "I think, therefore I am," a piece of knowledge that cannot be uprooted by doubt, said: "I accept this truth without any doubt as the first principle of the philosophy I study." ”
Step Four: Get rid of doubt and rebuild your mind.
The purpose of doubt is to eliminate the stereotypes that others have instilled in us, leaving only reliable knowledge. After that, we rebuild our own systems of thought on top of this reliable knowledge. In Descartes' words: remove the floating soil and sand in order to find the rock or clay.
The reconstruction of the body of knowledge should be as follows: starting from the most certain and firm axioms, as if it were to create simple tools first, and then on its basis through independent thinking to gradually deduce, step by step, from simple and crude tools to complex tools, from simple axioms to systematic systems of thought, and so on step by step, to infinity.
<h1 class = "pgc-h-arrow-right" > four, three contributions to Descartes mathematics. </h1>
Descartes, inheriting his father's inheritance, lived the material life he wanted. Ideologically, academically, and in the spirit of criticizing everything, he lived his free and free spiritual life. Here, only the great contributions he made independently in mathematics are listed.
First contribution: Euler-Cartesian formula.
This is a geometric formula, i.e. in an arbitrary convex polyhedra, let V be the number of vertices, E be the number of edges, and F is the number of faces, then V-E + F = 2. That is, in any regular polyhedron, the number of its "faces" is added to the number of "apex angles", and then the number of "edges" is subtracted, and the result is equal to two. The formula is: V-E + F = 2.
This formula was first discovered by the Swiss mathematician Euler in 1750, so it was originally called Euler's formula. The Euler-Cartesian formula is important in geometry, especially in geometric mathematics and physics.
The second contribution: analytic geometry.
Descartes' second greater contribution to mathematics was the establishment of "analytic geometry," the first chapter of his methodology, Geometry. Many junior high school students and high school students say that mathematics is difficult to learn every day, but in fact, the source is here, that is, the disaster caused by Descartes.
In Geometry, he proposed the concept of a planar coordinate system, that is, the "analytic method", to depict the plane geometry that describes various rules: each point (x, y) in the figure can find the corresponding values x and y on the coordinate axis.
In the past, when drawing pictures, we had to use a ruler to measure the length, draw slowly, and calculate slowly, and this practice was more troublesome and not precise enough. Now, Descartes transformed geometric problems into algebraic problems, drawing fast, calculating fast, and calculating them quite precisely. For example, the equation y= 2x, we quickly draw a straight line in the Cartesian coordinate system that is past the origin. Other figures such as circles, ellipses, hyperbolas, parabolas, etc., can be expressed mathematically and precisely drawn within the coordinate system.
Therefore, Descartes' "analytic method", whether then or now, is a good and advanced mathematical tool for understanding the world and portraying the world.
Descartes' contributions to mathematics, mainly the above two, have greatly promoted and influenced the course of world history.
Third contribution: Love formula: r=a(1-sinθ).
Descartes' mathematical contributions cannot be mentioned without mentioning his romantic story of love and the formula of love. Although it did not contribute as much as the first two, it promoted the development and maturity of another branch of mathematics, the polar coordinates.
It is said that during the Black Death outbreak in Europe, Descartes wandered to Sweden and met the 18-year-old Swedish princess Christina. Later, because of his profound knowledge, he became Christina's private teacher of mathematics. After a long time together, the two sparked love.
Descartes and the Princess
How could an 18-year-old princess be with a governess in her 50s? So the old king decided to execute Descartes. Under the princess's desperate affection, Descartes finally retreated and returned to France. But the princess was put under house arrest by the king.
Shortly after Descartes returned to France, he contracted the Black Death, knew that he did not have much life, and missed the princess, so he kept writing letters to the princess, but these letters eventually reached the king's hands.
Descartes, after sending the 13th letter, died in despair. The 13th letter is very brief, with only one mathematical formula: r =a(1-sinθ).
The king couldn't understand the formula, and felt that there was no out-of-the-ordinary language, so he transferred it to Christina. After Christina read the letter, her heart rejoiced. Because she understood that Descartes had always loved her.
Is there any magic to this short mathematical formula? Why was Christina overjoyed when she saw the letter? It turns out that this formula is expressed in the coordinate system, which is the shape of a loving heart. Princess Christina, who studied mathematics with Descartes, knew and understood the meaning of this formula: r=a(1-sinθ), the famous "heart line" equation.
Heart-shaped stones with crooked branches in life
A few years later, Princess Christina became king and immediately went to France to look for Descartes, only to learn that Descartes had died. This romantic love story ended in a tragic form.
The question of whether this story is true or not is not a question, but it is true that Descartes never married. And the "heart-shaped line" equation by Descartes really embodies his theory of analytic geometry to the fullest. At the same time, he brought another branch of mathematics, the polar coordinate equation, to its climax.
<h1 class = "pgc-h-arrow-right" >5. Conclusion: Descartes' Influence and Evaluation. </h1>
Descartes' whole life was to doubt everything and think independently, and we can divide his independent thinking into 4 stages to understand:
First, get out of the books and get reliable experiences from life.
Second, doubt is used to eliminate indoctrinated stereotypes.
Third, after doubt, find those reliable knowledge and use it as a basis.
Fourth, get rid of doubts and rebuild the knowledge system on a solid foundation.
"I think, therefore I am", this first philosophical principle has a great influence on the history of Western philosophy. Hegel once said, "From Descartes onwards philosophy has suddenly shifted into a completely different sphere, a completely different point of view, that is, into the realm of subjectivity, into what is certain."
Descartes spent his life thinking non-stop, and thinking also made Descartes, making him one of the most influential masters in the European philosophical and scientific circles in the 17th century and later, and was known as the "ancestor of modern science".
From Descartes' life of independent thinking, we can see the importance of thinking: as long as we can think a little more in our lives and learn, we will be closer to the great man.
Descartes, in the 17th and 18th centuries, was not only a famous philosopher, but also a fairly brilliant mathematician and scientist. Mathematically, he was the founder of analytic geometry. In the natural sciences, he is one of the main representatives of modern mechanistic theory.
Later, the following sentence was inscribed on his tombstone: "Descartes, the first man since the European Renaissance to fight for and guarantee the right to reason for mankind." ”
The church where Descartes was buried
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