1. Philosophical Thoughts

Descartes is widely regarded as the founder of modern Western philosophy. He was the first to create a complete philosophical system. Philosophically, Descartes was a dualist and a rationalist. Descartes believed that humans should be able to use mathematical methods—that is, reason—to engage in philosophical thinking.

He believed that reason was more reliable than sensory experience. (He gives an example: when we dream, we think we are in a real world, but in fact this is just an illusion). He discovered 4 rules from logic, geometry and algebra:

Never admit anything as true, only things that I have no doubt about are considered truth;

Each problem must be broken into several simple parts and dealt with;

Thoughts must proceed from simple to complex;

We should always conduct a thorough check to ensure that nothing is missed.

Descartes applied this method not only to philosophical thinking, but also to geometry, and founded analytic geometry.

Thus, Descartes’ first step is to believe that doubt is the starting point. The knowledge of sensory perception can be doubted, and we cannot trust our senses. So he would not say "I see, therefore I am" or "I hear, therefore I am". From here he realized a truth: what we cannot doubt is "our doubt".

It means: What we cannot doubt is the "doubt itself" when we are "doubting" this matter. Only in this way can we be sure that our "doubt" is authentic and not false. product. He was puzzled by things that people took for granted or were accustomed to, from which he derived the famous philosophical proposition - "I think, therefore I am" (Cogito ergo sum).

Descartes took this as the most basic starting point in metaphysics, from which he concluded that "I" must be a thinking thing independent of the body. Descartes also tried to prove the existence of God from this starting point.

Descartes believes that we all have the concept of perfect entities. Since we cannot get the concept of perfection from imperfect entities, there must be the existence of a perfect entity—that is, God. Let's get the concept.

Starting from the two points obtained, Descartes continued to deduce that since a perfect thing (God) exists, then we can be sure that the previous devil hypothesis cannot be established, because a perfect thing cannot allow Such demons deceive people, so through constant doubt we can be sure that "this world really exists", and the mathematical logic after proof should be correct.

There are many characteristics in the real world that can be detected rationally, that is, their mathematical characteristics (such as length, width, height, etc.). When our reason can clearly recognize a thing, then it should Things must not be illusory, they must be as we know them.

Although Descartes proved the existence of the real world, he believed that there are two different entities in the universe, namely thinking (mind) and the external world (matter), both of which come from God, and God exists independently. He believes that only humans have souls, and humans are dual beings that can both think and occupy space. And animals only belong to the material world.

Descartes emphasized that thoughts cannot be doubted, which had an important influence on subsequent European philosophy. The controversy arising from the cogito, therefore I am, lies in the so-called existence of God and animal monism (chimpanzees, octopuses, parrots, dolphins, elephants, etc. have all proven to have intelligence), and the main idea of ??doubt has indeed made a great contribution to research.

2. Contribution to mathematics and history

Descartes' most important contribution to mathematics is the creation of analytic geometry. Descartes succeeded in bringing together algebra and geometry, which at that time were completely separate. In his book "Geometry", Descartes proved to the world that geometric problems can be reduced to algebraic problems, and geometric properties can also be discovered and proved through algebraic transformations.

Descartes introduced the concept of coordinate systems and line segment operations. Descartes' achievements in mathematics provided a solid foundation for later generations' work in calculus, which in turn is the cornerstone of modern mathematics. He innovatively 'translated' algebraic equations from geometric figures, thereby solving geometric problems algebraically. This is today's analytic geometry (or "coordinate geometry").

In addition, many mathematical symbols used today were first used by Descartes, including known numbers a, b, c and unknown numbers x, y, z, etc., as well as exponent representation methods . He also discovered the relationship between the edges, vertices, and faces of a convex polyhedron, which was later known as the Euler-Descartes formula. He also discovered the Cartesian leaf-shaped lines that are common in calculus.

In physics, Descartes also made some achievements. In "Refraction" he first put forward a theoretical argument for the law of refraction of light. He also explained the causes of human vision disorders and designed lenses to correct vision. In mechanics, Descartes developed Galileo's theory of relativity of motion and emphasized the linearity of inertial motion.

Descartes discovered the original form of the principle of conservation of momentum (the momentum defined by Descartes is a scalar, not a vector, so his principle of conservation of momentum was later proven to be wrong). He also developed theories such as the theory of cosmology and the vortex theory. Although the specific theories had many flaws, they still had an impact on future natural scientists.

He also used the law of refraction of light to explain the rainbow phenomenon, and analyzed colors through the rotation speed of elemental particles.

In psychology, Descartes also made contributions. His views and major discoveries had a great influence on later psychology. He is a famous representative of modern dualism and idealism theories. His major discoveries of reflexes and reflex arcs provided important basis for the conclusion that "animals are machines". And put forward the hypothesis of response-stimulus.

But Descartes’ concept of reflection is mechanical. He emphasized the difference between humans and animals. Animals do not have minds, but humans do. This inference is a typical manifestation of dualism.

In addition, the theory of mind-spirit sympathy is another typical manifestation of Descartes’ dualism in the relationship between body and mind. He believed that the human body is composed of material entities, and the human mind is composed of spiritual entities. The mind and human body can influence each other, cause and effect each other, and interact with each other.

He believes that there are six primitive human emotions: surprise, love, hatred, desire, joy and sorrow. Other emotions are branches or combinations of these six primitive emotions. ?

Although Descartes’s dualistic psychological thought was wrong in theory, it was very promoting and progressive in the social context of the time. He used dualism to get rid of the absolute control of science by theology , guiding people's thoughts to rational thinking and specific research, so his contribution to psychology cannot be ignored.

Extended information:

Introduction

René Descartes (French: René Descartes, also translated as Descartes; March 31, 1596 - 1650 February 11, 2011), a famous French philosopher, mathematician, and physicist. He made important contributions to the development of modern mathematics and is considered the father of analytic geometry because of his formulation of the geometric coordinate system.

He is a representative figure of dualistic idealism and rationalism. He left behind the famous saying "I think, therefore I am" (or translated as "Thinking is the only certain existence"), and put forward the idea of ??"universal doubt" , is the founder of modern Western philosophy. His philosophical thoughts deeply influenced subsequent generations of Europeans and pioneered the philosophy of continental rationalism (rationalism).

Reference: Baidu Encyclopedia-Rene Descartes