The philosophical system of the school of number theory

The three major schools of mathematics are the three schools formed around the philosophical foundation of mathematics, mainly referring to logicism and formalism.

and intuitionism. It was formed mainly in the three decades from 1900 to 1930. Representative figures include Russell and Hilbert.

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Logicism: The main representative is Russell, in "The Primordial Cave of Mathematics" and "Principia Matmatics".

Russell's goal was to prove that mathematics and logic are congruent in logic.

Formalism: It is generally believed that the founder of formalism was Hilbert. Hilbert argues for two of the most basic principles: the principle of formalism and the principle of finitarianism.

Intuitionism: The founder and representative of intuitionism was the Dutch mathematician Brouwer. In the philosophy of mathematics, intuitionism, or neo-intuitionism (corresponding to pre-intuitionism), is the method of mathematical research using the constructive thinking activity of human beings.

The basic schools of philosophy are materialism and idealism.

1. Materialist philosophy.

There are three basic forms of materialism: ancient naïve materialism, modern metaphysical materialism, dialectical materialism, and historical materialism.

1) Ancient naïve materialism.

Basic view: Metal, wood, water, fire, and earth are the origin of the world.

Progressive stupidity: denying that the world was created by God, believing that the world is material, and adhering to the fundamental direction of materialism, is essentially correct.

Limitations: aThis is a valuable speculation with no scientific basis. b.It reduces matter to concrete forms of matter and simplifies complex problems.

2) Modern metaphysical materialism.

The basic point of view is that atoms are the origin of the world, and the properties of atoms are the properties of matter.

Progressive: enriches and develops materialism.

Limitations: The concrete form of matter is still equated with matter. It is mechanical, metaphysical, and incomplete.

3) Modern dialectical materialism and historical materialism.

The basic viewpoint is that matter is the origin of the world, and the essential attribute of matter is objective reality.

Progressiveness: It put an end to the idealistic view of history, founded a materialist view of history, and achieved the unity of the view of nature and the view of history.

2. Idealistic philosophy.

1) Subjective idealism.

Regard the human spirit as the origin of the world.

2) Objective idealism.

The "objective spirit" independent of human beings is regarded as the origin of the world.

Materialism 1Nurnaf materialism.

2.Marx materialism.

3.Woodforth materialism.

Idealism 1Ryle idealism.

2.Alukiac idealism.

This is what I personally read from the book, and I hope it will be helpful to you.

There are many Chinese ones such as Confucius, Laozi, Mozi, etc.

In the West, there are the Syado school, skepticism, positivism, etc.