First, Russell's thought and methodology
1. 1 Russell's Philosophical Thought
Rosell's philosophical thoughts mainly focus on analytical philosophy and logical philosophy. He believes that philosophy should be a rigorous way of thinking and solve philosophical problems through analysis and logical reasoning. His thoughts had an important influence on the philosophy of the 20th century, especially the philosophy of language and analytical philosophy.
Russell's philosophy mainly includes the following aspects:
(1) logical atomism
Russell believes that the basic unit of language and thinking is logical atom, which is the smallest unit that cannot be separated, and they constitute the basic elements of language and thinking. Russell's logical atomism is an in-depth discussion of the essence of logic and language, which has an important influence on the development of modern logic and philosophy of language.
(2) analytical philosophy
Russell's analytical philosophy emphasizes the analysis of language and concepts and solves philosophical problems through analysis. He believes that the core of philosophical problems is the problem of language and concept, and only through the analysis of language and concept can philosophical problems be solved. Russell's analytical philosophy has had an important influence on the development of modern philosophy, especially in the philosophy of language and cognitive science.
1.2 Russell's methodology
Rosell's methodology mainly includes logic and mathematics. He believes that logic and mathematics are the basic tools of thinking, and only through the analysis and reasoning of logic and mathematics can complex problems be solved. His methodology had an important influence on the development of modern logic and mathematics.
Russell's logic methodology emphasizes the formalization and rigor of logic. He believes that logic should be a rigorous reasoning method to solve problems through logical reasoning. His logical methodology has had an important impact on the development of modern logic, especially formal logic and model theory.
Russell's mathematical methodology emphasizes the foundation and logic of mathematics. He believes that mathematics is a subject based on logical reasoning, and only through logical reasoning can mathematical theorems be proved. His mathematical methodology has had an important impact on the development of modern mathematics, especially in mathematical logic and set theory.
Second, Russell's contribution to logic and mathematics
2. 1 Russell's contribution to logic
Russell's contribution to logic mainly includes the following aspects:
(1) logical atomism
Russell's logical atomism is an in-depth discussion of the essence of logic and language, which has an important influence on the development of modern logic and philosophy of language. He believes that the logical atom is the smallest indivisible unit, which constitutes the basic elements of language and thinking.
(2) Formal logic
Russell's formal logic is an in-depth discussion on the formalization and rigor of logic, which has an important impact on the development of modern logic. His formal logic mainly includes propositional logic and predicate logic, and solves logical problems through formal reasoning rules.
2.2 Rosell's contribution to mathematics
Rosell's contribution to mathematics mainly includes the following aspects:
(1) mathematical logic
Rosell's Mathematical Logic is an in-depth discussion on the combination of mathematics and logic, which has had an important impact on the development of modern mathematical logic. His mathematical logic mainly includes set theory and type theory, and solves mathematical problems through logical reasoning.
(2) Set theory
Rosell's set theory is an in-depth discussion of the essence of set, which has an important influence on the development of modern set theory. His set theory mainly includes logical set theory and mathematical set theory, and solves the problem of set theory through logical reasoning.