Philosophical Perspective Mathematical Crisis

In the long development history of mathematics, mathematical paradoxes caused three mathematical crises, especially the third crisis that caused by paradoxes in set theory is most influential in the mathematical community. Since the emergence of the third crisis, mathematicians and logicians have formed a variety of schools,in the process of seeking the solution to the foundations of mathematics, such as the logical school of thought that Russell is the chief representative, the intuitive school of thought that Brouwer is the main representative, the formalism of Hilbert as the main representative, as well as Zermelo axiomatic set theory, represented such school,and so on. At the same time, a various of branches of set theory began to take shape, such as Russell theory, Zermelo axiomatic set theory and so on. Undoubtedly, These theories contributed much to the development of set theory, and they promoted the development of other interrelated subjects. The thesis elaborates the third mathematical crisis in development history of mathematics from the perspective of philosophy in detail, which explains that a mathematical crisis is not a kind of disaster and desperation, but to guide people to explore the unknown fields and promote mathematics'prosperity and development,and is a powerful lever of science development, and the crisis has important methodology significance; at the meanwhile, this paper analyzes its influence on mathematical concepts and the development of modern mathematics and other subjects, which makes it clear that the third mathematical crisis stimulates the mathematical study to enter a new golden age; moreover, we can realize that mathematical crises are releted to practical development, which occur periodically, by means of analyzing the essence and regularity of mathematical crises viewed in line with philosophy.The thesis contains four main parts:The first chapter introduces and analyzes the background of the third mathematical crisis. The second chapter elaborates the solution situation of the third mathematical crisis, including Zermelo axiomatic set theory's reaction to paradoxes of set theory, and the controversy about mathematic basis which was caused by the third mathematical crisis.The third chapter expounds the influence of the third mathematical crisis in the development of modern science, which brings so new gold era.The last chapter discusses the philosophic meaning of the third mathematical crisis, which concretely analyzes upon three respects: the third mathematical crisis leads to the change in the absolute doctrine of mathematical truth; the third mathematical crisis gives rise to the change of the way of thinking; combining previous mathematical crises in the history of mathematic, it illustrates that practical development is the root of mathematical crises which have common characteristics, and which occurs periodically, and which is predictable and recognizable to a certain degree.