On Husserl’s Programme Of Phenomenology Of Mathematics And Its Passive Transcendence

As the founder of Phenomenology, Edmund Husserl is famous for its grand and elaborate theoretical system. Husserl devoted himself to establish a kind of philosophy with "presuppositionless" in life, which is different from the traditional metaphysics, and the core problem in this philosophy is that how it can be reached the transcendence which it ought to be on the basis of "givenness". Through reviewing the background of the history of mathematical development and the theories related to phenomenology, it’s clear that Husserl’s dual roles as a mathematician and a philosopher make him want to realize the theoretical goal of laying the foundation of mathematics at the beginning, and it is closely related to the contribution on his philosophy in future. Therefore, this paper focuses on investigating phylogeny of the theory of Husserl’s phenomenology of mathematics and its inner structure, and this structure is the core of the whole Husserl’s phenomenological theory, which reflects the combination of the "givenness" and the transcendence in it.Based on the thought above, this paper is divided into four main parts:first part reviews the development of geometry related to mathematical phenomenological theory and the phylogeny of phenomenology itself in 19th century, and introduces the mathematical methods used for reference in phenomenology of mathematics and phenomenology — axiomatic. Second part focuses on the crisis of the mathematical foundations caused by paradox during the end of the 19th century and the beginning of 20th century, and in order to compare with the attitude of Husserl’s phenomenology of mathematics toward treating the problem of mathematical foundations, this part else introduces the three schools of mathematics produced on the basis of this crisis and the final response from Godel by his proof to the debate of the three schools of mathematics. Discussion of third part is main about the structure of programme of Husserl’s phenomenology of mathematics and the problems it related to. Fourth part is based on three parts of discussion above, by taking the analysis of address syntax in the Husserl’s phenomenology for case, it attempts to explain that there is a fact of isomorphism between the passive transcendental structure and the programme structure of phenomenology of mathematics, so that the passive transcendence in the structure of Phenomenology of mathematics will be highlighted, thus the discussion of core issues is finished for this article.