A Study On The Origin Of Phenomenology In The Mathematical Approach Of Early Husserl

This study is to clarify the genetic relationship between Husserlian early mathematical thought and phenomenology.It sets out to locate precisely the path that leads from consideration of the origin of the concept of number to the symbolic operations and axiomatic construction of pure logic by clarifying the ideological fission in the Philosophy of Arithmetic and the centre problem of Logical Investigations.In this way,it is Husserl who uses the formalization principle of meaning transformation in manifold to solve the problem of arithmetic and symbolization arising from the interpretation of the origin of number concepts.The specify of the origins of the basic concepts of pure logic and the evidentiary defence of them led him to a phenomenological approach to the fixed intentionality and category intuition.Eventually,Husser make a phenomenological breakthrough from the pure logic to the pure consciousness.The first chapter,we will examine the development of mathematics and the birth of Phenomenology.we trace the roots of Husserlian phenomenology in Weierstrass' approach to analysis and get the pointcuts in the phenomenological genesis.Since the geometric representations of numbers formed in the first mathematical crisis is failed to solve the problems of imaginary numbers and the foundations of mathematical analysis caused by the numerical-system expansion in the nin eteenth century,Weierstrass's rigorously analysis of arithmetization finally laid the foundations of analysis on the logical structure of real number systems and on the interpretation of the concept of integers,thus solving the second mathematical crisis.Through Weilstrass' s fundamental view of arithmetic,Husserl eventually developed the problem of the origin of the concept of number into a phenomenological epistemological problem.In the second and third chapter,it is Husserl 's investigations about arithetic.The PA(Philosophy of Arithmetic)consists of descriptive psychological and logical investigations of arithmetic.Husserl analyzed the origins of the natural number concept in PA by focusing on mental presentation and collection.As a result,some of the critics of the book,most notably Frege,thought they detected a form of psychologism in PA.Furthermore,We analyzes the mutual criticism and respective defenses of the two men against Husserl's early psychological problems.In Part II of PA Husserl investigates this symbolic or logical component of arithmetic.In this second half of PA Husserl develops a kind of formalism about arithmetic and some other parts of mathematics.we shall also discuss in his development of a propositional calculus of the axiomatic-deductive kind,which is found in the final section of a lecture course on logic held in summer 1896,that gave rise to the Prolegomena and the Logical Investigations.In the four and five chapter,Husserl takes the demands contained in the concept of traditional formal logic seriously,especially the demand that logic be pure.He is in fact more extreme in adhering to the demand for purity than most proponents of traditional logic.we shall consider Husserlian assignment of the task of investigating the pure logic,the structural problems of meaning catergery and object catergery are discussed,and the problems of arithmetic and algebraicization in Husserl's early arithmetic philosophy are solved by applying formalistic operations in manifold theory.The chapter concludes with a preliminary demonstration of the completeness and consistency of the manifold theory.In the six chapter,we arrived at the famous problem of the relation between the first and second volumes of LU.Which involves the structure of the relationship between psychology,pure logic and phenomenology.We concluded that Husserl defends their ideality in the Prolegomena,In the six investigations these structures are further described and clarified.In both parts of LU,Husserl is interested in the same logical structures,Thus the two parts forms a solid unity.Through the consciousness analysis,Husserl aims to clarify the origins and evident of the basic concepts of pure logic and the origin of phenomenology.