The Concept Of Manifold In Husserlian Philosophy-From Mathematics To Transcendental Phenomenology

This thesis aims to studying Husserl’s concept of manifold(Mannigfaltigkeit).For this purpose,I will diachronically examine the meanings and functions of the concept of manifold in different stages and constitutive levels of phenomenology based on the developmental sequence of Husserl’s thought.In view of the close relationship between Husserl’s Phenomenology and modern mathematics,the concept of manifold plays the role of leading clue and mathematical foundation for transcendental phenomenology.I will begin with the quotidien concept of manifold and gradually reveal its mathematical background,its meaning in Kant’s philosophy,and its important position in Husserl’s phenomenology.Deriving from modern mathematics,the phenomenological concept of manifold deepens Kant’s manifold and manifoldness.Secondly,I will examine the manifold and manifold theory in Husserl’s early mathematical philosophy and phenomenology.Through an in-depth reflection on Riemann’s and Cantor’s concepts of manifold and Hibert’s axiomology,Husserl’s understanding of manifold has changed from the technically-oriented topological space and set of variants to the formally consistent,definite,and extendable theoretical system,which originates from the conformal variation of act material in categorical intuition.In the third chapter,I will focus on the concept of manifold during the transcendental turn and in Ideas I.On the one hand,manifold provides an internal perspective for transcendental phenomenology,which is intrinsically linked with phenomenological reduction;on the other hand,pure consciousness and Eidetik in transcendental phenomenology have a one-directional foundational relationship between the manifold of consciousness and manifold theory.Both the former and the latter must manifest themselves in the eidetic intuition based on the invariant of a manifold.In the fourth chapter,I will focus on two specific dimensions of the manifold of consciousness,namely the "orthogonal manifold" of time-consciousness,and the"kinetic manifold" of space-consciousness,each of which has its essential structure and genetic constitution.In the part on time-consciousness,I will examine in what sence the manifold pattern breaks throught the mode of apprehension of the now point,investigate double-intentionality and the retention-protention interweaving in the temporal stream,and reveal the genesis of the original process from the onedimensional manifold to the two-dimensional continuum.As to spatial consciousness,I will examine the double constitutive function of kinesthetic manifold,namely,the constitution of three-dimensional objects and spatial depth,and the constitution of the habit and nature of the zero-point body.Lastly,I will select a key topic related to manifold in genetic phenomenology,that is,the relationship between subjectivity and temporalization.We will see that there are two different levels,namely,the constitution of the experiential manifold of personality along the longitudinal dimension and the constitution of the manifold of original impressions on the width of the deepest layer.We will then follow Husserl’s late exploration into the living present to probe the origin and limitations of the manifold of consciousness.Through the diachronic investigation,I try to demonstrate that for Husserl,the consciousness is a multi-dimensional manifold.The structural manifold is a premetrical region with topological relations,while the genetic manifold can represent the reduction from the high-dimensional manifold to the low-dimensional manifold,or the unfolding from the latter to the former.In conclusion,the manifold structure of consciousness from passive genesis to active constitution has different levels:from the two-oneness genesis and boundary variation of Ur-hyle and Ur-ich in the living present,the genesis of the manifold of personal ego from instinct/drive to habit through timeconsciousness and space-consciousness,the manifold structure of noesis-noema in the realm of pure consciousness,to the manifold theory(universal mathematics)as the idealized achievement of the highest order.