G(?)del's Mathematical Realism In Phenomenological Perspective

G(o|¨)del,whose thought is one of the few castles in the logical way in European,is"the most significant discoverer of the mathematical truth in 20th century". To some extent, we can compare him with Aristotle. Understanding his philosophy of mathematics may not only help us to understand his achievements in logic and mathematics, but also allow us to taste the Western rational civilization in his mysterious meditations.The motif of this dissertation is to demonstrate the reasonable of G?del's mathematical realism from the perspective of Husserl's phenomenology. The core of G?del's thought is the objective existence of mathematical truth and mathematical objects which are independent of material world and human heart. Both of them can be apprehended by people's mathematical intuition. Husserl's phenomenology emphasizes intentionality, on which he based the construction of numbers and he defended the reasonability of mathematical law by his deposition phenomenology. Meanwhile, he contended that human can understand the essential of objects with categorical intuition.In the introduction part, I briefly depict G?del's as a thinker, and present the theme and structure of the thesis based on recalling the study of domestic scholars on G?del's mathematical realism.The first chapter discusses various schools on mathematical foundations. On the one hand, the minority point of views are described which include empiricism, psychologism and logical positivists'conventionalism; and on the other hand, under the perspective of the hierarchy conception of sets, three major factions like formalism, intuitionism and logicism in traditional point are discussed in order to integrate them into a linear sequence.The second chapter focuses on G?del's mathematical realism. Beginning with the metaphor of Plato's cave, I discuss"Platonism", say,"realism". And next I talk about various realism perspectives from the period of Plato to contemporary. Then, I stress on the unique G?del's realism embraced G?del's increasing ontological thought and his attitude about epistemology, and analyze his unique ideas and concepts in detail. Meanwhile, I justify pragmatically for"mathematical realism"by using Incompleteness Theorem which is an important logical outcome. Finally, I illustrate the basis of his epistemology with"mathematical intuition".The third chapter gives G?del's mathematical realism a"philosophy certificate"mainly with Husserl's phenomenology. This chapter has two parts. In terms of ontology, the intention construction of numbers demonstrates the objectivity of"numbers", and deposition phenomenology, which takes the geometry as the example, explains the objectivity and rationality of the"mathematical laws"; in terms of epistemology, there is an inherent relation between the categorical intuition of Husserl and G?del's mathematical intuition.