Gödel's Concept Of Realism

Mathematics has played an important role in two thousand years of civilization in human history. Today, the development of mathematics has been far beyond the imagination of many people. However, some philosophy questions of mathematics had been never resolved. Although this does not affect mathematicians moving forward in the field of mathematics, we believe that if the ontology and epistemology in mathematics problems can be clarified, it will help the development of mathematics.This dissertation gives Godel's answers to these two issues. This article is divided into three parts; the first section introduces the Godel's Concept Realism, including what the object of mathematics is, as well as how to understand mathematical objects and so on. The second section introduces Godel's demonstrations of the Concept Realism in different articles. This section includes five contents:firstly, the demonstration of Realism on the analogy of the application of induction in mathematics and physics; Secondly, three reasons brought forward by Godel to argue that mathematics is not created by us in his speech in 1951; thirdly, the proving of the factuality of mathematics by explain the source of the truth on axioms in "What is Cantor's continuum problem?"by Godel; fourthly, getting the conclusion of the factuality of Mathematics starting from the Godel's Incompleteness Theorem; fifthly, getting the result of factuality based on the view of Cantor's Continuum Problem. The third section focuses on the analysis of the work of Russell by Godel, which means demonstrating Factuality inversely, because Godel opposed the way to solve the paradox based on "no-class Theory" made by Russell.