G(?)del's Incompleteness Theorem And Its Methodology

When it comes to Kurt G(?)del's position in logical study,he is commonly regarded as Aristotle and Gottfried Wilhelm Leibniz.His incompleteness theorem has changed mathematics and also has a great influence on science and philosophy that can be connected with this incompleteness theorem,and even could change our attitude on the world of science.Besides,his theorem has a great influence on philosophy area connected to it.Researchers on mathematics and logic study have always paid more attention on his achievements on mathematics,and judge him as a talented scientist,excellent logician and profound ideologist.However,there is little knowledge about G(?)del's life experience,because of G(?)del's eccentric personality.And this will have an influence on our judgment of him in some way.Thus,this essay will begin with his own lifetime and academic career,present his achievements on basic study and rationalistic philosophical tradition,and focus on his most important achievements--incompleteness theorem.This essay will elaborate its background and details in the process of proof,then discuss on its great influence on mathematics,and philosophical inspiration to the basic research of mathematics.In the last part of this essay,an extended discussion will be presented,particularly on its methodology applying to the field of Chinese classical culture,materialistic dialectics and judicial principles.