Russell's Mathematical Logic Ideology Research

This thesis makes an exposition of the mathematics logicism thought of Russell ,the great mathematician and logician in phytogeny of logic.In preface, Russell's mathematics logicism is introduced in brief. It is thought to be include not only the idea of mathematics can be deoxidized to logic, but also the work of settle Russell' paradox.In chapter one, it gives a historical introduction to Russell' mathematics logicism and introduces how Russell put forward his idea. As a mathematician, Russell is critical of arithmetization of mathematics theory underlying the basic of mathematics. In Russell's opinion, logic should be the foundation of mathematics. Then he put forward his topic that mathematics is the same as logic and it can be deoxidized to logic.In chapter two, how Russell proved his topic of mathematics logicism is introduced in detail. On the base of Frege's study, Russell put forward the theory of types to settle Russell's paradox. On the base of non-set, Russell brought forward axiom of infinity and axiom of option as the premises and built a system. He tried to defined the non-negative integer in logic terms and derive the theorems of arithmetic from the laws of logic by deductive method.In chapter three, the author makes a comment on Russell's mathematics logicism. She thinks it impossible for Russell to deoxidize mathematics to logic because he couldn't derive arithmetic from purely logic laws. In this meaning, we can say that Russell's trying is failed. Russell's failure is mainly due to his mistakes in his philosophical ideas. But it is not a whole failure. Russell' contribution lies in his study of mathematics logicism promoting the development of mathematics logic.