The Transformation Of The Theory Of Types

The theory of types was an important outcome of the development of Russell's philosophy and logic, and It is closely linked. with his logic position. It can be said that the theory of types is a means to achieve Russell's dream.Beginning with analyzing Russell's opinion of mathematic, this article analyze the impact on his subsequent studies .He believes that all pure mathematics are those proposition ,like "p → q" .In Russell's opinion, mathematics and logic have the same disciplines ,but different stages. Russell have tried to make mathematical derived from logic, thereby achieving his logic position. To that end, he began writing the "Principia Mathematica", but then he discovered a question, which at the time seemed insurmountable, "Russell paradox." In order to complete the " Principia Mathematica '"s writing, he creatively put forward the theory of types.. Then, this article detailed the simple type theory's building, and analyzed its core concepts, including type, function of proposition orders. We know that the simple theory of types have already eliminated Russell paradox, but why Russell introduced the theory of order types . Therefore, this article first comparative analyze the branchesb between simple type theory and the theory of order type then described the reason is that Russell want to hold on his perspective of the position of philosophy, from simple theory of types to the theory of order types is a necessity across. Finally, the article came to Russell's response. In the fifth part of the foundation, article give a evaluation, both from philosophical and several logical reasons...