Shapiro's Ante Rem Structuralism

Since the beginning of the 19 th century,with the development of mathematics and logic in the early 20 th century,structuralism,as a natural product of mathematics and philosophy came into being.Stewart Shapiro,as a representative of structuralism,from the standpoint of the realism,puts forward the structure as a kind of unique universal,so called ante rem structuralism,which gradually developed into an important branch of mathematical structuralism.This article in detail analyzes the background,basic theories and the facing challenges of Shapiro's ante rem structuralism,thus further analyzes its insufficiencies,influences and significances.This thesis includes 5 parts: the introduction,3 systematic chapters of arguments and the conclusion.The introduction first introduces the background and theoretical source of Shapiro's ante rem structuralism.Through detailed investigation of researches of this theory both in domestic and abroad,the main questions and core content of it are shown.On basis of this,it further explains the significance of this research.The first chapter discusses the background of Shapiro's ante rem structuralism.Through discussing the origin of the theory,the philosophical position and the basic framework of it are clarified.The second chapter discussed the basic idea of Shapiro's ante rem structuralism.From the perspective of ontology,epistemology and methodology,the basic contents of this theory are discussed.First Shapiro's ante rem structuralism's emphasize on places-are-objects is clarified;Secondly the three cognition methods :pattern recognition,reflection and implicit definition are analyzed;Finally,from the perspective of mathematical language and second order logic,the methodological characteristics of ante rem structuralism and its theoretical strength are shown.The third chapter analyzes the challenges and developments of Shapiro'sante rem structuralism.Through analyzing the two main challenges Shapiro's ante rem structuralism faced,this part rethinks their logical defects existing in the basic position and contradictions,and reveals the overall trend in the development of structuralism.The conclusion reframes Shapiro's ante rem structuralism,and points out that the innovation and the deficiency of this article.