Analysis Of Maddy's Second Philosophy

Second philosophy is a new way to explore the philosophy of mathematics that is put forward by Penelope Maddy when she inquires about defending the axioms of set theory.Maddy's whole idea has been presented in her book?Second Philosophy:A Naturalistic Method?which was printed in 2007 and?Defending the Axioms:On the Philosophical Foundations of Set Theory?which was printed in 2011.In these two books,Maddy appealed to the researchers should pay attention to mathematical practice based on which she put forward second philosophy.This paper aims to analyze how Maddy's second philosophy is put forward,how it accounts for set-theoretic practice and what influences it brings about on the philosophy of mathematics.On this base,we will clearly grasp the problems in the philosophy of mathematics and its directions.This thesis consists of introduction,four systematic argumentations and conclusion.The introduction mainly elaborates the reason for the thesis to research Maddy's Second Philosophy and analyze the situation of this topic at home and abroad.On the basis of this,the thesis wants to clarify the problem which should be solved,the basic idea of writing and the main content,the research significance of the thesis.The first chapter mainly elaborates the philosophical problems in set theory from the perspective of history focusing on the origin and development of set theory.Then it studies how these problems generate and how mathematicians deal with them.On this base,it can make it clear that how Maddy pays attention to mathematical practice when she contemplates the philosophical problems in set theory.The second chapter mainly discusses the motivation of Maddy's second philosophy.It analyzes Godel's robust realism and Maddy's naturalistic set theoretic realism,and then points the difficulties these two realisms encounter when they explain the ontological and epistemological problems in set theory.After being aware of the defects of these two realisms,Maddy thinks these problems in set theory again.This time Maddy focuses on set-theoretic practice,and finally puts forward second philosophy.The third chapter mainly discusses Maddy's second philosophy.It analyzes two philosophical positions arising out of second philosophy,thin realism and arealism.It also illustrates these two positions are the same within mathematics,their difference lies in their philosophical aspects.And finally it discusses the naturalistic basis of second philosophy,which is taking mathematical practice as its base and rejecting first philosophy.The fourth chapter mainly criticizes the second philosophical accounts for set theory.From dissolving the traditional first philosophy to the presentation of mathematical objectivity,it also elaborates the influences second philosophy brings about on the philosophical enquires about mathematics.In conclusion,it summarizes the main work of the thesis,and points out the new ideas and deficiencies,and makes prospects for the future philosophy of mathematics.