Indispensability Argument Of Mathematical Realism

The indispensability argument is an important defence of mathematical realism,which was put forward by Willard Van Orman Quine.In 1953,Quine has put forward his philosophical ideas of mathematics in his book《From a Logical Point of View 》;in 1960,he started the discussion about mathematical objects in the book of《Word and Object》;then,he put forward the validity of scientific research on epistemology in the article《Naturalized Epistemology》;finally,he presented his philosophical viewpoint of science in the book《The Web of Belief》,which was published in 1970,and his kernel thoughts is confirmation holism.Quine’s indispensability argument for mathematical realism took mathematics as a part of science,Quine’s indispensability argument for mathematical realism related traditional problems of metaphysics to scientific methodology and scientific realism for the first time,which was of great significant to the philosophy of mathematics.This thesis aims to elaborate the background and the ideas of indispensability argument,the comment on the impact and significance of the indispensability argument,and then discuss the development trend of philosophy of mathematics.This thesis consists of introduction,background,refutation,re-examinations of the indispensability argument,and conclusion.The introduction mainly discusses the reasons for the research,the research status at home and abroad,and the basic ideas and the content of the thesis.Chapter one gives a summary of the background of the indispensability argument.Firstly,we elaborate problem about the reality of mathematics,then we discuss the dilemma in mathematical realism,which leads to the indispensability argument,finally we comb the research ideas of the indispensability argument.Chapter two mainly discusses the indispensability argument of mathematical realism.The indispensability argument developed into various versions.First,we elaborate Quine-Putnam indispensability argument,then analyze the pragmatism’s indispensability argument and Colyvan’s indispensability argument,and make evaluations.Chapter three discusses the disapprovals of the indispensability argument.First,we elaborate Field’s factionalism.Second,we analyze the causal naturalism;Third,we demonstrate the opinion of the causal version of naturalism;last but not least,we discuss Sober’s contrastive empiricism.Chapter four is the re-examination of Quine’s indispensability argument of mathematical realism.In this chapter,we discuss the meaning of indispensability argument for mathematical realism.We elaborate the relationships between the indispensability argument and the mathematical realism.In this way,we can see that Quine has finished his defence for his mathematical realism.The conclusion summarizes the thesis,analyzes the work we have done,and points out the innovation and shortcomings of this thesis.Finally,we point out the future trend of mathematical realism.