Study Of The Quine-Putnam Indispensability Argument

On the contemporary studies of philosophy mathematics, there are a lot of discussions on whether abstract mathematical objects exist. The Quine-Putnam indispensability argument is one of them. This paper, from the perspective of realism, makes a systematically illustration of the basic content of the Quine-Putnam "indispensability argument ", reveals the connotation of "indispensable" and arguing the necessary basis of the indispendsable of mathematics science. It also points out the difficulities of the indispensability argument by analyzing different objections on the indispensability argument of mathematics. Finally, on basis of Colyvan’s indispensability argument, it expounds the contemporary development of the indispensability argument.This paper is divided into three parts:introduction, four chapters of systemic discussion and conclusion.The first chapter:the introduction part expounds the background, the writing ideas, innovation point, in comtemporary researches on the indispensability argument.The second chapter:it mainly elaborated the theory basis of indispensability argument:"the Quine-Putnam indispensability argument ". First of all, it clarifies the source of the core theory of Quine’s argument; then it analyzes Putnam’s further development of the theory on the basis of Quine’s thought, elaborating the emergence and theoretical background of indispensability argument.The third chapter:it focuses on the premises of the argument of Quine-Putnam indispensability argument:" indispensability", "naturalism", "confirmation holism" and "ontological commitments", carrying on a specific analysis of four futures of the indispensability argument.The fourth chapter:it mainly discusses the challenges faced by the indispensability argument by analyzing the critisms of precondition of indispensable argumentation from the current academic fields, and illustrating the problems of indispensability argument in its development.The fifth chapter:it mainly introduces the contemporary development of the theory. It systematically introduces the basic content and the main idea of the Colyvan indispensability argument, introducing the contemporary development of the indispensability argument from the persepective of realism. And by comparing the connection between the mathematical realism and the scientific realism in contemporary development, it reveals the rule that the development of mathematical realism relies on scientific realism.The sixth chapter:the conclusion part carries on the summary to the full text.