In recent 50 years,the debate between mathematical realism and anti-realism has been dominating the mainstream development in the contemporary philosophy of mathematics. Penelope Maddy proposed a naturalistic set theoretic realism in 1990. This project brings the philosophy of mathematics a new research idea,that is,philosophy should attach importance to mathematical practice. This article will critically analyze Maddy’s naturalistic set theoretic realism on the basis of research paradigm background belief. By analyzing Maddy’s strategy,this article will try to make the task of the philosophy of mathematics clearer and put forward some necessary conditions needed by a reasonable research paradigm for the philosophy of mathematics.
