The Defense of Pluralism in Mathematical Foundation Based on the Approach to Mathematical Practice
In recent years,there have been three competing foundational theories in the research of mathematical foundations:set theory,category theory,and univalent foundations.This has sparked a debate between monism and pluralism in the foundation of mathematics.Various approaches within the academic community have been taken to defend different philosophical positions,with the most significant being the focus on mathematical practice.On this approach,the pluralism of"natural"mathematical foundation has been successfully defended,based on practical objects and methods as mathematical practice facts.However,the defense is inadequate due to the con-cerns about the reliability of mathematical practice and the incompleteness of arguments.In view of this,by demon-strating the reliability of mathematical practice and providing additional evidence about"mathematical foundation",based on the meaning of"natural mathematical foundation",we can achieve a full defense of the pluralism about mathematical foundation.
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