Mou Zongsan's Interpretation and Criticism Towards the Axiom of Reducibility
In his early years,Mou Zongsan put a lot of effort into studying Principia Mathematica,and realized that the three axioms of existence are closely connected and run through the entire Principia Mathematica system.They led Principia Mathematica to a realistic standpoint and established it on assumptions,which made the foundation of mathematics and logic unstable.Among them,the axiom of reducibility is the most fundamental part.Mou Zongsan judged the axiom of reducibility as a kind of realistic thought,and criticized that Principia Mathematica fell into an entanglement between logic and knowledge.Based on such point of view,in one aspect,Mou Zongsan proposed a kind of standpoint named Luoji Yixian(the development line of logic-itself),which eliminates the assumption of the axiom of reducibility;in the other aspect,he unraveled the entanglement between logic and knowledge and placed them in parallel lines,thus,in the epistemological sense,the so-called Manlei Gongli(the axiom of proving full class)could be transformed from the axiom of reducibility.
Mou ZongsanPrincipia Mathematicathe axiom of reducibilityphilosophy of logiclogicism
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