摘要
牟宗三早年对《数学原理》有过深入了解,意识到三大存在公理在其中一线贯穿,它们将《数学原理》建立在假定之上,使数学和逻辑的基础不保,而还原公理又是其中最基础的一环。牟宗三对还原公理进行了实在论指认,并判定《数学原理》由此陷入逻辑与知识双线的“顺逆之交叉”。他进而一方面提出“逻辑一线”的立场,取消了还原公理的假定性;另一方面取消了“顺逆之交叉”而做“双线之骈行”,在知识论上将还原公理改造成“满类公理”。
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.
作者
蒋昊
JIANG Hao(School of Philosophy,Zhejiang University,Hangzhou 310058,China)
出处
《湖南科技大学学报（社会科学版）》
北大核心
2024年第2期41-50,共10页
Journal of Hunan University of Science and Technology(Social Science Edition)
关键词
牟宗三
《数学原理》
还原公理
逻辑哲学
逻辑主义
Mou Zongsan
Principia Mathematica
the axiom of reducibility
philosophy of logic
logicism
